'%GUIDEBOOK FOR ANALYSIS 1 OF TETHER Perturbations 1 E … · PREFACE. , . This Guidebook is...

CONTENTS:

n z '"%GUIDEBOOK H FOR ANALYSIS r n

E P* M

a w o 3c

m ( b w

d r m w o OF TETHER APPLICATIONS

w o o w Joseph A. Carroll k

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cn CJtJ cD u,

-I v,

w w March 1985

Final Report on Contract RH4-394049 with the Martin Marietta Corporation

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William Nobles, Technical Monitor

I @ M I A Z 7L i f hanging release

<14L if swinging release- i f spun o r winched

Effects of Tether Deployment and Release

PREFACE

Generic Issues

ORBIT BASICS

Orbit Equations 1 Perturbations 1 Aerodynamic Drag 1 Thermal Balance 1 Micrometeoroids I

& Debris

TETHER DYNAMICS

Gravity Gradients 1 Dumbbell Libration1

Control Strategies I Momentum Transfer 1 Orbit Transfer 1 Energy Balance I

THE TETHER ITSELF

Strength & Mass I Impact Hazards 1

ELECTRODYNAMICS

Basic Principles 4 Orbit Changes

J I Libratim Cmtro!

BIBLIOGRAPHY

https://ntrs.nasa.gov/search.jsp?R=19870000736 2020-03-23T19:05:29+00:00Z

PREFACE. , . T h i s Guidebook i s i n t e n d e d as a t o o l t o f a c i l i t a t e i n i t i a l a n a l y s e s of proposed t e the r a p p l i c a t i o n s in space. The guid ing phi losophy is t h a t a t the beginning of a s t u d y e f fo r t , a br ie f a n a l y s i s of ALL the common problem areas is far more u s e f u l t han a detailed s t u d y in any one are& Such analyses can minimize t h e waste of resources on e l egan t bu t fatally flawed concepts, and can identify the areas where more e f f o r t is needed on concepts which do survive the initial analyses.

In areas in which hard decisions have had t o be made, the Guidebook is:

Broad, rather than deep Simple, rather than precise Brief, rather than comprehensive Illustrative, rather than definitive

Hence the simplified formulas, approximations, and analytical tools included in t h e Guidebook should be used only for preliminary analyses. For detailed analyses, the references wi th each topic & in the bibliography may be usefuL Note that topics which are important in general bu t ngt particularly relevant to tethered systems analysis (ag., radiation dosages) are not covered.

CREDITS

This Guidebook was prepared by the author under subcontract RH4-394049 with the Martin Marietta Corporation, as part of its contract NAS8-35499 (Phase II of a Study of Selected Tether Applications in Space) with the NASA Marshal l Space Flight Center. Some of the material was adapted from references listed with the various topics, and this assisted the preparat ion greatly. Much of the other material evolved or w a s clarified in discussions wi th one or more of the following: Dave Arnold, James Arnold, Ivan Bekey, Guiseppe Colombo, Milt Contella, Dave Criswell, Don Crouch, Andrew Cutler, Mark Henley, Don Kessler, Harr i s Mayer, Jim McCoy, B i l l Nobles, Tom O'Neil, Paul Penzo, Jack Slowey, Georg von Tiesenhausen, and Bil l Thompson. The author is of course responsible for all errors, and would appreciate being notified of any that m found.

Joseph k Carroll Energy Science Laboratories 11404 Sorrento Valley Rd, C113 San Diego, CA 92121 6 19-45 2- 7039

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Generic Issues

ORBIT TETHER TETHER TETBW BASICS DYNAMICS PROPERTIES OPERATIONS

in Various Tether Applications

MAJOR CON'STRAINTS IN MOMENTUM-TRANSFER APPLICATSONS

A l l types

L i b r a t i n g

SP-

Winohing

Rendezvous

Mul t i - s tage

High deltaV

ORBIT TETHER TETHER TETHER BASICS DYNAMICS PROPERTIES OPERATIONS

Apside Foroes on p e t e o r o i d Tether recoil location end masses s e n s i t i v i t y at release

Tether aan go slaak

HI@ loads on payload

Ugh l o a d s on pwload

Orbit p l a n e s must match

D i f . nodal r e g r e s s i o n

G r a v i t y Con t ro l of lOaU8s dpnami-

~ ~~

F a o i l i t y a t t i t u d e h mgns v a r i a b l e

Retrieval oan be diff icul t

Fktremely high power needed

Short l aunah & oapture windows

W a i t i n g time between stagpa

Tethe r mam R e t r i e v a l energy; & lifetime F a c i l i t y A a l t .

W O R CONSTRAINTS WITH PERNBNENnY-DEPLOYED

All t y p e s Aero. drag L i b r a t i o n Degradat ion, Reooil & o r b i t p e t s o r o i d 8 & changes after d e b r i s inrpaot. tether break

Elec t rodynamic

Aer od ymmi c

Beans t a l k (Ear th)

Misc changes Plasma High-voltage i n orbit d i s t u r b a n a e a i n s u l a t i o n

Tether drag & h e a t i n g

Tether mass; Consequanoes d e b r i s impact of failure

Li br-semi t ive <.1 gae only. Docking awkward I Grav i ty Use:

Rlnniw S P i a n g I

. -1-

Basic orbit nomenclature & equations are needed frequently in following pages. Comparison of tether & rocket operations requires orbit transfer equations. KEY ''INTS

The figures and equations at r igh t are a summary of t h e a s p e c t s of o rb i t a l mechanics most relevant t o tether applications analysis. For more complete and detailed treatments and many of the derivations, consult refs 1-3.

The f i r s t equation in t h e box is known as t h e V i s Viva formulation, and t o t h e r igh t of i t is the equation for t he mean orbital angular rate, n. Much of the analysis of orbit transfer AVS and tether behavior follows from those two simple equations. Some analyses require a close attention t o specific angular momentum, h, so an expression for h (for compact objects) is also given here.

In general, six parameters are needed t o completely specify an orbit. Various parameter sets can be used (e.g., 3 position coordinates & 3 velocity vectors). The six parameters listed at r igh t are commonly used in o r b i t a l mechanics. Note tha t when i=O, ~2. becomes indeterminate (and unnecessary); similarly with w when e=O. Also, i &SLare here referenced to the cent ra l body's equator, as is u s u a l l y done for Low Earth Orbit (LEO), For high orbits, the ecl ipt ic or other planes are often used. This simplifies calculation of 3rd body effects.

The effects of small AVS on near-circular orbits are shown at right. The relative effects are shown t o scale: a AV along the velocity vector h a s a maximum periodic e f f ec t 4 times larger than t h a t of t h e same AV perpendicular t o i t ( p l u s a secular e f f e c t in 9 which the others don't have). Effects of oblique or consecutive ~ V S are simply the sum of the component effects. Note tha t out- of-plane AVS a t a point other than a node also af fec t&

For l a rge AVS, t he ca l cu la t ions are more involved. The perigee and apogee velocities of t h e transfer orbit are first calculated from t h e V i s Viva formulation and the constancy of h. Then the optimum distribution of plane change between the two AVS can be computed i terat ively, and t h e required t o t a l AV found. Typically about 90% of the plane change is done at GEO.

To find how much a given in-plane tether boost reduces the required rocket AV, the f u l l calculation should be done for both t h e unass i s ted and t h e te ther - assisted This is necessary because the tether affects not only the perigee velocity, but a l so t h e gravity losses and t h e LEO/GEO plane change split. Each m/s of t e the r boost typically reduces the required rocket boost by -89 m / s (for hanging release) t o -93 m / s ( for widely l ibrating release).

Note that for large plane changes, and large radius-ratio changes even without plane changes, 3-impulse "bi-elliptic" maneuvers may have the lowest total AV. Such maneuvers involve a boost t o near-escape, a s m a l l plane and/or perigee- adjusting AV a t apogee, and an apogee adjustment (by rocket or aerobrake) a t the next perigee. In par t icu lar , this may be t h e bes t way t o r e t u r n aero- braking OTVs from GEO t o LEO, if adequate time is available,

~ 0 " ~ s

rocket.

1, L E . Roy, Orbital Motion, Adam Hilger Ltd., Bristol; 1978. REFERENCES 2. Bate, Mueller, & White, Fundamentals of Astrodynamics, Dover Pub., 1971.

3. M.H. Kaplan, Modern Spacecraft Dynamics & Control, John Wiley dr Sons, 1976.

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Orbit & Orbit Transfer Equations

M = Me+nt Satellite

p=a(l-e 2 1

- Position at t=O Periapsis Direction

I ORBITAL ELEMENTS I a = semi-major axis e = ecoentricity i = inclination a = long. of asc. node Y = argument of jmriapsis kf.= poaltion at epoch

0 \ / - - -

Effects of Small AVs on Near-Circular O r b i t s

Total At' is minimized when ;er s i

Large O r b i t Transfers (e .g . , LEOIGEO)

-3-

'LEO

Differential nodal regression severely l imits coplanar rendezvous windows. Apsidal recession affects STS deboos t requirements from e l l ip t ica l orbits. Third bodies can change the orbit plane of high-orbit facilities.

KEY POINTS

The geoid (earth 's shape) is roughly tha t of a hydrostatic-equilibrium oblate ellipsoid, with a 296:297 po1ar:equatorial radius ratio. There are departures from th is shape, b u t they are much smaller than the 1:297 oblateness effect and have noticeable effects only on geosynchronous and other resonant orbits.

The focus here is on oblateness, because it is qui te large and b e c a u s e i t h a s l a rge secular e f f e c t s o n A and w f o r nearly all orbits. (Ob la t eness a l so affects n, but this can usually be ignored in preliminary analyses.) A s shown at r igh t , s a t e l l i t e s o r b i t i n g an o b l a t e body are attracted not only t o its center but also towards i ts equator. This force component imposes a torque on all orbits that cross the equator at a n angle, and causes the direct ion of the orbi ta l angular momentum vector t o regress as shown.

A is largest when i is s m a l l , but the plane change associated with a given var ies with sin i. Hence t h e ac tua l plane change rate varies with sini cosi, or sin2i, and is h ighes t near 45'. For near-coplanar rendezvous in LEO, t he required out-of-plane AV changes by 78 sin 2i m / s for each phasing "lap". This is independent of the al t i tude difference ( t o f i r s t order) , s ince phasing & differential nodal regression rates both scale with @. Hence even at best a rendezvous may requim an out-of-plane AV of 39 m / s At other times, out-of- plane AVS of 2 s i n i s i n M / 2 ) Vcirc ( = u p t o 2 Vcirc!) are needed.

The linkage between phasing and nodal regression rates is beneficial in some cases: if an ob jec t i s boosted s l igh t ly and then allowed t o d e c a y u n t i l it

Hence recapture need not involve any significant plane change.

Apsidal recession generally has a much less dominant effect on operat ions, s ince aps ida l adjustments (par t icu lar ly of l o w - e orbits) involve much lower AVS than nodal adjustments. However, tether payload boosts may often be done from e l l i p t i ca l STS orbits, and perigee drift may be a n issue. For example, OMS deboost requirements from an el l ipt ical STS orbi t are tonnes lower (and payload capabi l i ty much higher) if per igee is near t he landing site latitude a t t h e end of t h e mission. Per igee motion relat ive t o day/n ight var ia t ions is also important for detailed drag calculations, and for electrodynamic day- night energy storage (where it smears out and limits t he eccentricity-pumping effect of a sustained day-night motor-generator cycle).

Jus t as torques occur when the cent ra l body is non-spherical, there are also torques when the sa te l l i t e is non-spherical. These affect t he satellite's spin axis and cause i t t o precess around the orbi ta l plane at a rate t h a t depends on the satellite's mass distribution and spin rate.

effects more important. In GEO, the main perturbations (-47 m/s/yr) are caused by the moon and SUL The figure at right shows how t o estimate these effects, using the 3rd body orbi ta l plane as the reference plane.

NOTES

I passes below the boosting object , t h e total 61 is nearly identical for both.

I In high orbits, central-body perturbations become less important and 3rd-body

I

.

c L REFERENCES 2. LE. Roy, Orbital Motion, Adam Hilger Ltd., Bristol, 1978.

Bate, Mueller, & White, Fundamentals of Astrodynamics, Dover Pub., 1971.

I

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Orbital Perturbations

Nodal R e m e s s i o n i n LEO: i < 9 $ i > g d

For sun-synchronous o r b i t s :

COS i 5 - . 0988(a / r e )3*5( 1-e2)2

(it 100' A#)

+a Y r

For cop lana r lOW-AV rendezvous between 2 o b j e c t s (e, =exto, i, =iz), nodal co inc idence i n t e r v a l s are:

AT 4,

OBLATENESS CAUSES LARGE SECULAR CHANGES I N A&o:

(j: up t o 2 rauweek in LEO

&:UP t o 1 rad/week i n LEO

I

Apsida l r e c e s s i o n i n LEO:

Motion of t h e l o n g i t u d e of p e r i g e e w i t h respect t o the sun's d i r e c t i o n (%oonn) is:

r n l siiird-Body - P e r t u r b a t i o n s (non-resonant o r b i t s )

-5-

body

Tethe r d rag affects tether shape & orbi ta l life; at. oxygen degrades tethers. Out-of-plane d r a g component c a n i n d u c e out-of-plane t e t h e r l ib ra t ion . The main va lue of payload boost ing by t e t h e r is t h e increased orb i ta l life.

I I Unboosted orbital life of space facil i t ies is affected by tether operations.

The f igure a t r i gh t shows t h e o rb i t e r t ro l l ing a satellite in the atmosphere, as i s planned for t h e 2nd TSS mission in t h e late 1980s. T h e tether d r a g g rea t ly exceeds t h a t on the end-masses and should be estimated accurately. The drag includes a s m a l l out-of-plane component t h a t can cause #-libration

Tether drag is experienced over a range of a l t i tudes, over which most of t h e terms in the d r a g equat ion vary: t h e air d e n s i t y p , t h e a i r speed Vrel, and t h e t e t h e r width & angle of attack. In free-molecular flow, C L is small, and CD (if based on A 3 is near ly cons t an t at 2.2. (CD rises near grazing incidence, but then A& is low.)

O n l y p var ies rap id ly , b u t it var ies in a way which l ends i t s e l f t o s i m p l e approximations. Empirical formulae have been developed by the author and are shown at right. They give values t h a t are usually within 25% of ref. 1, which is still regarded as r ep resen ta t ive for air densi ty as a function of al t i tude & exosphere temperature. These estimates hold only forp>lE-14, beyond which helium & hydrogen dominate & the density scale height H increases rapidly.

Note t h a t over much of LEO, atomic oxygen is the dominant species. Hyperther- m a l impact of atomic oxygen on exposed surfaces can cause rapid degradation, and is a problem in low-altitude applications of organic-polymer tethers.

The space age began in 1957 at a 200-yr high in sunspot c o u n t A new estimate of mean solar cycle temperatures (at right, from ref. 21, is much lower than earlier estimates. Mission planning requires both high & mean estimates for proper analysis. Ref. 2 & papers in the same volume discuss models now in use.

If the tether length L is <a, t he total tethered system drag can be estimated from the to ta l AL & t he midpoint V &p. If L>>H, the top end can be neglected, the bottom calculated normally, and the tether drag estimated from L1Pbot tom

tether diameter H VZrel, with H & Vrel evaluated one H above the bottom of the tether. For L between these cases, the drag is bounded by these cases.

As shown at right, t he orbi ta l life of more compact objects (such as might be boosted or deboosted by te ther) can be estimated analytically if Te, is known. For c i rcu lar o r b i t s with t h e same r, Vre1 & p bo th vary with i, but. t h e s e variations tend to compensate & can both be ignored in first-cut calculations.

The conversion of e l l i p t i c a l to "equal-life" circular o rb i t s is a n empirical fit to a n unpublished parametric study done by the author. I t app l i e s when aps ida l motions relative t o the equator and relative t o t h e diurnal bulge are large over t h e o rb i t a l life; th i s usua l ly holds in both low & high-i orbits. For a detailed study of atmospheric drag effects, ref. 3 is still useful.

L U.S. Standard Atmosphere Supplements, 1966. ESSA/NASA/USAF, 1966. 2. K. S. W Champion, "Properties of the Mesosphere and Thermosphere and

Comparison w i t h CIRA 72", in The Terrestrial Upper Atmosphere, Champion and Roemer, ed.; Vol 3, #1 of Advances in Space Research, Pergmon, 1983. D.G. King-Hele, Theory of Satell i te Orbits in a n Atmosphere, Butterworths, London, 1964.

~

NOTES

REFERENCES

3.

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.- .

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F drag = . 5 / p cD V:el Width 6r

Aerodynamic Drag

L i f t & Drag i n Free-Moleoular Flow

1 1 M ( 1 + 2.9(r-65?8)/Tex) - 3000 - Tsx CDA

- 7-

A e r o t h e r m a l h e a t i n g of t e t h e r s i s s e v e r e a t low a l t i t u d e s (<120 km) . Tether temperature a f f e c t s s t rength , toughness , & e l e c t r i c a l conductivity. E x t r e m e t h e r m a l c y c l i n g may d e g r a d e p u l t r u d e d c o m p o s i t e t e t h e r s . "View factors" are a l so used in refined micrometeoroid risk calculations.

KEY POINTS

Preliminary hea t t r ans fe r ca l cu la t ions in space a re of ten fa r simpler than typ ica l heat t r a n s f e r ca l cu la t ions on t h e ground, s ince t h e compl ica t ions introduced by convection are absent. However the absence of t he "clamping" e f f e c t of large convect ive coupl ings t o a i r or l iqu ids a l lows very high or low temperatures t o be reached, and makes thermal design important.

A t altitudes below about 140 km in LEO, aerodynamic heat ing is the dominant heat input on surfaces facing the ram d i r e c t i o n The hea t ing scales w i t h p as long as the mean f r e e pa th A is much larger than the object 's radius. I t is about equal t o the energy d iss ipa ted in s topping inc iden t air molecules. In denser air, shock & boundary layers develop. They shield the surface from the incident flow and make 6 rise slower a s p increases further. (See ref 1.)

Because tethers are narrow, they can be in free molecular flow even at 100 km, and may experience more severe heat ing than the (larger) lower end masses do. Under intense heating high temperature gradients may occur across non-metallic tethers. These grad ien ts may cause either overstress or stress relief on the hot side, depending on the sign of t h e axial thermal expansion coef f ic ien t

A t higher altitudes the environment is much more benign, but bare metal (low- emi t tance) tethers can still reach high temperatures when resistively heated or in t h e sun, s ince they r ad ia t e h e a t poorly. Sil ica, alumina, or organ ic coa t ings >1 pm thick can increase emittance and hence reduce temperatures. The temperature of electrodynamic tethers is important since their resistance losses (which may be the major system losses) scale roughly with Tabs.

For a good discussion of solar, albedo, and longwave radiation, see ref. 2. The solid geometry which determines the gains from these sources is simple but subtle, and should be done carefully. Averaged around a tether, ear th viewfactors change only slowly with alt i tude & attitude, and a re near .3 in LEO.

Surface property changes can be an issue in long-term appl ica t ions , due t o the effects of atomic oxygen, W & high-energy radiation, vacuum, deposition of condensible volatiles from nearby surfaces, thermal cycling, etc. Hyper- thermal atomic oxygen has received attention only recently, and is now being studied in film, fiber, and coating degradation experiments on t h e SI'S & LDEF.

Continued thermal cycling over a wide range (such as shown at bottom r igh t ) may degrade composite tethers by introducing a maze of micro-cracks. Also, temperature can affect the strength, stiffness, shape memory, and toughness of tether materials, and hence may affect tether operations and reliability.

NmS

L R.N. Cox & L.F. Crabtree, Elements of Hypersonic Aerodynamics, The English Universities Press Ltd, London, 1965. See esp. Ch 9, "Low Density Effects"

R E F E R m ~ E ~ 2. F.S. Johnson, ed., Satellite Environment Handbook, Second Edition, Stanford University Press, 1965. See chapters on solar & e a r t h thermal radiation.

3. H.C. Hottel, nRadiant Heat Transmission," Chapter 4 of W.H. McAdams, HEAT TRANSMISSION, 3rd edition, McGraw-Hill, New York, 1954, pp. 55-125.

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Thermal Balance

= 1368 ( 4 0 ) GAL W/m2 (if in sun)

= O h m i c + any others

oC,e.1 - -9 (Kevlart:.4)

= 05 p Adrel

= -37 (*.3) 1368 ( ~ 4 0 ) W/m2

(see "Aero. Drag")

- .2 (metals) v t a h d o

*USA F Cos(SunZenithAng1e) (if

2 = 215 (*loo) A f F W/m

of sphere or its projection onto appropriate circle ~

GEOMETRY FOR EARTH VIEW FACTOR CALCULATIONS

0-23 50

n nnn , , . c r - . 4 - I w - y w -

0.

0.

Altitude i n gm Earth Viewfactors in LEO

Earth Viewfactors for Tethers

260

240 D

g

200

180 0 90 le0 270

Deg. past Widnight" (@ = Sun out-of-plane anae) Tether Temperature Over 1 Orbit

-9-

Micrometeoroids can sever thin te thers & damage te ther protection/insulation. Orbiting debris can sever te thers of any diameter. KEY

At the start of t h e space age, estimates of meteoroid f luxes var ied widely. Earth was thought t o have a dus t cloud around it, due t o misinterpretation of data such as microphone noise caused by thermal cycling in spacecraft. By the late 1960s most meteoroids near earth were recognized to be in heliocentric rather than geocentric orbit. The time-averaged f lux is mostly sporadic, but meteor showers can be dominant during their occurrence.

There is a small d i f f e rence between LEO and deep-space fluxes, due t o the focusing effect of t h e ear th 's gravi ty (which increases t h e ve loc i ty & f lux) , and the partial shielding provided by the ear th & "sensible" atmosphere For a typical meteoroid velocity of 20 km/sec, these e f fec ts combine t o make t h e risk vary as shown at right in LEO, GEO, and beyond. The picture of a metal plate after hypervelocity impact is adapted from ref. 3.

The estimated frequency of sporadic meteoroids over t h e range of interest for most t e t h e r applications is shown by the straight l ine plot at right, which is adapted from ref. 4 & based on ref. 1, (Ref 1 is still recommended for design purposes.) For masses<lE-6 gm (c15 mrn diam. at an assumed density of .5), the frequency is lower than a n extension of t h a t line, s ince several e f f ec t s clear very s m a l l objects from heliocentric orbi ts in geologically shor t times.

Over a n increas ing range of altitudes and pa r t i c l e sizes in LEO, t h e main impact hazard is due not t o natural meteoroids but rather t o man-made objects. The p l o t s a t r ight, adapted from refs 4 & 5, show the risks presented by t h e 5,000 or so objects tracked by NORAD radars (see ref. 6). A s t e e p "tail" in t h e 1995 d i s t r i b u t i o n is p r e d i c t e d s i n c e it is l ikely t h a t s eve ra l debris- generating impacts will have occurred in LEO before 1995. Such impacts are expec ted t o involve a 4-40 c m object s t r iking one of t h e few hundred largest objects and generating millions of s m a l l debris fragments.

Recent optical detection s tudies which have a size threshold of a b o u t 1 cm i n d i c a t e a populat ion of a b o u t 40,000 objects in LEO. This makes it likely t h a t debris-generating collisions have already occurred. Studies of res idue in small sur face p i t s on t h e s h u t t l e and o the r objects recovered from LEO indicate that they appear to be due t o titanium, aluminum, and pa in t fragments (perhaps flaked off satellites by micrometeoroid hits). Recovery of t h e Long Duration Exposure Facility (LDEF) later this year should improve this database greatly, and will provide data for LEO exposure area-time products comparable t o those in potential long-duration te ther applications.

NOTES

2.

3, e

REFERENCES

5. 6.

Meteoroid Environment Model-1969 [ N e a r Earth t o Lunar Surface], NASA

Meteoroid Environment Model-1970 [Inttlrplanetary and Planetary], NASA SP-8038, October 1970.

Meteoroid Damage Assessment, NASA SP-8042, May 1970. Shows impact effects. D. J. Kessler, "Sources of Orbital Debris and the Projected Environment for Future Spacecraft", in J. of Spacecraft & Rockets, Vol 18 #4, Jul-Aug 1981. D. J. Kessler, Orbital Debris Environment for Space Station, JSC-20001, 1984. CLASSY Satel l i te Cata log Compilations. Issued monthly by NORAD/J5YS, Peterson Air Force Base, CO 80914.

SP-8013, March 1969. c

i

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Micrometeoroids & Debris

1 .o

. t t

- - - 100200 460 660 800 1000

Altitude in Km R e l a t i v e p Risks i n LEO

L R ~ a ( 1 - F-U) (.57 + .43re/rg _.

It ' -

L I O + Population Corrected -

t o 4 L i m i t i n g S ize

Observed Debris Flux (corrected to 4-cm l imi t ing s ize)

3 c Inclination: 30" - 0.4

Q t LL

0 0.3

h / s e c D e b r i s Impact Velocity

-11-

"hlicrogee" environments are possible only in small regions (-5 m) of a LEO facility. Milligee-level gravity is easy t o get dr adequate for propellant settling, e t c

The figure at right shows the reason for gravity-gradient effects. The long tank-like object is kept aligned with the local vertical, so t ha t the same end always faces the ear th as i t orbi ts around it. If one climbs from t h e bottom t o t h e top, the force of gravity gradually decreases and the centrifugal force due to orbital motion increases. Those forces cancel out only at one altitude, which is (nearly but not exactly) t he alt i tude of the vehicle's center of mass.

A t other locations an object w i l l experience a net force vertically away from the center of mass (or a ne t accelerat ion, if t h e ob jec t i s allowed t o fall). This net force is referred t o as the "gravity-gradient force." (But note tha t 1/3 of the net force is actually due t o a centr i fugal force gradient!) Exact and approximate formulas for finding the force on an object are given at right.

The fo rce occurs whether or not a tether is present, and whether or not it is desirable. Very-low-acceleration environments, which are needed for some types of materials processing and perhaps for assembling massive structures, are only available over a very limited ve r t i ca l extent , as shown a t right. Put t ing a vehicle into a slow retrograde spin can increase the "height" of this low-gee region, but t ha t then l i m i t s the low-gee region's other in-plane dimension.

Since gravity gradients in low o r b i t s around var ious bodies vary with p/r3, the gradients are independent of t he size of t he body, and linearly dependent on its density. Hence the gradients are highest (.3-.4 mill igee/km) around the inner planets and Earth 's moon, and 60-80% lower around the outer p lane ts In higher orbits, t he effect decreases rapidly ( t o l.6 rnicrogee/km in GEO).

The relative importance of surface tension and gravity determines how liquids behave in e tank, and is quantified with the Bond number, B o ~ d / a If Bo>lO, liquids will settle but higher values (Bo=50) are proposed as a conservat ive design c r i t e r ion ' On t h e o the r hand, combining a s m a l l gravi ty gradient effect (Bo<lO) with minimal surface-tension fluid-management hardware may be more p rac t i ca l than e i the r option by itself. Locating e propellant depot at the end of e power-tower structure might provide an adequate gravity-gradient contribution. If higher gravi ty is desired, but without deploying the depot, another option is t o depoy an "anchor" mass on a tether, as shown at right.

Many nominally "zero-gee" operations such 8s electrophoresis may actually be compatible w i t h useful levels of gravity (i.e., useful for propellant settling, simplifying hygiene activities, keeping objects in place at work stations, etc). This needs to be studied in detail t o see what activites are t ruly compatible.

NOTES

I. D. Arnold, "General Equations of Motion," Appendix A of Investigation of Electrodynamic Stabilization and Control of Long Orbiting Tethers, Interim Report for Sept 1979 - Feb 1981, Smithsonian Astrophys Observ., March 1981,

2. ILL Kroll, "Tethered Propellant Resupply Technique for Space Stat ions," IAF-84-442, presented at the 35th IAF Congress, Lausanne Switzerland, 1984.

REFERENCES

-12-

Gravity Gradient Effects

& 1 / 3 centrif.)

Origin of "Gravity-GradientW Forces

PI OTV W

I

W W Attached /n

"Anchor Tethered

(any mass)

Two Propellant-Settling Options -13-

~ I I O - ~ over gee 50 m

J

<lo-3 gee over 5 km

Magnitude of Gravity Gradient Effects i n LEO

Potential Overlap of Regions for Low-Gee & Gee-Dependent Operations

KEY P o r n

NOTES

Libration periods are independent of length, bu t increase at large amplitude. Out-of-plane libration can be driven by weak forces that have a 2n component Tethers can go s lack if Bmax>65' or $max>60°.

The two figures at right show the forces on a dumbbell in circular orbit which has been displaced from the vertical, and show the net torque on the dumbbell, returning i t towards the vertical. The main difference between the two cases i s t h a t t h e cen t r i fuga l force vec to r s are rad ia l in t h e in-plane case, and parallel in the out-of-plane case. This causes t h e ne t force in t h e out-of- plane case to have a smaller axial component and a larger restoring component, and is why $-libration has a higher frequency than @-libration.

Four aspects of this l ibration behavior deserve notice. Firs t , t h e res tor ing forces grow w i t h the tether length, so l ibration frequencies are independent of the tether length. Thus t e t h e r systems tend t o I i b r a t e "solidly", l ike a dumbbell, rather than with the tether trying to swing faster than the end-masses as can be seen in the chain of a child's swing. (This does not hold for very long tethers, since the gravity gradient itself varies.) For low orbits around any of the inner planets or the moon, l ibration per iods are roughly an hour.

Second, tethered masses would be in f ree-fal l excep t for t h e te ther , so t he sensed acceleration is always along the tether (as shown by the stick-figures). Third, t h e axial force can become negative, for #>60° or near t h e e n d s of r e t rog rade in-plane l ib ra t ions >65.9O. This may cause problems unless the tether is released, or retrieved at an adequate rate t o prevent slackness.

And fourth, although &libration is not close t o resonance with any significant driving force, #-libration is in resonance with several, such as out-of-plane components of aerodynamic forces ( in non-equatorial orbits tha t see different air densi ty in northward and southward passes) or eledtrodynamic forces (if tether currents varying at the orbital frequency are used). The frequency droop a t large amplitudes (shown at right) sets a finite l imi t t d the effects of weak but persistent forces, but this l i m i t is qui te high in most cases.

The equations given at right are for an essentially one-dimensional s t ructure , with one principal moment of inertia far smaller than the other two: A<<B<C. If A is comparable t o B & C, then the @-restoring force shrinks with (B-A)/C, and the &libration frequency by Sqrt( (B-A)/C). Another limitation is that a eoupling between 9 & 8 behavior (see ref. 1) has been l e f t out. This coupling is caused by t he var ia t ion of end-mass a l t i t udes twice in each $-libration. This induces Cor io l i s acce lera t ions t h a t a f f e c t 9. This coup l ing is of ten unimportant, s ince 4n is far from resonance with L 7 3 n

Librat ion is referenced t o t he l o c a l ver t ical , and when a dumbbel l is in an eccen t r i c orbit, var ia t ions in t h e o r b i t a l r a t e cause l i b r a t i o n s which in t u r n e x e r t pe r iod ic t o r q u e s on a n i n i t i a l l y uniform1 - r o t a t i n g objec t . In highly eccentric orbits this can soon induce tumbling. H

1. D. Arnold, "General Equations of Motion," Appendix A of Investigation of Electrodynamic Stabilization and Control of Long Orbiting Tethers, Interim Report for Sept 1979-Feb 1981, Smithsonian Astrophys Observ., March 1981,

2. P.A. Swan, "Dynamics & Control of Tethers in Elliptical Orbits," IAF-84-361, presented at the 35th IAF Congress, Lausanne, Switzerland, October 1984.

REFERENCES

- 14-

Dumbbell Libration in Circular Orbit

-1.6 cycles/orbit for 6max = 30'

t F a x i a l Frestore

c-

k ) Fgravi ty

In- Plane Libration ( 0 )

ILY Y = c o s 2 8 + F + f i

I

Fgravi t y k

Out-Of-Plane Libration ($1

Open-loop control is adequate for deployment; fu l l retrieval requires feedback. KEYPOINTS Tens ion laws c a n c o n t r o l 0 & # - l i b r a t i o n p l u s t e t h e r o s c i l l a t i o n s .

Many other options exist for libration, oscillation, & final retrieval control.

The table at right shows half a dozen distinct ways in which one or more aspects of tethered system behavior can be controlled. In general, anything which can affect system behavior (and possibly cause control problems) can be part of the solution, if it itself can be controlled without introducing other problems.

Thus, for example, s t i f f te thers have sometimes been considered undesirable, because the stiffness competes with the weak gravity-gradient forces near the end of retrieval. However, if t he final section of t e the r is s t i f f AND nearly s t r a igh t when stress-free (rather than pig-tail shaped), then "springy beam" control laws using a steerable boom tip might supplement or replace other laws near the end of retrieval. A movable boom has much the same effect as a stiff tether & steerable boom tip, since i t allows the force vector t o b e adjusted,

The basic concepts behind tension-control l aws are shown at right, Libration damping is done by paying out tether when the tension is greater than usual and retrieving it at o ther times. This abso rbs energy from t h e l ibrat ion. As shown on t h e previous page, in-plane l ibration causes large variations in tension (due t o the Coriolis effect) , so "yoyo" maneuvers can damp in-plane librations quickly. Such yoyo manuevers can be superimposed on deployment and retrieval, t o allow large length changes (>4:1) plus large in-plane l i b ra t ion damping (or initiation) in less than one orbit, as proposed by Swet.l

Retrieval laws developed for the TSS require more time than Ref. 1, because they also include damping of out-of-plane l ibration built up during stationkeeping. Rupp developed the f i rs t TSS control l a w in 1975;2 much of the work since then is reviewed in (3). Recent TSS control concepts combine tension and t h r u s t control laws, with pure tension control serving as a backup in case of thruster f a i l ~ r e . ~ Axia l thrusters raise tether tension when t h e tether is short , while others control yaw & damp out-of-plane l ibration t o a l l o w faster retrieval.

A novel concept which in essence eliminates the f inal low-tension phase of r e t r i eva l is t o have t h e end mass climb up t h e t e t h e r e 5 S ince t h e t e t h e r itself remains deployed, i ts contribution t o gravity-gradient forces and stab- i l ization remains.

NOTES

The practicali ty of this w i l l vary with the application.

l. C. J. Swet, "Method for Deploying and Stabil izing Orbiting Structures", U.S. Patent #3,532,298, October 6, 1970,

2. C.C Rue?, A Tether Tension Control Law for Tether Subsatell i tes Deployed Along L o c a l V e r t i c a l , NASA TM X-64963, MSFC, September 1, 1975.

3. V.J. Modi, G e n g Chang-Fu, AK. Misra, and Da Ming Xu, "On the Control of t h e Space Shuttle Based Tethered Systems," Acta Astronautica, Vol. 9, NO. 6-1, pp. 437-443, 1982. REFERENCES

4, A. K, Banerjee and T.R. Kane, "Tethered Satel l i te Retrieval with Thruster Augmented Control," AIA# 82-1-21, presented at the AIAA/AAS Astrody- namics Conference, San Diego, Calif., 1982.

Satell i te," J. of t h e Astronaut. Sci., Vol 32, No. 3, July-Sept. 1984 5. T.R. Kane, " A N e w Method for the Retrieval of the Shuttle-Based Tethered

1-

-16-

Tether Control Strategies

E F F E C T I X E R E S S OF V A R I O U S CONTROL CONCEPTS

\APPLICATION Libra t ion q Tether Osc i l l a t ions Endmass Att i tude Osc,

CONTROL OUTPUT\ In-plane lout-of-plane Longitudinal ITx-ansverse P i t c h 6t ~014 Yaw

Tension Strong1 weak 11 Strong I Strong 11 Strong None (Note: t ens ion control is w e a k when tether is s h o r t )

I, I I El. Thrust 1 Only i f M1 # M2 11 None I harmonics OdLg Odd 11 None 1 None

Strong, but cos t ly None if prolonged Thruster Strong, bu t cos t ly i f prolonged

I I I Movable mass Good w/short tether Possible but awkward None None

St i f f tether, Movable boom

A e r o d y n a m i c H i g h drag-use only if low a l t i t u d e needed f o r o ther reasons.

Strong i f tether is very s h o r t ; w e a k otherwise

\ \ \ \ pS4\ \

/ \ \. Stretch

i Damping

Swing Tension = kl (L-Lc) + k d

CII. O r b i t a l motion

Deploying & r e t r i e v i n g tether at d i f f e r e n t tens ions absorbs energy and d a q s l i b r a t i o n .

( k l & k2 are cont ro l gains; L & LC are the actual and the commanded tether length.)

Deployment

pa ths of t i p

t. N 1 r e t r i e v a l takes ~6 hours with thrusters h -24 uithout .

in 4.6 hours .

TEILSIOI: COIX'XOL FOR L I B R A T I O N DAMPING. . . AND DEPLOYMENT/RETRIEVAL

-1 7-

Tethe r s merely r ed i s t r ibu te a n g u l a r momentum; t h e y do n o t c r e a t e it. KEY POINTS C h a n g e s in t e t h e r length, l ibrat ion, and spin all r ed i s t r ibu te momentum.

Momentum transfer out-of-plane or in deep space is possible bu t awkward. 1

-

The two figures a t right show two different tether deployment (and retrieval) techniques. In both cases, t h e in i t ia l deployment (which i s not shown) is done with RCS burns o r a long boom In t h e case a t left, t h e tether is paid o u t under tension s l igh t ly less than t h e equilibrium tension leve l for t h a t t e the r length. The tether is s l igh t ly t i l t ed away from t h e ver t ica l during deployment, and librates slightly af ter deployment is complete.

In t h e other case, af ter the in i t i a l near-vertical separa t ion ( t o abou t 2% of the ful l tether length) , the two end masses are allowed t o drift apart in n e a p free-fall, with very low but controlled tension on the tether. Just under one orb i t later, the tether is almost all deployed and the range rate decreases t o a minimum (due to orbital mechanics). RCS burns or tether braking are used t o cushion the end of deployment and prevent end m a s s recoil. Then the tether system begins a large-amplitude prograde swing towards t h e vertical.

In both cases, the angular momentum transferred from one m a s s t o t h e other is simply, as s t a t ed in t h e box, t h e in t eg ra l over time of the radius times the horizontal component of tether tension. In one case, transfer occurs mainly during deployment; in the other, mainly during the libration after deployment. In each case, momentum transfer is greatest when the tether is vertical, since the horizontal component of tether tension changes sign then.

An intermediate strategy-deployment under moderate tension-has also been investigated.' However, th i s t echn ique r e s u l t s in very h igh deployment ve loc i t ies and large ro t a t ing masses. I t a l so requires powerful brakes and a more massive tether than required with the other two techniques.

As discussed under Tether Control S t r a t eg ie s , changing a t e t h e r ' s length in resonance with variations in tether tension allows pumping or damping of libration or even spin. Due t o Coriolis forces, in-plane l ibration and spin cause far la rger tension variations than out-of-plane l ibration or spin, so in-plane behavior is f a r easier t o adjust than out-of-plane behavior. Neglecting any paras i t ic losses in tether hysteresis & the reel motor, the net energy needed t o induce a given l ibration or spin is simply the system's spin kinetic energy relative t o the local vertical, when the system passes through the vertical.

Two momentum transfer techniques which appear applicable for in-plane, out-of- plane, or deep-space use are shown at right. The winching operation can use lighter tethers than other tethered-momentum-transfer techniques, but requires a very powerful deployer motor. The tangential AV simply prevents a collision.

The spin-up operation (proposed by Harris Mayer) is similar t o the winching operation. I t uses a larger tangent ia l AV, a tether with straight and tapered sections, and a small motor. Retrieval speeds up the spin by a factor of L3. Surpr i s ing ly , t h e long tapered sect ion of tether c a n be less than ha l f as massive as the short s t ra ight section tha t remains deployed after spin-up.

NOTES

._-

I

L J. Tschirgi, "Tether-Deployed SSUS-A, report on NASA Contract NAS8-32842, REFERENCE McDonnell Douglas, April 1984.

-18-

Momentum Transfer During Deployment & Retr ieval

1: /

Libration Pumping L 3 * *

Deployment Followed by Winching ( i n orbit or i n deep space)

- i.

Momentum Transfer During Libration (after low-tension deployment)

Straight Tether Section Tapered Tether

Small -

-19-

.-

KEY POINTS

NOTES

The achievable orbit change scales w i t h the tether length (as long as &<< r). Retrograde-l ibrat ion releases are inef f ic ien t , bu t allow concentric orbits. Apogee & perigee boosts have d i f fe ren t values in d i f f e r e n t appl ica t ions . Tethered capture can be seen as a time-reversal of a tether release operatioh

The figures to the right show the size of the orbi t changes caused by various t e t h e r operations. When released from a vertical tether, the end masses are obviously one t e t h e r length a p a r t in a l t i tude , The alt i tude difference 1/2 o r b i t l a te r , ~ h , var i e s with t h e opera t ion b u t i s usua l ly far larger. The linear relationship shown becomes inaccurate when a approaches r. Tethered plane changes are generally limited t o a few degrees and are not covered h e m

Tether release leaves the center-of-mass radius at each phase angle roughly unchanged: if t h e upper mass is heavier, then i t will rise less than t h e lower mass falls, and vice-versa. Note t h a t the l ibration amplitude, emax, is taken as positive during prograde l ibration & negative during retrograde l i b r a t i o n Hence retrograde l ibration resul ts in Ar < 7L. In particular, the pre-release & post-release o r b i t s will all be c o n c e n t r i c if Bmax = -60'. B u t s i n c e methods of caus ing -60' l ib ra t ions usua l ly involve +60° l ib ra t ions (which allow much larger boosts by the same tether), prograde releases may usually be preferab le unless concent r ic orbi ts are needed or other constraints enter in

The relative t e t h e r length, mass, peak tension, and energy absorbed by the deployer brake during deployment as a function of (prograde) libration angle a r e a l l shown in t h e p l o t a t r i g h t Libra t ion has a large e f f e c t on brake energy. This may be important when re t r ieva l of a long t e the r is required, after release of a payload or af ter tethered-capture of a free-flying payload,

The double boost-to-escape operation at right was proposed by k Cutler. It is shown simply as an example that even though momentum transfer is str ictly a "zero sum game", a tethered release operation can be a "WIN-win game" (a large win & a small one). The small win on the deboost-end of t he tether is due t o the reduced gravity losses 1/2 orbi t after release, which more than compensate for the deboost itself. Another example is t ha t deboosting the shut t le from a space s ta t ion can reduce both STS-deboost & station-reboost requirements,

Rendezvous of a spacecraf t wi th the end of a tether may appear ambitious, but with precise relative-navigation data from GPS ( the Global Positioning System) i t may not be difficult. The relative t ra jector ies required are simply a the- reversal of relative t ra jector ies that occur after tether release. Approach t o a hanging-tether rendezvous is shown at r i g h t Prompt capture is needed with th i s technique: if capture is not achieved within a few minutes, one should s h i f t t o normal free-fall techniques. Tethered capture has large benefits in safety (remoteness) and operations (no plume impingement; large fuel savings). The main hazard is collision, due t o undetected navigation or tether failure.

1, G. Colombo, "Orbital Transfer & Release of Tethered Payloads," SA0 report on NASA Contract NAS8-33691, March 1983.

2. W.D. Kelly, "Delivery and Disposal of a Space Shuttle External Tank t o Low Earth Orbit," J. of t h e Astronaut. Sci., Vol. 32, No. 3, July-Sept 1984.

3. J.A. Carroll, "Tether-Mediated Rendezvous, TI report t o Martin Mariet ta on Task 3 of contract RH3-393855, March 1984.

4. LA. Carroll, "Tether Applications in Space Transportation", IAF 84-438, at t h e 35th IAF Congress, Oct 1984. To be published in ACTA ASTRONAVTCA.

REFERENCES

-20-

Orbi t Transfer by Tethered Release or Capture

= M I X %

7L i f hanging release if swinging release i f spun or winched

Effects of Tether Deployment and Release

-

a RelTension/Length

0: Length *MaxTension

1 / ( l+. 866 Sinemax )

(r (Length CoSemax)* 0" 30" 60" 90"

Amplitude E f fec t s o f L i b r a t i o n

L

*6 03

= 7L (09

rnR =13L (+60°)

Effect of L ib ra t ion on Boost (release at middle of s w i n g )

Y

If done r i g h t , a tether boost/deboost opera t ion can reduce AV-to-escape for end masses!

(for equal-& boosts)

-or- &

-

F Phasinc -

K nrnt w - L - - - - w Trzjectary for Tethered t a p t l l r e frna! Bbove STS hcyel-s U b b I c i L L c L 3 S J

.-- ( i n tetner-centered LV-LE re ference frame) till captured pass ive t a r g e t 9

f -*- -21-

Tether operations cause higher-order repartitions of energy & angular momentum First-order approximations tha t neglect these effects may cause large errors. Extremely long systems have strange properties such as positive orbital energy.

KEY POINTS

The question a n d answer a t right are deceptively simple. The extent t o which this is so, and the bizarre effects which occur in extreme cases, can be seen in the 3 graphs a t right. A t top, deploying & retrieving two masses on a very long massless tether changes not only the top & bottom orb i ta l radii but also that of theCM, In addition, the free-fall location drops below the CAI. Other key parameter changes under the same conditions are plotted underneath.

Note t h a t when t h e t e t h e r length exceeds a b o u t 30% of t h e or ig ina l orbi ta l radius, the ent i re system lies below the original altitude. Also, a t a rad ius ratio near L95:1, t h e maximum tether length compatible with a circular orbit is reached. A t greater lengths (and the init ial amount of angular momentum), no circular orbit is possible at any altitude.

Te the r retrieval at t h e maximum-length point can cause the system t o either rise or drop, depending on the system state a t t h a t t ime. If it cont inues t o drop, there is a rap id rise in tether tension, and the t o t a l work done by the deployer quickly becomes positive. This energy input eventually becomes large enough (at 289:l) t o even make the t o t a l system energy positive, The system is unstable beyond this point: any small disturbance w i l l grow and can cause the tether system t o escape from the body it was orbiting. (See ref. 2.)

The case shown is rather extreme: except for orbi ts around s m a l l bodies such as asteroids , t e t h e r s e i the r w i l l be fa r shor te r than t h e o r b i t a l radius, or will greatly outweigh t h e end masses. Either change greatly reduces the size of t h e effects shown. The effects on arbitrary s t ruc tures can be ca l cu la t ed using the equat ions listed a t right, which are based on a generalization of the concept of "moments" of the vertical mass distribution. Changes in tether length or mass distribution leave h unchanged, so other parameters (including rem, n, and E) must change. (For shor t tethers, the changes scale roughly with t h e square of t h e system's rad ius of gyration.) In many cases different conditions are most easily compared by f i r s t f inding t h e o r b i t a l rad ius t h a t the system would have if i ts length were reduced t o 0, rLtZO.

The mechanism that reparti t ions energy and angular momentum is tha t length changes cause temporary system displacements from the vertical. This causes both torques and ne t tangent ia l forces on the system, which can be seen by calculating t h e exac t n e t forces and coup les for a non-vertical dumbbell. The same effect occurs on a periodic basis with l ibrat ing dumbbells, causing the orbital t ra jectory t o depart slightly from a n el l ipt ical shape.

Other topics which are beyond the scope of this guidebook but whose existence should be noted are: eccentricity changes due t o deployment, orbit changes due to resonant spin/orbit coupling, and effects of 2- & 3-dimensional structures.

NOTES

I.. G. Colombo, M. Grossi, D. Arnold, & RI. Martinez-Sanchez, "Orbital Transfer and Release of Tethered Payloads," continuation of NAS8-33691, final report for the period Sept 1979-Feb 1983, Smithsonia Astrophysical Observatory, M a r c h 1983.

2. D. Arnold, "Study of an Orbiting Tethered Dumbbell System Having Positive Orbital Energy," addendum t o f inal report on NAS8-35497, SAO, Feb 1985.

REFERENCES

(in particular, see t h e table on page 21) I

-22-

Energy ti Momentum Balance

Question: What a r e the sources of t h e dumbbell s p i n angular momentum and deployer brake energy?

r e p a r t i t i o n h & E. Answer: O r b i t changes which

CM r a d i u s M1 = M2SMt

For ar b i t rar y near ly-one- dimensiona 1 v e r t i c a l s t r u c t u r e s i n circular o r b i t , analysis can be based on 5 "momentsn:

IN = EMi riN ( f o r N: 02.~2)

Each of t hese has phys ica l meaning:

T - M i ri 4" Mi

Fgrav = P 1-2 Epot = -P I-1

IO F,,, = n2 I, Mass =

Ekin =.5n I2 2&=sL

VERY-LONG-TETHER EFFECTS:

0.ow 1 1.0 2; 0 3iO 4 :O

Radius Ra t io ( r 2 / r l ) Equal-Angular-Momentum Orbi t s

1.0 2.0 3.0 4;O Radius Rat io ( r z / q )

Angular Momentum Repar t i t ion ing , Tether Length, & Deployer Work

10 7

8

-8 -1 44 0 1.0 2.0 3.0 4.0

-23-

Tether strength/ weight ra t io constrains performance in ambitious operations. Required tether mass is easily derivable from deltaV and payload mass. KEY ''INTS

-

Usable specific strength can be expressed in various ways. Three ways are shown at r i g h t Vc, Lc, and L l g are here defined in terms of a typical design stress (new/mZ) rather than the (higher) ultimate stress. Including the safety factor here streamlines the subsequent performance calculations. Higher safety factors am needed with non-metals than wi th metals since non-metals are often more variable in their properties, brittle, abrasion-sensitive, and/or creep-sensitive. A safety factor of 4 (based on short-term fiber s t rength) is typical for Kevlar, but t h e most appropriate safety factor w i l l vary with the application.

The "character is t ic veloci ty ," V c , is t h e most u s e f u l parameter in te ther - boost calculat ions, because the tether mass can be calculated direct ly from aV/Vc, independently of t he orbit, and nearly independently of t he operation. The table at t h e bottom, which lists tether/rocket combinations tha t have the lowest lifecycle mass requirements, holds whenever kVc=l km/sec & Isp=350 sea

The characteristic length Lc is useful in hanging-tether calculations. I t varies with t h e orbi ta l rate n. (The simple calculation given assumes L<<r; if this is not true, l/r effects enter in, and calculations such as those used in r e f s 3-5 must be used.) The safe l-gee length L l g is m a i d y useful in terrestrial applications, but is included since specific s t rength is often quoted this way. (Note that Vc and L c vary with Sqrt(strength), and L lg directly with strength.)

The spec i f ic modulus i s of interest because i t determines the speed of sound in the tether (C=the speed of longitudinal waves), the s t ra in under design load U / L = {Vc/C}2), ti the recoil speed after failure under design load ( = Vc2/C).

Te ther mass calculations are best done by considering each end of t he tether separately. If Mpl>>Mp2, then M t l can be neglected h preliminary calculations.

Du Pont's Kevlar is the highest-specific-strength fiber commercially available. Current R&D effor ts on high-performance polymers indicate that polyester can exhibit nearly twice the strength of gevlar.2 Two fiber producers have already announced plans t o produce polymers with twice the specific strength of Kevlar.

In t h e long run, t h e po ten t i a l may be greater with inorganic fibers like Sic & graphi te Refs. 3-5 focus on the requirements of "space elevators." They d iscuss labora tory tests of s ingle-crystal f ibers and sugges t t h a t l b f o l d improvements in specific s t rength (or 3-fold in Vc & Lc) are conceivable.

NOTES

1. Charac te r i s t ics and Uses of Kevlar 49 Aramid High Modulus Organic Fiber. available from Du Pont's Textile Fibers Department, 1978

2. G. Graff, "Superstrong Plastics Challenge Metals, " High Technology magazine, February 1985, pp. 62-63.

REFERENCES 3. J. Isaacs, H. Bradner, G.Backus, and kVine , "Satellite Elongation into a True "Skyhook"; a le t ter t o Science, Vol. 151, pp. 682-683, Feb 11, 1966.

4. J. Pearson, T h e Orbital Tower: a Spacecraft Launcher Using the Earth's Rotational Energy, Acta Astronautica, V01.2, pp. 785-799, Pergamon, 1975.

5. H, Moravec, "A Non-Synchronous Orbital Skyhook," J. of the Astronautical Sciences, Vol. XXV, No. 4, pp. 307-322, Oct-Dec 1977.

I

-24- -

Specific Strength and Required Tether Mass

c = 20 km/s I

OFpOORQ U N - W G r a p h i t e / sic-'* .' 8

C = speed of sound

49. 'Advance&- / Kevlar polymers

'29. S t y e l ,Ti

5 h / s 1 I . '* '

k 8 = p o t e n t i a l

T SPECIFIC MODULUS

Gauss ian "normal" be l l - shaped curve \ (if L c '? L<< r) ,

B e s t tether AV, h / s

Requcired Mt/Mp

L I

L I

. 1 4 .9 1.8 2.6

.02 I 1 I 11 , 95

L U C LZLC L>Lc Mt<(Mp Mt=Mp M t > k

L1 u c L2>Lc

Mtl<< Mpl Mt2> Mp2

Te the r Length h Required Mass

1 .oo; * - b o o

I .oo 0.00 0.50 1.00 1.50 2.00

X (= AV/kVc, or L/Lc)* Required T e t h e r Mass (Mt)

1.21k.01 for swinging

1Expected # of u s e s I 1 I 10 I 100 I 1000 I

(For kVo = 1 km/s and rocket Ispar 350 seoonds; marginal d e p l o y e r & dry roaket maases n e g l e c t e d . )

Best T e t h e r AV for Combined Tether /Rocket Boos t s

-25-

Micrometeoroids can sever thin te thers & damage tether protectionlinsulation. O r b i t i n g d e b r i s ( o r o t h e r t e t h e r s ) c a n seve r t e t h e r s of any diameter. Debris could impact an Earth-based "Space Elevator" over once per year.

KEYPOINTS

Sporadic micrometeoroids are usually assumed t o have a n t y p i c a l densi ty of a b o u t . 5 and a t y p i c a l impact velocity in LEO of approximately 20 kmlsec.' A t impact speeds above the speed of sound, solids become compressible and the impact shock wsve has e f fec ts l ike those of an explosion For this reason, the risk c u m assumes that if the EDGE of an adequately large meteoroid comes close enough t o the center of t h e te ther (within 45' or ,3S Dt), fa i lure will r e s u l t

Experiments done by Martin Marietta on TSS candidate materials have used glass projecti les fired at 6.5 km/sec, below t h e (ax ia l ) speed of sound in Kevlar. Two damaged te thers from those tests are shown at r i g h t The scaling law used @ . 5 Y * 6 7 ) i n d i c a t e s t h a t t h i s is r e p r e s e n t a t i v e of o r b i t a l c o n d i t i o n s , but t h a t law (used for impacts on sheet metal) may not apply to braided fibers.

For t e t h e r s much th icker t han 10 mm or so (depending on alt i tude), t he risk does not go down much as Dt increases, because even though the micrometeoroid risk still decreases, the debris risk (which INCREASES slightly with Dt) begins t o dominate. As with micrometeoroids, t h e t e t h e r is assumed t o f a i l if any par t of t h e debris passes within -35 Dt of t h e center of the tether.

The d e b r i s r isk a t a given al t i tude varies with the total debris width at tha t altitude. This was estimated from 1983 CLASSEY radar-cross-secton (RCS) data, by simply assuming that W = Sqrt(RCS) and summing Sqrt(RCS) over a l l tracked objects in This underestimates W for objects with appendages, and over- estimates it for non-librating elongated objects without appendages.

CLASSEY RCS data are expected to be accurate for RCS > 7 m2. The 700 objects with RCS > 7 m2 account for 3 km of the total 5 km width, so errors with smaller objects are not critical. Small untracked objects may not add great ly t o t h e total risk: 40,000 objects averaging 2 cm wide would increase t h e risk to a l-cm tether by only 20% was assumed independent of altitude, so the distribution of risk with altitude could be estimated by simply sca l ing Figure 1 from Ref. 4.

As shown at right, debris impact with a space e leva tor could be expected more than once per year at cur ren t debris populations. The relative density at 0' lat i tude was estimated from data on pp. 162-163 of ref. 6.

Similar calculations can be made for two tethers in different orbits at t h e same altitude. If at least one is spinning or widely.librating, t h e mutual risks can exceed .1 cut lkmyr . This makes "tether t raff ic control" essential,

I.. Meteoroid Environment Model-1969 [ N e a r Earth t o Lunar Surface], NASA

2. Meteoroid Environment Model-1970 [Interplanetary and Planetary], NASA

3. Meteoroid Damage Assessment, NASA SP-8042, May 1970, (Shows impact effects) 4. D. J. Kessler, "Sources of Orbi ta l Debris and t h e Projected Environment for

Future Spacecraft", in J. of Spacecraft & Rockets, Vol 18 #4, Jul-Aug 198L 5. D. J. Kessler, Orbi ta l Debris Environment for Space Station, JSC-20001, 1984. 6. CLASSY Satellite Catalog Compilations as of 1 Jan 1983, NORAD/J5YS, 1983.

SP-8013, March 1969.

REFERENCES SP-8038, October 1970. c

-26-

Impact Hazards for Tethers

4 B r a i d e d Kevlar , grazed

Stainless s t e e l w i r e , d i r e c t h i t

2

c u t s Km * Y r i n 1 LEO

-

0 . Max non-fatal p diameter Dm

pMeteoro id Risks t o a 1 mm Tether

Effec t ive Width, W (Any pos i t i on between

@ t he 2 extremes shown tether . )

For tethers w i t h D t > 1 (m), & Max non-fatal Dm = .25 D t ,

-. . 1 I I t I t

10-21 Assumptions: fW 4 5 Irm I

I f I

/

- -

D e b r i s Risk t o the Lowest 4000 Irm of an Earth-based Space Elevator:

EWidth RelDensity a t X=O E a r t h RSurface Arean a t Aln Risk =

I - -27-

Tether ( & other) res i s tance can l i m i t t he ou tpu t of electrodynamic tethers. Electron collection methods & effectiveness are important-and u n c e r t a i n

I

Since the publication of ref. 1, 20 years ago, electrodynamic tether proposals and concepts have been a frequent source of controversy, mainly in these areas:

1, What plasma instabil i t ies can be excited by the current? 2. What is the current capacity of the plasma return loop? 3. What is t h e best way t o co l lec t electrons from the plasma?

The f i r s t Tethered S a t e l l i t e mission may do much t o answer these questions. The discussion below and graphics at right merely seek t o introduce them.

The cur ren t f lowing through an e l ec t rodynamic t e t h e r i s r e tu rned in t h e surrounding plasma. This involves e lectron emission, conduction along the geomagnetic field lines down t o the lower ionosphere, cross-field conduction by collision with neutral atoms, and return along other field lines.

The tether current causes a force on the tether (and on the field) perpendicular t o both t h e f ie ld and t h e t e t h e r (hor izonta l , if t h e t e t h e r i s ver t ical) . Motion of the te ther through the geomagnetic field causes an EMF in the tether. This allows the tether to act as a generator, motor, or self-powered ultra-low- frequency broadcast a n t e n n a 2 The motion a l so causes each region of plasma t o experience only a short pulse of current , much as in a commutated motor.

Based on experience with charge neut ra l iza t ion of s p a c e c r a f t in high orbi t , it has been proposed tha t e lectrons be collected by emitting a neutral plasma from t h e end of t h e t e the r , t o a l low l o c a l c ros s - f i e ld c o n d ~ c t i o n . ~ In GEO, the geomagnetic field t raps a plasma in the vicinity of t he spacecraft , and "escape" along field lines may not affect its utility. This may also hold in high-inclination orbits in LEO. But in low inclinations in LEO, any emitted plasma might be promptly wiped away by the rapid motion across f ie ld lines.

A passive collector such as a balloon has high aerodynamic drag, but a end-on sail can have a n order of magnitude less drag. The electron-collection sketch at bottom right i s based on a preliminary ana lys i s by W. Thompson5 This analysis suggests t ha t a cur ren t moderately higher t han t h e electron thermal current ( =Ne * -200 km/sec) might be collected on a surface normal to the field. This is because col lect ing electrons requires tha t most ions be reflected away from the collection region as i t moves forward. This p r e h e a t s and densifies the plasma ahead of t he collector. The vol tage required for collection is just the vol tage needed t o repel most of t h e ions, about 1 2 V.

NOTES

1. S.D. Drell , H.M. Foley, & M.A. Ruderman, "Drag and Propulsion of Large Satellites in the Ionosphere: An Alfven Propulsion Engine in Space," J. of Geophys. Res., Vol. 70, No. 13, pp. 3131-3145, July 1965.

2. M. Grossi, "A ULF Dipole Antenna on a Spaceborne Platform of t h e PPEPL Class," Report on NASA Contract NAS8-28203, May 1973.

REFERENCES 3. RD. Moore, "The Geomagnetic Thruster-A High Performance "Alfven Wave" Propuls ion System Util izing Plasma Contacts , AIAA Pape r No. 66-257.

4. ST. Wu, ed., University of Alabama at HuntsvilleMASA Workshop on The Uses of a Tethered Satel l i te System, Summary Papers, Huntsvil le AL, May 1978. See papers by M. Gross i e t al, R. Will iamson e t al., a n d N. S tone .

Report t o Martin Marietta Corp. on Task 4 of Contract RH3-393855, Dec. 1983. 5. W. Thompson, "Electrodynamic Properties of 8 Conducting Tether, " Final

-28- ,/

Electrodynamic Tether PLASMA CONTACTOR r /

CURRENT I 555 /

QLoad Electron- - LJ emitter

Collisional cross-field conduction i n lower ionosphere.

PLASMA COHTACTOR

r n I I I I I

9 10 11 12 0' " a

Log,, 1;~/rn3

Generator Performance

Top V i e w of Electron Collection

-29-

Electrodynamic tether use w i l l a f f e c t t h e orbit-whether desired o r not. Stationkeeping and/or large orbi t changes without propellant use are possible. I

KEY ''INTs

The offset dipole approximation shown at right is only a first approximation t o t h e geomagnetic field: harmonic ana lyses of t h e f ie ld give higher-order coe f f i c i en t s up to 20% as large as t h e fundamental term. Ref. 1 con ta ins computerized models suitable for use in detailed electrodynamic studies.

The geomagnetic field weakens rap id ly as one moves into higher orbits, and becomes seriously distorted by solar wind p r e s s u ~ beyond GEO. However, ohmic lo s ses in a te ther are already significant in LEO, so electrodynamic tethers are mainly useful in low orbi ts where such distortions are not s ign i f icant

A s t h e e a r t h rotates, the geomagnetic field generated within i t rotates also, and the geomagnetic radius and lati tude of a point in inertial space vary over the day. If a maneuvering s t ra tegy which r epea t s i t s e l f each orbit is used (necessary unless t h e spacec ra f t has large diurnal power s torage capacity), then the average effect, as shown at right, w i l l be a due east t h r u s t vector.

Variations in geomagnetic lati tude (and thus in Bh) cance l o u t var ia t ions in the component of flight motion perpendicular t o the field, so these variations do not cause large vol tage variations in high-inclination orbits. (Note t h a t t h e relevant motion i s motion relat ive t o a ro t a t ing earth.) Out-of-plane l ibrat ion, variations in geomagnet ic radius, and d i u r n a l v a r i a t i o n of t h e "geomagnetic inclination" of an orbit can all cause vol tage variations. Peak EMFs (which drive hardware design) may approach 400 V/km.

However these variations need not affect the thrus t much if a s p a c e c r a f t has a variable-voltage power supply: neglect ing var ia t ions in parasit ic power, constant power investment in a c i rcu lar orb i t has t o give cons t an t in-plane t h r u s t The out-of-plane thrus t is provided "free" (whether desired or not). Average voltage 13 th rus t equations for vertical te thers are shown at right.

The table shows how to change all six orbi ta l elements separately or together. Other strategies are also possible. Their effects can be calculated from the in t eg ra l s listed. For o r b i t s within 11' of polar or equator ia l , d iu rna l ly - varying s t ra tegies become more desirable. Computing their effects requires using the varying geomagnetic inclination instead of i ( & moving it inside t h e integral) . Note t h a t t h e "DC" orbi t -boost ing s t r a t egy also affects i. This can be cancelled out by superimposing a -2 Cos(24) curren t on the DC c u r r e n t

As discussed under Electrodynamic Libration Control Issues, eccentricity and apside changes can strongly stimulate $-libration unless the spacecraft center of mass is near t h e center of t he tether. Other maneuvers should not do this, but th i s should be checked using high-fidelity geomagnetic field models.

L LG Stass~opoulos & GD. Mead, AL,LMAG, GDALMG, LINTRA:Computer Programs for Geomagnetic Field Er Field-Line Calculations, Feb. 1972, NASA Goddard.

~ F ~ ~ C E S 2. R D . Moore, "The Geomagnetic Thruster-A High Performance "Alfven Wave" Propulsion System Util izing Plasma Contacts , " AIAA Pape r No. 66-257.

3. H. Alfven, "Spacecraft Propulsion; New Methods," Science, Vol. 176, 14 April 1972, pp. 167-168.

-30-

'P-

EARTH'S

OFFSET DIPOLE APPROXIMATION

O r b i t a l

TO GEOMAGNETIC FIELD EFFECT OF EARTH'S SPIN ON TIME-AVMAGED FIELD

HOW TO CHANGE ORBllS usbl6 AN ELECTRODYNAMIC TETHER

-31-

Properly controlled AC components can be used t o control 8 and +-libration. Solar-energy s to rage and e or w changes s t r o n g l y s t i m u l a t e $- l ibrat ion. AC currents other than 1 ti 3/orbit should not affect $-libration much,

KEY POINTS

The maneuvering strategies on the previous page have assumed t h a t electrodynamic t e the r s wil l s t ay vertical, However, as shown at right, the distributed force on the tether causes bowing, and that bowing is what allows net momentum transfer t o the attached masses, Note that net momentum can be transferred to the system even if the wire is bowed the wrong way (as when the cur ren t is sud- denly reversed); momentum transferred t o the wire gets t o t h e masses later.

This figure also i l lust rates two other issues: 1, Bowing of the tether causes it t o cross fewer field lines. 2, Unequal end masses and uniform forces cause overall torques & tilting.

The bowing causes the te ther t o provide less thrust while dissipating the same paras i t ic power. The n e t force on t h e system is the same as i f t h e t e t h e r were straight but in a slightly weaker magnetic field.

torque is balanced by gravity-gradient restoring torques. For a given system mass and power input, d i s turb ing torques vary with L and restoring torques with L2, so longer systems can tolerate higher power, The m a s s distribution

Modulating the tether current modulates any electrodynamic torques, Current modulation at L73 n can be used t o control in-plane libration. Out-of-plane torques can also be modulated, but another control logic is required. This is because the once-per-orbit variation in out-of-plane thrust direction makes a current with frequency F (in cycles per orbit) cause out-of-plane forces and to rques with frequencies of F-1 and F+1, as shown in the Fourier analysis at bottom right. Hence $ libration control ( F = 2 ) requires properly phased F = l or F = 3 currents. Higher frequencies can damp odd harmonics of any tether bowing oscillations, Control of both in- & out-of-plane oscillations may be possible since they have the same frequencies and thus require different currents.

Applications tha t require significant F =1 components for o ther reasons can cause problems, Four such strategies are shown at right. Sin & Cos controls allow adjustment of e or u The two "Sign of ..." laws allow constant power s torage over 2/3 of each orbi t and recovery the rest of the orbit. These laws would be useful for storing photovoltaic output for use during da rk periods.

These strategies drive out-of-plane l ibration (unless the center of mass is a t t h e center of t h e tether). The l ibration frequency decreases at large amplitudes, so i f the system i s not driven t o o s t rongly, it shou ld settle i n t o a finite-but-large-amplitude phase-locked loop. This may be unacceptable in some applications, due t o result ing variations in gravi ty or t e t h e r EMF. In some cases, such as eccentricity changes, adding a F=3 component might cancel the undesired effect of an F=l current while keeping the desired effect.

I The to rque on t h e system causes it t o tilt away from the vertical, unt i l the

NOTES I also affects power-handling capability, as seen in t h e sequence at top right. I

.-

L G Colombo, M. Grossi, M, Dobrowolny, and D. Arnold, Investigation of E l e c trodynamic Stabil ization 2i Control of Long Orbiting Tethers, Interim Report on Contract NASS-33691, March 1981, Smithsonian Astrophysical Observatory.

REFERENCE

-32-

Electrodynamic Libration Control Issues

0 Raising

W

INCREASING STABILITY - ( f o r f i x e d t o t a l length h mass & I )

FOR CONTROL OF:

Out-of-plane l ibrat ion , 1 n o r 3 n I MODULATE I AT:

I I I 1.73 n In-plane l ibrat ion*

1 >5 n Tether oscillations 1 4 I or mass d i s tr ibut ion must

t t

Tether Current:

I = 1.0

I = cos #

be lopsided

Fourier Analysis of Out-Of-Plane Forces:

ln 2n 3n

50 0 0

* 0 0

0

39

07

.50 O r"l 03

.50 0 50

.50 0 SO

BIBLIOGRAPHY OF SPACE-TETHER LITERATURE

The number of references listed with each topic in the body of t he Guidebook was intentionally limited A more comprehensive bibliography follows. I t was compiled by merging bibliographies previously compiled by Mark Henley, Peter Swan, Georg von Tiesenhausen, and others. I t w i l l be expanded and updated in future revisions of t he Guidebook.

Many references (particularly final reports) cover several topics. However they are listed here only under t h e most specific re levant heading. For example, t r anspor t concepts exp l i c i t l y intended for use on a space s ta t ion are listed under space stations. For thoroughness, check related headings.

BIBLIOGRAPHY HEADINGS:

General The Tethered Satellite System Space Station & Constellation Applications Transportation Electrodynamics Dynamics, Controls, & Simulations (incl. TSS) Beanstalks and Other Ambitious Concepts Tether Materials

SOME FREQUENTLY OCCURRING ABBREVIATIONS:

CSI = California Space Institute, SIO/VCSD, La Jol la CA IAF = International Astronautical Federation JSC = Johnson Space Center, Houston TX MSFC = Marshall Space Flight Center, Huntsvil le AL SA0 = Smithsonian Astrophysical Observatory, Cambridge, MA

GENERAL

- , Applications of Te the r s in Space, Vol. 1 & 2, Workshop P roceed ings , 15-17 June 1983.

- , Proposed 1984-1987 Program P lan f o r Te the r Applicat ions in Space, prepared by NASA Tether Applications in Space Task Group, Sept 1983.

-, Selected Tether Applications in Space-An Analysis of 5 Selected Concepts, Ju ly 31, 1984, Martin Marietta final report, NASA Contract NAS 8-35499.

- , Selected Tether Applicat ions in Space- Phase 11, Preliminary Draft of Final Report on NASA Contract NAS 8-35499, Martin Marietta, February 1985.

-, Movies for Gemini Missions XI and X I , a v a i l a b l e from P u b l i c A f f a i r s Office, AP2, NASA JSC, Houston TX 77058. (See tethelcexperiment sequences)

Bekey, Ivan, Tethers Open New Space Options, Astronautics & Aeronautics, April 1983. Reprint available from OSF, RIT-3, NASA Headquarters, Wash. D.C. 20546.

-34-

Carroll, JI, Some Tether-Related Research Topics, prepared under JPL contract LC 778278 for the NASA Tether Applications in Space Task Force, November 1984.

Lang, D.D., and R.K. Nolting, "Operations with Tethered Space Vehicles," in Proceedings of t he Gemini Summary Conference, NASA SP-138, 1967.

Laue, J., U.S. / I t a l i a n Di scuss ion on Tether-Related Activities a t NASA Headquarters, NASA/MSFC, Nov.18, 1982

Von Tiesenhausen, G, Tethers i n Space-Birth and Growth of a New Avenue t o Space Utilization, Feb. 1984 NASA-TM-82571, NASA/MSFC.

THE TETHERED SATELLITE SYSTEM

l -

-, Shuttle Tethered Satellite System Design Study, NASA TM X-73365, MSFC,1976.

- , Shuttle Tethered Satel l i te System Definition - Final Study Report, NAS8- 32854, Mart in Marietta Aerospace, April 1979.

- , Shuttle Tethered Satellite System Definition - Final Study Report, NASI- 32853, Ball Aerospace Systems Division, April 1979.

-, Shuttle Tethered Satellite System, Final Report from the Facility Require- ments Definition Team; sponsored by MSPC under NASA Contract NAS8-33383 to the Center for Atmospheric and Space Sciences, Utah State Univ., May 1980.

- , TSS Final Review, Martin Marietta presentation at MSFC, Dec 14-15, 1982.

Arnold, D., G Colombo, N. Hanham, and G Nystom, System Noise Analysis of the Dumbbell Tethered Satellite for Gravity-Gradient Measurements, f inal report on NASA grant NSG-8063, 1979.

Baker, W., J.A. Dunkin, Z.J. Galaboff, ILL. Johnson, RR Rissel, M.H. Rhein- furth and M.P.L. Siebel, Tethered Subsatellite Study, NASA TM X-73314, MSFC, March 1976.

Colombo, G, EM. Gaposchkin, M.D. Grossi, and GC, Weiffenbech, T h e Skyhook": A Shuttle-Borne Tool for Low Orbital Altitude Research", MECCANICA, March 1975.

Colombo, G, EM. Gaposchkin, M.D. Grossi, and GC Weiffenbach, "Long Tethered Sa te l l i t es for the Shuttle Orbiter", presented at t h e International Conference on Technology of Scientific Space Experiments, Paris, Fance, May 1975.

Colombo, G, EM. Gaposchkin, M.D. Grossi, and GC Weiffenbach, "Shuttle-borne Long-tethered Satellites, A New Tool for Low Cost Space Science & Applicationsw, presented at A A S / W Conference, Nassau, Bahamas, July 1975.

Coiombo, G, D. Arnold, 3. Bhsack, R Gay, M. Grossi, D. Lautman, and 0. Orrin- ger, Dumbbell Gravity-Gradient Sensor: A New Application of Long Tethers, SA0 Reports in Geoastronomy, no. 2, 1976.

Colombo, G, E Oaposchkin, M. G m i , and G Weiffenbach, OravitpGradient M m - surenents down t o 103 kn; Height bq' Xeaiis ef Leiig Tetl-~ered Sa€eiii€ees, presented at 27th IAF Congress, Anaheim CA, Oct 1977.

-35-

G Colombo, D. Arnold, E. Gaposchkin, M. Grossi, P. Kalaghan, and L, Kirschner, Tethered Sa te l l i t e System for Gravi ty Gradiometry a t Low Orb i t a l Height, presented a t t he E a r t h Dynamics Summer Workshop, Boulder CO, July 1977.

Colombo, G., e t al., "Sa te l l i t e Connected by Means of a Long T e t h e r t o a Powered Spacecraft," US Patent 4,097,010.

Colombo, G., S, Bergamaschi, and F. Bevilacqua, "The I ta l ian Participation t o the Tethered Satel l i te System", IAF#81-33, 32nd IAF Congress, S e p t 1981.

Crouch, Donald S., "Shuttle Tethered S a t e l l i t e System Program Overview", Applications of Tethers in Space Workshop, Williamsburg, VL, June 15, 1983.

Laue, Jay H., "Tethered S a t e l l i t e System-Project Overview", Briefing given NASA/MSFC/PF17, Jan 19, 1983.

Laue, J.H. and F. Manarini, "The Tethered Retrievable Platform Concept and Utilization", IAF-82-13, 33rd IAF Congress, Sept-Oct 1982, Paris France.

Lundquist, C, and G. Colombo, "Advanced Technologies in Space and Opportunities for Gravity Experiments", presented at the International School of Relativist ic Astrophysics, Trapani, I ta ly , Fa l l 1977,

Manarini, G. and F, Mariani, "The Tethered Satellite System Technical Aspects and Prospect ive Science Missions", Riena, A t t i 22 Convegno I n t e l e S u l l o Spazio, Roma 1982

Mariani, F., " S c i e n c e by T e t h e r e d Sa te l l i t e " , D i p a r t i m e n t o d i F i s i c a , Universita di Roma "La Sapienza", Piazzale Aldo Moro, 2-00185, Roma, Italy.

Merlina, P., Double Tethered Satellite System, Nov, 23, 1982, Aer i t a l i a - Set tore Spazio.

Rupp, C.C. and J.H. Laue, "Shut t le /Tethered S a t e l l i t e System", Journal of Astronautical Sciences, Vol. 26, No. 1, Jan 1978, p. 1-17.

Snoddy, W.C., "Scientific and Technical Applications of a Tethered S a t e l l i t e System," AIAA Aerospace Sciences Meeting, New Orleans, La., Jan 15-17, 1979.

Wu, S.T., ed., University of Alabama at HuntsvilleMASA Workshop on The Uses of a Tethered Satel l i te System, Summary Papers, Huntsvil le AL, May 1978.

June 27, 1978.

SPACE STATION AND CONSTELLATION APPLICATIONS

-, Space Station Requirements for Tether Applications, July 26, 1984, Martin Marietta final report, NASA Contract NAS 8-35499.

Arnold, J.R., et al, The Process of Space Station Development Using External Tanks, Report t o the Office of Technology Assessment, March 1983. CSI.

Carroll, J.A., Tetner Mediated Rendezvous, report t o M a r t i n Marietta on Task 3 of contracr RK3-393855, March 1984, CSI.

Carroll, LA., A Scerkario for Tether Uses in a Space Station, AIAA/NASA Space Systems Technology Conference Paper 84-111O-Cp. Costa Mesa, June 5, 1984, CSL

-36-

,

I ~

Colombo, G., A Preliminary Study of the Orbiting Platform-Tether System Space Operation Center, M I T Dept. of Aeronautics and Astronautics, 1980.

Colombo, G., A Straightforward Use of the Shuttle ET, presented at the Workshop on t h e Utilization of t h e External Tanks of the STS, 1982, CSI.

Colombo, G, and J! Slowey: On a New Concept for a Space Station Architecture, Appendix I1 of Repor t on the Util ization of t h e External Tanks of t h e STS, CSI, April 1985

Cclombo G, A New Tethered Dual Platform Space Station Concept, Oct, 1983, NASA Contract G 82678-3286, SAO.

English, R, Characteristics of a Tethered Space Station, NASA LeRC, Oct 21, 1983.

Hamlyn, K., et al., Tethered Orbital Refueling Study, Martin Marietta, NASA contract NAS 9-17059, Interim Report, January 1985.

Kroll, EGR, "Tethered P rope l l an t Resupply Technique for Space Stations," IAF-84-442, presented at t h e 35th IAF Congress, Lausanve Switzerland, 1984.

Lorenzini, E., Analytical Investigation of Dynamics of Tethered Constellations in Earth Orbit, Aug. 17, 1984, NASA contract NAS 8-35497, SAO.

Mayer, H. L., "Swarms: Optimum Aggrega t ions of Spacecraft, Aerospa'ce Corporation ATR-80(7734)-1, Feb. 29, 1980.

Nobles , W., S e l e c t e d Te the r Applicat ions in Space, J u l y 31, 1984, Martin Marietta final report/presentation on NASA Contract NAS 8-35499.

Penzo, P. , Tether Induced Gravity for Space Station-Preliminary Assessment, JPL, March 12, 1 9 8 2

TRANSPORTATION

-, Preliminary Feasibi l i ty Study of t h e Ex te rna l Tank (ET) Deorb i t by a Tether System, May 24, 1983, Martin Marietta Memo 83-SES-665.

-, Tether Applications for the Inertial Upper Stage, Jan 1985, available from G Ryan, IUS Futures Organization, Boeing Aerospace Company.

Arnold, D.A., Orbital Pumping, NASA Contract NAS 8-35036, Aug. 24, 1984, SAO.

Bentz, D.J. Tethered Momentum Launching Systems, NASA Lewis Research Center.

Carroll, LA., Tethers and External Tanks: Enhancing t h e Capab i l i t i e s of t h e Space Transportation System, final report t o M a r t i n Marietta Corp. on contract PJI2-393G73, Dee 1982.

Carroll, 3.A., Tethers & External Tanks, ch. 3 of Report on t h e Utilization of --- t h e External Tanks of t h e SI'S;

Carroll, J.A., and A.H. Cutler, 1 tion", AXAA-84-1448, presented at

Cincinnati OH, June 1984

I L

CSf, April 1983.

"Potential Role of Tethers in Space Trmsporta- AIAA/SAE/ASME 20th Joint Propulsion Conference,

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Carroll, J.A., Tether Applications in Space Transportation, IAF Paper 84-438, 35th IAF Congress, Lausanne, Switzer land, 1984. To be publ ished in ACTA ASTRONAUTICA.

Carroll, J.A., Disposable-Tether Payload Deploying System for t he STS, final report on NASA S I R Contract NAS 8-35843, Energy Science Labs , In&, June 1984.

Contella, M.C., Tethered Deorbit of the External Tank, April 24, 1984, NASA JSC,

Colombo, G, Study of Certain Launching Techniques Using Long Orbiting Tethers,

Colombo, G., et ai,, "Use of Tethers for Payload Orbi ta l Transfer," report on NAS8-33691, M a r 1982, SAO.

Colombo, G, Orbital Transfer and Release of Tethered Payloads, report on NASA Contract NAS 8-33691, March 1983, SAO.

Hunter, M.W., "Near E a r t h Transportation Options and High Payoff Choices", A M International Annual Meeting, Baltimore, MD, May 1982.

Hunter, M.W., "Advanced Space Transportation Options", Lockheed, August 1982.

Martinez-Sanchez, M., The Use of Large Tethers for Payload Orbi ta l Transfer, MIT, 1983.

NASA-CR-164060, March 1981, SAO.

Martinez-Sanchez, M., and SA. Gavit, "Four Classes of Transportation Applica- tions Using Space Tethers-Preliminary Concept AssessmentsR, progress report t o Martin Marietta, MIT Space Systems Laboratory, March 1984.

Stuart, D.G and Martinez-Sanchez, M., Shuttle Tether Use for Payload Deploy- ment t o Circular Orbits, MIT, Aug. 10, 1984.

Penzo, P.A. and Mayer H.L., Tethers and Asteroids for Artificial Gravity Assist in t h e Solar System, JPL, AIAA Paper 84-2056, Aug. 1984.

Tschi rg i , J., Tether Deployed SSUS-A, McDonnell Douglas, April 1984, NASA Contract NAS 8-32842

ELECTRODYNAMICS

-, "Report of t he Plasma Physics and Environmental Per turbat ion Laboratory Working Groups," Program Development Contract, NASA TM X-64856, March 1974.

Alfven, H., "Spacecraft Propulsion; New Methods", Science, Vol. 176, 14 April

Anderson, A, D. Arnold, G. Colombo, M. Grossi, & L. Kirshner, Orbiting Tether's Electrodynamic Interactions, f inal report on NAS5-25077, April 1979, SAO.

Arnold, D., and M. Dobrowolny, Transmission Line Model of the Interactionss of a 'Long Metal Wire with the Ionosphere, submitted t o Radio Science, 1979.

Arnold, D.A., and M.D. Grossi, Natural Damping in the Electrodynamic Tether, January 1983, SAO.

1972, pp. 167-168.

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Banks, P.Rl., P.R. Williamson, and K.L. Oyama, "Shut t le Orbi te r Tethered Subsa te l l i t e for Explor ing and Tapping Space Plasmas, As t ronaut ics and Aeronautics, February 1981.

Chu, C., and R Gross, Alfven Waves and Induction Drag on Long Cylindrical Satellites, AlAA Journal, Vol 4, pg 2209, 1966.

Colombo, G., M. Grossi, M. Dobrowolny, and D. Arnold, Investigation of Elec- trodynamic S tab i l iza t ion d: Control of Long Orbiting Tethers, Interim Report on Contract NAS8-33691, March 1981, SAO. (Also, monthly progress r epor t s 81-15 through September 1982.)

Dobrowolny, M., G. Colombo and M.D. Gmsi, "Electrodynamics of Long Conducting Tethers in the Near Earth Environment," Interim Report on NASA Contract #NAS 8-31678. Jan 5, 1976, SAO.

Dobrowolny, M., G Columbo, and M.D. Grossi, wElectrodynamics of Long Tethers in the N-Earth Environment," Final report on NAS 8-31678, June 1976, SAO.

Dobrowolny, M., D.A. Arnold, G Colombo, and M. Grossi, "Mechanisms of Electro- dynamic In te rac t ions w i t h a Tethered S a t e l l i t e System and the Ionosphere", Reports in Radio and Geoastronomy, No. 6, August 1979.

Dobrowolny, hL, Wave and Particle Phenomena Induced by an Electrodynamic Tether, SA0 Special Report #388, November 1979.

Drell, S. D., ELM. Foley, Er M.A. Ruderman, "Drag and Propulsion of Large Satel- lites in the Ionosphere: An Alfven Propulsion Engine in Space," J. of Geophys Res., Vol. 70, No. 13, pp. 3131-3145, July 1965.

Finnegan, P.M. A Preliminary Look at Using a Tethered Wire t o Produce Power on a Space Station, NASA LeRC, May 10, 1983.

Giudici,R, Electrodynamic Tether for Power or Propulsion Design Considera- tions, March 20, 1984, NASA MSFC-PD.

Grossi, M., "A ULF Dipole Antenna on a Spaceborne Platform of the PPEPL Class", Report on NASA Contract NAS8-28203, May 1973, SAO.

Grossi M., On The Feasibility of Electric Power Generation and Electromagnetic Wave Injection by Electrodynamic Tethers, Jan 1983, T e c h Note TP 83-003, SAO.

Grossi, hl., Engineering Study of the Electrodynamic Tether as a Spaceborne Generator of Electric Power, April 1984. NASA Contract NAS 8-35497, SAO.

King, R.W.P., The Thin Wire Antenna Embedded in a Magneto-ionic Plasma, 1980, Harvard University.

McCoy, J.C. Electrodynamic Tether Applications-Massive Tether Dynamics Study, General S ta tus Review, May 3, 1984, NASA JSC-SN 3.

McCoy, J. C. Piasma nl otor/Generator-Electrodynamic Tether Applicat ions in Space, NASA JSC-ShT 3, June 13, 1984.

McCoy, JX. Plasma Motor/GeneratoPProof of Function Experiment, NASA x- -SN 3, J u l y l i 1984,

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Moore, R.D., "The Geomagnetic Thruster-A High Performance "Alfven Wave" Propulsion System Utilizing Plasma Contacts, AIAA Paper No. 66-257.

Tang, W.Y., "Comparison of Three Kinds of Possible Power Generators as Space Shuttle Power Extension Package," Dec 31, 1981, SAO.

Thompson, W.B., Electrodynamics of a Conducting Tether, Final Report t o Martin Marietta on task 4 of contract RH 3-393855, De& 1983, CSI & UCSD Physics D e p t

Weiffenbach, G.C., "A Study of the Electrodynamics of Long Conducting Tethers in t h e Near Earth Environment", NAS8-31678, SAO.

Williamson, D.P., and Banks, P.M., The Tethered Balloon Current Generator: A Space Shuttle-Tethered Subsatell i te for Plasma Studies and Power Generation, final report on NOAA Contract #03-5-022-60, Jan. 16, 1976.

Williamson, P a , P.M. Banks, and K. Oyama, "The Electrodynamic Tether," report on NASA Contract NAS5-23837, 1978, Utah S ta t e University, Logan UT.

TETHER DYNAMICS, CONTROLS AND SIMULATIONS (incl. TSS)

-, Symposium on Passive Gravity Gradient Stabilization, NASA SP-107, May 1 9 6 5

- , Evaluation of Te ther Dynamics and Con t ro l System Interaction, F ina l Report, NASA Contract NAS 8-34667, June 30, 1983.

Arnold, D., "General Equat ions of Motion," Appendix A of Inves t iga t ion of Electrodynamic S tab i l i za t ion and Cont ro l of Long Orbiting Tethers, Interim Report, March 1981, SAO.

Allias, E. and S. Bergamaschi, "Dynamics of Tethered Satellites-Two Alter- native Concepts for Retrieval", MECCANICA June 1979, p. 1 0 3 - l l L

Anderson, W. W., On L a t e r a l Cab le Osc i l la t ions of Cable-Connected Space Stations, NASA TN 5107, NASA Langley Research Center.

Bainum, P.M. and V.K. Rumar, "Optimal Control of the Shuttle-Tethered System", ACTA ASI'RONAUTICA, VoL 7, May 80, p. 1333-1348 Presented as IAF#79-190 at the 30th IAF Congress, Munich, Germany. Sept. 1979.

Bainum, P.M., RE Harkness and W. Stuiver, "Attitude Stability and Damping of a Tethered orbiting Interferometer Satel l i te System", Journal of Astronautical Sciences, Vol. XM, No. 5, p. 364-389, Mar-Apr. 1 9 7 2

Banerjee, kK. and T. R Kane, "Tethered S a t e l l i t e Re t r i eva l with Thrus te r Augmented Control", A I A A I A A S Astrodynamics Conference, San Diego Calif, 1982 # A M 82-1-21.

Banerjee, A.K. and T O R Kane, "Tether Deployment Dynamics", Journal of Astro- nautical Sciences, Vol. m, No. 4, pp. 347-365, Oct-Dec 1 9 8 2

Beletskii, V.V. and M. Guivertz, m e Motion of an Osdillating Rod Subjected to a Gravitational Field", Rosmitcheskie Issledovania 5, no. 6, 1967.

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Beletskii, V.V., The Motion of Ce le s t id Bodies, Nauka, Moscow, 1971.

Beletskii, V.V., "Resonance Phenomena at Rotations of Artificial and Natural Celest ia l Bodies,' COSPAR-IAU-IUI'AM Satellite Dynamics Symposium, June 1974, Sao Paulo, Brazil; Springer-Verlag, 1975.

Beletskii, V.V. and EM. Levin, "Mechanics of an Orbi ta l Cable System", trans- lated from Kosmicheskie Issledovaniya, Vol 18 #5, pp. 678-688, Sept-Oct, 1980.

Bergamaschi, Silvio, "Tether Motion after Failure", Journal of Astronautical Sciences, Vol. XXX, No. 1, pp. 49-59, Jan-Mar 1982.

Buckens, F., "On t h e Motion Stabil i ty of Tethered Satellites Configuration", Proceedings of t h e 12th In te rna t iona l Symposium on Space Technology and Science, €3. Nagasu, ed., AGNE Publishing, Inc., 1977, Tokyo, pp. 351-358.

Chobotov, V., "Gravity-gradient Excitation of a Rotat ing Cable-Counterweight Space Station in Orbit", Journal of Applied Mechanics, Vol. 30, P. 547-554.

Colombo, G., The S t a b i l i z a t i o n of an A r t i f i c a l Satellite a t t h e Infer ior Conjunction Point of t h e Earth-Moon System, SA0 Special Report #8, 1961.

Colombo, G., "Study of Tethered Satellite Active At t i t ude Control", NASA Contract NAS 8-33691, Interim Report, Oct 1982, SAO.

Colombo, G, Tether Dynamics Software Review; High Resolution Tether Dynamics; and Advanced Tether Applications (Damping through Reel Motor Control; Payload Aqukit ion by Space Station), Jan. 1984, NASA Contract NAS 8-35036, SAO.

Diarra, C.M., "The Effects of Tether Mass on t h e Stabil i ty and t h e Controlla- bi l i ty of t h e Shut t le-Tethered Subsa te l l i t e System", LAF#82-06, 33rd IAF Congress, Paris, France, Sept 1982.

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Eads, J.B. and Wolf, H,, Tethered Body Problems and Relative Motion Orbi t Determination, NAS-5-21453, Analytical Mechanics Association, In&, Aug. 1972.

Farquhar, R., The Control and Use of Libration Point Satellites, NASA TR R-346, Washington DC, 1970.

Farquhar, R., The Utilization of Halo Orbits in Advanced Lunar Operations, NASA T N D-6365, Washington DC, 1970.

Garber, T.B., "A Preliminaq Investigation of t h e Motion of a Long, F lex ib le Wire in Orbit", Rand Report-RM-P'IOS-ARPA, March 23, 1961.

Glaese, J.R. and H. L. Pastr ick, "Modal Synthesis Simulation of t h e Shut t le Orbiter Tethered Satellite System", AXA4/AAS Astrodynamics Conference, San Diego, W - 8 2 - 1 4 2 4 , 1982.

Hagedorn, P., b S Otterbein, "Some Remarks on the Control of Variable Length Tethered Satellites with Attitude-Orbit Coupling", Institut Fur Mechanik, T,H. Darmstadt, Darmstadt, Federal Republic of Germany.

Kalaghan, P.M., et al., Study of t h e Dynamics of a Tethered Satellite System (Skyhook)," Final Report on Contract NAS8-32199, March 1978, SAO.

Kane, T-R., "A New Method for the Retr ieval of t h e Shuttle-Based Tethered Satellite," J. of t h e Astronaut. ScL, Vol 32, No. 3, July-Sept. 1984.

Kirschner, L.R., "The Skyhook Program: A Software Package for a Tethered Satellite System, Including Electrodynamic Interactions", NASA Techn ica l Report Contract NAS 8-33691, May 1980.

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Kohler, P., W. Maag, R Wehrli, R Weber, & H, Brauchi, "Dynamics of a System of Two Satellites Connected by a Deployable and Extensible Te the r of Fini te Mass", ESTEC Contract #2992/76/NL/AK(SC), Vol 1 and 2.

Kulla, P., " S t a b i l i z a t i o n of Tethered Sa te l l i t e s " , ESTEC Report TMMl78- O'IIPKIAVS, 1977.

Kulla, P., "Dynamics of Tethered Satel l i tes" , Proceedings of t h e Symposium on Dynamics and Control of Non-Rigid Spacecraft, Frascati, I ta ly ,

Lang, D.D., Tethered Object Simulation System (TOSS) Reference Manual, NASA Contract NAS9-16715, Sept 1983.

Lips, K.W. and V.J. Modi, "General Dynamics of a Large C l a s s of F l ex ib l e Satell i te Systems", ACTA ASTRONAUTICA, Vol. 7, 1980, pp. 1349-1360.

Misra, LK. and Modi, V. J., "A General Dynarnical Model for the Space Shuttle Based Tethered Subsatell i te System", Advances in t h e Astronautical Sciences,

Misra, A,K. and JJ. Modi, "Dynamics and Control of Tether Connected Two-Body Systems - A Brief Review", 33rd IAF Congress, Paris, France, Sept-Oct 1982.

Misra, AK. and V.J. Modi, "Deployment and R e t r i e v a l of a S u b s a t e l l i t e Connected by a Tether t o t h e Space Shuttle", paper U-8@-1693 presented at t h e AIAAIAAS Astrodynamics Conf., Danvers, M a s s ,

Modi, V. J. and A& Misra, "Deployment Dynamics and Con t ro l of Tethered Satellite Systems", AIAA/AAS#7&1398, AIAAIAAS Astrodynmics Conference, Palo Alto, Calif, Aug 1978.

Modi, V.J., G Chang-fu, and A.K. Misra, "Effects of Damping on the Control Dynamics of t h e Space Shuttle Based Tether System", AAS/AIAA Astrodynamics Conference, Lake Tahoe, AAS-81-143.

Modi, V.J., G. Chang-fu, AIL Misra and D. J. Xu, "On the Control of t h e Space Shuttle Based Tether System", Acta Astronautica, Vol 9 No.6-7, 1982

Pengelley, C.D., "Preliminary Survey of Dynamic Stability of a Cable-Connected Spinning Space Station", Journal of Spacecraft, Oc t 1966.

Perrine, B.S, "A Method for Soft Tethered Station Keeping", NASA TMX-53643, Marshall Space Flight Center, July 31, 1967.

Pringle R, "Exploration of Nonlinear Resonance in Damping an Elastic Dumb- Bel l Satellite", AIAA Journal, 1968, N. ?, 1217-1222.

Raabe, LP., "Self-stabilizing Satellite," US Patent 3,206,142. Sept 14, 1965.

Rheinfurth, M.H. et al., Modal Analysis of a Non Uniform String with End Mass and Variable Tension, NASA-TP-2198, Aug. 1983.

Rupp, C.C., A Tether Tension Control Law for Tether Subsa te l l i t e s Deployed Along Local Vertical, NASA TM X-64963, MSFC, September 1, 1975.

Rupp, CC. and L.L Gresham, "A Preliminary Study of t he Attitude Control for the Shuttle Tether Satel l i te System", IEEE Journal, 1979.

Sarychev, V.A., "On t h e Dynamics of Tether-Connected Two-Body Systems", IAF-82-316, 33rd IAF Congress,Sept 27-0ct 2, 1982, Paris, France.

1978.

1976.

40, 537-557, 1979. .

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Singh, R.B., "Three Dimensional Motion of a System of Two Cable-Connected Satel l i tes in orbit", ASTRONAUTICA ACTA, Vol. 18, 1973, pp. 301-308.

Spencer, T.M., "Atmospheric Per turbat ion and Cont ro l of a Shut t le /Tether Sa te l l i t e" , Automatic Cont ro l in Space, Proceedings of t he 8th Symposium, Oxford, England Ju ly 2-6, 1979. p. 101-108.

Stuiver, W,, "Lagrange Configqrations in Space System Dynamics", Journal of t h e Astronautical Sciences, 25(1977), p. 91-106.

Stuiver, W., and P.M. Bainum, "A Study of Planar Deployment Control and Libra- t ion Damping of a Tethered Orbi t ing Interferometer Sa te l l i t e" , Journal of Astronautical Sciences, Vol. 20, No. 6, pp. 321-346, May-June 1973.

Swan, P.A., "Dynamics & Control of Tethers in Elliptical Orbits," IAF-84-361, presented at the 35th IAF Congress, Lausanne, Switzerland, October 1984.

Swet, CJ, & AM. Whisnant,"Deployment of a Tethered Orbiting Interferometer", Journal of Astronautical Sciences, Vol 17, No. 1, pp. 44-59, Jul-Aug 1969.

Swet, C. J., "Method fo r Deploying and Stabil izing Orbiting Structures," US Patent 3,532,298, Oct 6, 1970.

Synge, JL, "On the Behaviour, According to Newtonian Theory, of a Plumb Line or Pendulum Attached t o a n Art i f ic ia l Satellite", Proceedings of t h e Royal Irish Academy, Vol. 60, Sec A, 1-6, 1959.

Xu, D.M., A.K. Misra, and V.J. Modi, "Three Dimens iona l C o n t r o l of t h e Shuttle Supported Tether Satel l i te Systems During Deployment and Retrieval", Proceedings of the 3rd VPI!XJ/AIAA Symposium on Dynamics and Control of Large Flexible Spacecraft, Blacksburg, V&, 198L

BEANSTALKS & OTHER AMBITIOUS TETHER CONCEPTS

Anderson, J, G. Colombo, L. Friedman, E. Leu, "An Arrow t o the Sunn, presented at International Symposium on Experimental Gravitation, Pavia, Italy, Sept 1976.

k t su t anov , Yo, V Kosmos na Electrovoze; Komsomoldtaya Pravda, July 31, 1960. (summarized i n English in Science, Vol. 158, pp. 946-7.)

Birch, Paul , "Orbi ta l Ring Systems and Jacob ' s Ladders-l", Journal of the British !nterplanetery Society, Yo!. 35, No. 11, Nov 52, p. 414-497.

Birch, Paul, "Orbital Ring Systems and Jacob ' s Ladders-2", Journal of t he British Interplanetary Society, Vol. 36, No. 3, Dec 82, p. 115-138.

Clarke, A.C., The Foun ta ins of Paradise, Bal lan t ine Books, 1978. (Novel) Includes a postscript discussing the history of t h e "space elevator" concept.

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Clarke, ILC., The Space Elevator: 'Thought Experiment' or Key t o the Universe? Address t o the 30th IAF Congress, Munich, 20 Sept. 1979.

Collar, A.R., and J.W. Flower, "A (relatively) Low Altitude 24 Hour Satellite", Journal of the British Interplanetary Society, Vol. 22, 442-457, 1969.

Isaacs, J., H. Bradner, G Backus, and A. Vine: S a t e l l i t e Elongat ion into B True "Skyhook"; a le t te r t o Science, Vol. 151, pp 682-683, Feb 11, 1966. See also the discussions in Vol. 152, pg. 800, and Vol. 158, pp. 946-947.

Iwata, "Space Escalator, a quasi-Permanent Engine in Space", presented a t t he 30th IAF Congress, Munich, Sept 1979.

MacConochie, I., et, al. Capture-Ejector Satell i te, Oct. 1983, NASA-TM 85686, NASA Langley Research Center.

Moravec, H. "A Non-Synchronous Orb i t a l Skyhook," J. of t h e As t ronau t i ca l Sciences, Vol. XXV, No. 4, pp. 307-322, Oct-Dec 1977.

Niven, L., & S Barnes: The Descent of Anansi, Pinnacle Books, 1982 (Novel)

Pearson, J., "The Orb i t a l Tower: a Spacec ra f t Launcher Using t h e Ear th ' s Rotational Energy," Acta Astronautica, V01.2, pp. 785-799, Pergamon, 1975.

Pearson, J., "Using the Orbital Tower t o Launch Earth-Escape Payloads Daily", ALAA Paper 76-123, 27th IAF Congress, 1976.

Pearson, J., "Lunar Anchored Satellite Test", AIAA/AAs Astrodynamics Confep ence, Palo Alto, August 1978

Pearson, J., "Anchored Lunar S a t e l l i t e s for C i s l u n a r T r a n s p o r t a t i o n and Communication," J. of t h e Astronautical Sciences, Vol. 27, No. 1, pp. 39-62, Jan-Mar 1979.

Pearson, J., "Asteroid Re t r i eva l by Rotary Rocket", AIAA Pape r 80-0116, presented at t h e AIAA 18th Aerospace Sciences Meeting, Pasadena CA, Jan 1980.

Penzo, P.A. and H.L. Mayer, "Tethers and Astero ids for Art i f ic ia l Gravity Assist in the Solar System", A I U / M S Astrodynamics Conference, Sea t t l e NA,

Penzo, P A , "Tethers for Mars Space Operations", The Case for Mars XI, Univ. of Colorado, Boulder CO July 10-14, 1984.

Polyakov, A Space 'Necklace' about the Earth, (Kosmicheskoye ozherellye zemli), Teknika Molodezhi, No. 4, 41-43 (1977).

Sheffield, C., The Web Between the Worlds, Ace Science Fiction, 1978. (Novel)

Simberg, RE., "The Geosynchronous Tidal Web, A Method for Constructing an Ultra-Large Space Structure", Space Manufacturing 4, Proceedings of t h e 5th PrincetonIAIAA Conference, May 18-21, 1981, published by AIAA.

Tsiolkovsky,K.E., Grezy 0. Zemie i nebe (i) N a Veste (Speculations between earth & sky, & on Vesta; science fiction works). Moscow, izd-vo AN SSSR, 1959.

Aug 20-22, 1984.

(NASA TM-75174)

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TETHER MATERIALS

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G Graff, "Superstrong Plastics Challenge Metals", High Technology magazine, February 1985, pp. 62-63.

Holler, R A., Metallized Kevlar for Undersea Electromechanical Cables, Naval Air Development Center, Warminster, PA., S e p t 1984.

Ross, 3. H., "Superstrength-Fiber Applications," Astronautics & Aeronautics, December, 1977.

The following reports are available from Du Pont's Textile Fibers Department:

Kevlar 49 Aramid for Pu l t rus ion Characteristics and Uses of Kevlar 29 Aramid. Characteristics and Uses of Kevlar 49 Aramid High Modulus Organic Fiber. 1978. The E f f e c t of Ultraviolet Light on Products Based on Fibers of Kevlar 29 and

Kevlar 49 Aramid. 1977. Information only on terrestrial appl ica t ions

1975. 1976.

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