MSC-04334

NATIQNAL AERONAUTICS AND SPACE ADMINISTRATION

MSC INTERNAL NOTE NO. 71-FM-197

June 8, 1971

.v.v.

ROUND TRIP LANDING MISSIONS TO

THE ASTEROID EROS, 1981 OPPORTUNITY

Advanced Mission Design Branch

MISSION PLANNING AND ANALYSIS DIVISION

MANNEC> SPACECRAFT CENTERHOUSTON/TEXAS

https://ntrs.nasa.gov/search.jsp?R=19720006191 2020-03-02T12:32:54+00:00Z

MSC-04334

MSC INTERNAL NOTE NO. 71-FM-197

ROUND TRIP LANDING MISSIONS TO THEASTEROID EROS, 1981 OPPORTUNITY

By Gregory A. ZamboAdvanced Mission Design Branch

JuneS, 1971

MISSION PLANNING AND ANALYSIS DIVISION

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

MANNED SPACECRAFT CENTER

HOUSTON, TEXAS

Approved:Funk, Chief

/Aavanced Mission Design Branch

Approved; y_^V J<iJ v^~^John P./Mayer, Chief "MissionyPlanning and Analysis Division

CONTENTS

Section Page

SUMMARY .i .. 1

INTRODUCTION . .... . . . ... .'.' . . . . . 2

SYMBOLS '-'•.'-. . . . . . . . . . . . . . 2

"PROCEDURE . .. . . . .. ... ... ... . ... . .... . 3

RESULTS ... . . . . . . 1*

CONCLUSIONS . . . . . . . . ... . , '. ......' , . . . . . . . 5

REFERENCES . . .•.....'. . ..'.". . . . . ''.. . ... ... . 20

iii

TABLES

Table • Page

I 1981-82 EARTH TO EROS ONE-WAY MINIMUM AV REQUIRE- •MENTS ' . . . . . . . . 6

I.I 1982 EROS TO EARTH ONE-WAY MINIMUM AV REQUIRE-MENTS •.' . 7

III 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DAYSAND FLIGHT TIMES

(a) Staytime at Eros >_ 0 days 8(b) Staytime at Eros >_ 5 days 9(c) Staytime at Eros >_ 10 days . . . . . . . . . . . . . 10(d) Staytime at Eros >_ 15 days 11(e) Staytime at Eros >_ 20 days 12(f) Staytime at Eros .25 days .13(g) Staytime at Eros >_ 30 days lU

IV VEHICLE CONFIGURATIONS AND COST COMPARISON(5000-LB PAYLOAD) 15

IV

FIGUEES

Figure Page

1 . Total mission AV versus total trip time for "fast"round trip landing missions to .Eros in the 1981opportunity 16

2 Characteristics and heliocentric sketch ofmission A (fast mission) IT

3 Characteristics and heliocentric sketch ofmission B (opposition class mission) 18

i| Characteristics and heliocentric sketch ofmission C (conjunction class mission) . . . . . . . 19

ROUND TRIP LANDING MISSIONS TO THE ASTEROID EROS,

1981 OPPORTUNITY

By Gregory A. Zambo

SUMMARY

The asteroids may provide a key link in understanding the origin ofthe solar system and to this end a study of round trip landing missionsto the asteroid Eros in the 1981 opportunity was conducted.

A comprehensive AV study of short staytime (0 to 30 days), shorttotal trip time (10 to l60 days) round trip landing missions (fastmissions) is presented. In addition, the characteristics of threeselected round trip landing missions are described. These three missionshave the following characteristics.

a. Mission A (fast mission): 120-day total trip time, 0-day stay-time, 73 000-fps total mission AV

b. Mission B (opposition class): 380-day total trip time, 0-daystaytime, 52 000-fps total mission AV

c. Mission C (conjunction class): 5 0-day total trip time, 175-daystaytime, 39 000-fps total mission AV

A study using three different propulsion stages, the large-tankAgena, the chemical propulsion stage (CPS), and a nuclear stage was con-ducted to determine which and how many stages could perform each of thethree missions. A payload of 5000 pounds was assumed. The propulsionrequirements for mission A were found to be two large-tank Agenas andten CPS's (or alternatively, two large-tank Agenas and five nuclearstages) while mission B required two large-tank .Agenas and two CPS's.Mission C, the conjunction class mission, can be performed with onelarge-tank Agena and one CPS.

INTRODUCTION

As in reference 1,

As long as the asteroids were regarded as fragmentsof a broken-up planet, interest in them was limited.There are now good reasons to believe that theasteroidal belt represents an intermediate stage inthe formation of planets. This links the presentconditions in the asteroidal region with the epochin which the earth and the other planets wereaccreting from interplanetary grains. Hence, inorder to understand how the solar system originatedit may be essential to explore the asteroids.

Round trip landing missions to the asteroid Eros (designatednumber U33) in the 1981 opportunity are considered using a 262- by262-n. mi. altitude orbit at Earth departure and a 200- by 38 529-n. mi.altitude (l-day period) orbit at Earth return. The "landing" at Erosis actually a rendezvous with Eros, because of the small gravitationalattraction of the asteroid. In fact, the concept has been discussed ofcapturing a small asteroid, bringing it back to Earth, and storing it inorbit about the Earth for later investigations (ref. l).. The threemissions presented herein (missions A, B, and C) are representative ofdirect missions to Eros in the 198l opportunity. Both two-impulse directand three-impulse (intermediate heliocentric impulse) direct one-way tra-jectories were considered in this study.

The author acknowledges Stanley R. Sudol and Gus R. Babb of theAdvanced Mission Design Branch for their assistance.

SYMBOLS

a semimajor axis

e eccentricity

I specific impulsesp

i inclination relative to the ecliptic plane

M mean anomaly

m mass of usable propellant

m burnout mass of stages

V^ magnitude of hyperbolic excess velocity vector

AV magnitude of impulsive velocity-change vector

ft longitude of ascending node, heliocentric ecliptic system

to argument of periapsis, heliocentric ecliptic system

Subscripts

AE arrive Earth

AR arrive Eros

DE depart Earth-

DR • depart Eros

I intermediate impulse

PROCEDURE

A computer program that minimizes one-way (Earth to Eros, or Erosto Earth) three-impulse AV was developed and used in this study. For agiven launch date from the departure planet and flight time to thearrival planet, the sum of the departure AV, the intermediate impulse AV,and the arrival AV is minimized as a function of four independent variables:the position vector (dimensioned three) of the intermediate impulse, andthe time from the departure planet to the intermediate impulse. A gradientmethod is used in the minimization process. The two-impulse one-way AV(Lambert's solution) is also calculated by the program.

This program uses an analytic Earth ephemeris based on reference 2and a two-body motion ephemeris for Eros (a = 1. 581 astronomical unit,e = 0.2228, i = 10.828°, n = 30 .012°, u = 1T8.08U0, and M = 238.913° onJanuary 6, 19 1). A 262- by 262-n. mi. altitude orbit at Earth departureand a 200- by 38 529-n. mi. altitude capture orbit at Earth return wereused in this study. The AV on arrival at Eros was assumed to be equal tothe V upon arrival at Eros and the AV on departure from Eros wasassumed to be equal to the V^ upon departure from Eros. A masslessplanet model (V^ vector defined as the heliocentric-transfer-conicvelocity vector minus the velocity vector of the planet) was assumedthroughout.. Impulsive (ideal) AV's and collinear burns at Earth departure,Eros arrival, Eros departure, and Earth arrival were also assumed throughout.Only one-way.trajectories with transfer angles of less than 360° were con-sidered.

The propulsion stages used herein were defined as follows:

a. Large-tank Agena: m = 1985 pounds; m = 35 000 pounds;S X

I = 292.5 secondssp .

b. CPS: m = 60 000 pounds; m = 5^0 000 pounds; I = k60 secondss , x sp

c. Nuclear stage: m = 88 000 pounds; m = 300 000 pounds;S , • I

I = 784 secondssp

RESULTS

Table I presents Earth to Eros one-way minimum two-impulse andthree-impulse AV requirements. In generating this table, only arrivalJulian dates at Eros of 2 4U4 960 through 2 HI* 5 020, in increments of5 days, and Earth to Eros flight times of 5 days through 100 days, inincrements of 5 days, were considered.

Table II presents Eros to Earth one-way minimum two-impulse andthree-impulse AV requirements. In generating this table, only departurefrom Eros Julian dates of 2 khk 980 through 2 hk5 QUO, in increments of5 days, and Eros to Earth flight times of 5 days through 100 days, inincrements of 5 days, were considered. In tables I and II, only one-waylegs with a minimum three-impulse AV of less than 900 000 fps are presented.

Table III presents the launch dates, the flight times, and the two-impulse and three-impulse minimum total mission AV's for round tripmissions. On each subtable of table III, the staytime at Eros is heldfixed and the total trip time is varied. Each mission of table III wasgenerated by choosing from all possible combinations of one-way trajec-tories from tables I and II, the round trip mission having, for the givenminimum staytime and the given total trip time, the minimum total missionAV. Staytimes of 0 through 30 days, in increments of 5 days, and totaltrip times of 10 through 160 days, in increments of 5 days, are presentedin table III.

Figure 1 graphically presents the table III results. Minimum totalmission AV is plotted against total trip time, with the contour linesbeing lines of fixed minimum staytime at Eros. No difference betweentwo-impulse and three-impulse total mission AV was found, thereforefigure 1 represents identically both two-impulse and three-impulse roundtrip missions.

Three missions representative of the 1981 opportunity were selectedand their characteristics are presented in figures 2, 3, and k. Mission A,a "fast mission" to Eros, is represented in figure 2. This mission has a

0-day staytime at Eros and is seen to be the 120-day total trip timemission of table Ill(a). Mission B, an "opposition class" mission toEros, is characterized in figure 3 while mission C, a "conjunctionclass" mission to Eros,, is shown in figure h.

Table IV presents the vehicle configurations capable of performingeach of three aforementioned missions. A gross cost comparison isalso presented.

CONCLUSIONS

The "fast mission" to Eros (120-day total trip time) required73 000-fps total mission AV and is too costly to be considered seriously.The "opposition class" mission (380-day total trip time) requires52 000-fps total mission AV and can be performed with two large-tankAgenas and two CPS's. The "conjunction class" mission (5 0-day totaltrip time) requires 39 000-fps total mission AV and, although l60 dayslonger in total trip time than the "opposition class" mission, it requiresonly one large-tank Agena and one GPS. Furthermore, it has a staytimeat Eros of 175 days as compared to the 0-day staytime of the "oppositionclass" mission.

For an unmanned (5000-lb payload) mission to Eros in the 198lopportunity, a cost consideration dictates the "conjunction class" missionas the obvious choice.

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TABLEIU.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES

(a) Staytitne at Eros £ 0 days

TTT= Total trip time, daysDV2 = Total mission AV, two-impulseDV3 = Total mission AV, three-impulseJDDE = Julian date of Earth departure - 2 440 000

Tl = Earth to Eros flight time, daysS = Staytime at Eros, daysT2 = Eros to Earth flight time, daysJDDR = Julian date of Eros departure - 2 440 000

T H R E E - I M P U L S E

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TABLE HI.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued

(b) Staytime at Eros 2.5 days

TTT

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DV2

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10

TABLE EL- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued

Cc) Staytime at Eros £10 days

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35 5005.-.JL5 5..QJ1540 500540 500S45 500545 snniibO 5005bfi . _5n.r)555 500575 SOln

75 501080 bnlQ85 50109U E-niO90 50109i 5Q1 n

100 501010.0- . 50 in

Q gn

4980

llll4980497549/51970 _

497C

4965

4960

4955M9 SO

4950

49H&49654940

4960

49S?49b&i?&.0_

10in1015152.CU202525

30-IS-354040

MS5050

40

40

45

4560

101 0101010

101010

10-J-0-10

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101 010in10101010101 D1010

51 015)b20

252530

35„ ..AS--

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100.- 1 on

500060 0">5005500-5 . .5005

5005

6005

50055005.. -.5005

&OfTi5005SJDOS5005

500550 1 05010501 050105-Q-l_n.5010sn i oSDIO501.0. -

11

TABLEIU.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued

(d) Staytime at Eros £15 days

25 99999930 92470635 66893540 52541015 411631

0V 3

999999921705668935525110111631

50 371074 371074

55 329601 .32.9601 _60 28921165 2621/670 23900375 22012280 20543085 19156190 18Q96395 170847100 16201H105 1S3966110 116475115 H0013120 134374125 129206

130 124214135 119847140 1 15935115 i 12414150 1UB992155 105875

28921 1262176239Q032201222051301915611 80963170847162044153966116475140013

1343741292061242441 1 98471 159351 12444108992105875

1r£o-

J.DUE TJ_

1890 100199549854985498Q19BQ198Q19/519/5197049/049654965496549754975197Q

197019/0197019651965196519651965

I960I960

5101015IS152G20252530303025253030303035353535351010

•IMPULSE^

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30 1001515ISISISL5_

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12

TABLE IH.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued

(e) Staytime at Eros £20 days

TWO-iMF'U

TTT

30.354045bOb56065707580859095

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1 52U._2530

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9V 9 9.9 9..9999998!0_438_^477715424224622/84U1981357920320642292745268244246526229087214727201 3061892421 /8945170C4516_196.7.15419947371413413 6 0 U 430836

26(141219551 18503

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54 1994737 14134130Q043083626| 1421 95b

1 18503

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TABLEEL- 1981-82 EROS ROUND TRIP MISSIONS:.LAUNCH DATES AND FLIGHT TIMES - Continued

(0 Stay.time.at Eros £25 days

TWO-IMPULSE

TTT

351015SO5560.657075808590951001051 101 1512012513013511011515015516C

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999999VV99999618137/118863355053S6'93'I706b911781237139133619530921228171 1262713•211512229213•21582220275119115118161117298916191 II!>73121*0705111925139757131805

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TABLEBI.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Concluded

fg) Staytime at Eros £30 days

TWO-

TTT

45

65606570758C85

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t2£12513013514C

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300

280

Staytimeat|Eros, day

262- by 262-n. mi. altitudetat Earth departure

200- by 38 529-n. mi.altitude at Earth return

20 60 80Total trip time,

140 160

Figure 1.- Total mission AV versus total trip time for "fast" round trip landing missionsto Eros in the 1981 opportunity.

210°

220°

230°

240°

250°

260°

270°

280°

290°

300°

310°

320°

200° 190°

IT

180° 170° 160° 150°

120 day total trip time0 day staytime at ErosTotal AV = 73 161 fps

262- by 262-n. mi. altitude at Earth departure200- by 38 529-n. mi. altitude at Earth return

' HffTito vernal equinox)

140°

130°

120°

110°

100°

go-

70°

60°

50°

40°

330° 340° 350° 0 10'

Figure 2.- Characteristics and heliocentric sketch of mission A (fast mission).

18

210° 200° 190° 180° 170° 160° 150°

220°

230°

240°

250°

260°

270°

280°

290°

300°

310"

320°

July 19, 1982

380 day total trip time0 day staytime at ErosTotal AV = 52 069 fps

--- Spacecraft trajectory

tffttttH2b2- by 262-n. mi. altitude at Earth departure200- by 38 529-n. mi. altitude at Earth return

T (to vernal equinox)

60°

50°

40°

330° 340° , 350° 0 10° 20° 30°

Figure 3.- Characteristics and heliocentric sketch of mission B (opposition class mission).

210° 200° 190° 180° 170° 160° 150°

220°

230°

240°

250°

260°

270°

280"

290°

300°

310°

320°

545 day tots' trip time175 day staytime at ErosTotal AV = 39 395 fps

Spacecraft trajectory-

262- by 262-n. mi. altitude at Earth departure- by 38 529-n. mi. altitude at Earth return

"J w .1'. . . _ . . , „ , .^ v ^. v* \ X V\X \

T (to vernal equinox)

140°

130°

120°

110°

100°

90°

80°

70°

60°

50°

40°

330° 340°, 350° 0 10° 20° .30°

Figure 4.- Characteristics and heliocentric sketch of mission C (conjunction class mission).

20

REFERENCE

1. Alfven, H.; and Arrhenius, G.: Mission to an Asteroid. Science,Vol. 167, Jan. 9, 1970, pp. 139-1 1.

NASA MSC