Advanced  Propulsion  

An1ma3er  Propulsion  

Why  an1ma3er?  An1ma3er  has  an  extremely  high  energy  density.  

An#ma&er  rocket  uses  the  reac1on  of  ma3er  and  an1ma3er  to  create  electricity,  to  generate  thrust  by  expelling  the  products  of  the  reac1on;  or  to  heat  a  gas  which  well  be  expelled  for  thrust.  

An1ma3er  rockets  would  have  extremely  high  exhaust  veloci1es  (over  105  km/s)  

Also  capable  of  producing  high  thrusts   Fast  missions  to  Mars  or  outer  planets  

 Poten1al  for  unmanned  or  manned  interstellar  missions  

Storing  requires  magne1c  field  traps  

2  

An1ma3er  Propulsion  Many  technical  challenges  to  be  overcome:    Trapping  an1ma3er  is  difficult    The  world  produces  between  1  and  10  nanograms  of  an1ma3er  per  year    Most  expensive  substance  on  Earth:  $62.5  trillion/gram    Energy  conversion  requires  some  technical  miracles  to  be  overcome  

PENN  State  is  studying  an1ma3er  trapping  and  produc1on    They  also  design  an1ma3er  rockets   3  

Planetary  Mo1on  and  Orbital  Mechanics  

4  

Kepler’s  Laws  

1. Planets move in elliptical orbits with the Sun at one focus of the ellipse.

5  

Eccentricity  =    distance  between  foci/length  of  major  axis  

a  

Kepler’s  Laws  

2. The orbital period of a planet varies such that a line joining the Sun and the planet will sweep equal areas in equal time intervals. 6  

Kepler’s  Laws  

2. The orbital period of a planet varies such that a line joining the Sun and the planet will sweep equal areas in equal time intervals. 7  

Kepler’s  Laws  3. The amount of time a planet takes to orbit the Sun is related to its orbit’s size such that the period P, squared, is proportional to the semi-major axis, a, cubed

Planets around the sun

P2 = a3

where P is in years and a is in astronomical units (AU).

 

In general

P2 ∝ a3

P2 = k a3

P and a are in arbitrary units

k was a measured quantity for Kepler  

8  

Kepler’s  3rd  Law  and  the  Planets  Planet   Period  (years)   Distance  (AU)  

Mercury   0.24   0.38  

Venus   0.62   0.72  

Earth   1.00   1.0  

Mars   1.88   1.52  

Jupiter   11.85   5.2  

Saturn   29.46   9.54  

Uranus   84.07   19.18  

Neptune   164.82   30.06  

Pluto   248.6   39.44  

9  

Eccentricity  

0.206  

0.007  

0.017  

0.093  

0.049  

0.056  

0.044  

0.011  

0.249  

Kepler’s  3rd  Law  and  the  Planets  Planet   Period  (years)   Distance  (AU)  

Mercury   0.24   0.38  

Venus   0.62   0.72  

Earth   1.00   1.0  

Mars   1.88   1.52  

Jupiter   11.85   5.2  

Saturn   29.46   9.54  

Uranus   84.07   19.18  

Neptune   164.82   30.06  

Pluto   248.6   39.44  

10  

Eccentricity  

0.206  

0.007  

0.017  

0.093  

0.049  

0.056  

0.044  

0.011  

0.249  

What’s  really  governing  planetary  mo1on?  

Newton’s 1st Law of Motion:

From Newton’s Principia published in 1687:

“Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.”

An object at rest will remain at rest unless acted upon by an external and unbalanced force. An object in motion will remain in motion unless acted upon by an external and unbalanced force.

11  

What’s  really  governing  planetary  mo1on?  

Newton’s 2nd Law of Motion:

From Newton’s Principia published in 1687:

“Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.”

The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

12  

What’s  really  governing  planetary  mo1on?  

Newton’s 3rd Law of Motion:

From Newton’s Principia published in 1687:

“Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.”

For a force there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.

13  

What’s  really  governing  planetary  mo1on?  

Isaac Newton (1642-1727): Discoveries are the core for most of our understanding of gravity and motion

Law of Universal Gravity: Massive objects attract

F is gravitational force of attraction (Newton)

M = mass (kg) of one object

m is mass (kg) of second object

r = distance (m) between the two objects

G = 6.7 x 10-11 m3 kg-1 s-2 (gravitational constant) 14  

What’s  really  governing  planetary  mo1on?  

Newton discovered that the planets are moving and that they are attracted to the Sun. This allows for the elliptical orbits and can prove Kepler’s third law, which in general is

P = orbital period (seconds)

a = semimajor axis (m)

M = mass of system (kg)

G = 6.7 x 10-11 m3 kg-1 s-2 15  

Geosynchronous  Orbit  For  some  applica1ons,  we  want  to  keep  a  satellite  over  a  single  point  above  the  Earth.  P  =  24  hours  =  86,400  s    What  is  the  semimajor  axis?  

GMaP 32

2=⎟

⎠

⎞⎜⎝

⎛π

3/1

2

2

4 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

πGMPa

G  =  6.67  x  10-­‐11  m3  s-­‐2  kg-­‐1  Mass  of  the  Earth:  M  =  5.97  x  1024  kg  

= 4.16x107m = 41,640km = 6.6Re

( )( )( )3/1

2

22412311

4400,861097.51067.6

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−−−

πskgxkgsmx

16  

What  do  we  need  for  a  mission  to  Mars?  

17  

Mo1ons  to  consider  

18  

1)  Orbital  mo8on  of  the  Earth  2)  Orbital  mo1on  of  Mars  3)  Launch  of  spacecrae  off  Earth  4)  Escape  of  spacecrae  from  Earth    5)  Orbital  mo1on  of  the  spacecrae  6)  Capture  of  spacecrae  by  Mars  

Orbital  Velocity  of  Earth  For  orbits  that  are  approximately  circular,  the  orbital  speed  is  given  by:  

Pavorbitπ2

=

For  Earth:    a  =  1.5x108  km    P  =  3.1x107  s  (1  year)  

vEarth  =  29.8  km/s  skmvorbit 7

8

101.3)105.1(2

×

×=

π

19  

Mo1ons  to  consider  

20  

1)  Orbital  mo1on  of  the  Earth  2)  Orbital  mo8on  of  Mars  3)  Launch  of  spacecrae  off  Earth  4)  Escape  of  spacecrae  from  Earth    5)  Orbital  mo1on  of  the  spacecrae  6)  Capture  of  spacecrae  by  Mars  

Orbital  Velocity  of  Mars  For  orbits  that  are  approximately  circular,  the  orbital  speed  is  given  by:  

Pavorbitπ2

=

For  Mars:    a  =  2.3x108  km    P  =  5.8x107  s    

vMars  =  24.2  km/s  

Mars  

skmvorbit 7

8

108.5)103.2(2

×

×=

π

21  

Mo1ons  to  consider  

22  

1)  Orbital  mo1on  of  the  Earth  2)  Orbital  mo1on  of  Mars  3)  Launch  of  spacecraC  off  Earth  4)  Escape  of  spacecrae  from  Earth    5)  Orbital  mo1on  of  the  spacecrae  6)  Capture  of  spacecrae  by  Mars  

Escape  Velocity  Need  kine1c  energy  to  be  greater  than  poten1al  

energy  to  escape  Earth’s  gravity  What  speed  do  we  need?  

planet

planetesape R

GMv

2=

1.  Escape  velocity  is  independent  of  rocket  mass.  

2.  Only  depends  on  planet  mass  and  radius.  

3.  This  does  not  include  energy  lost  to  the  atmosphere.  

4.  This  assumes  the  rocket  is  not  fired  con1nuously.  

5.  Less  ini1al  speed  is  needed  to  get  to  orbit.   23  

Escape  Veloci1es  Planet   Mass  (kg)   Radius  

(m)  v  escape  (km/s)  

Mercury   3.3x1023   2.4x106   4.4  Venus   4.9x1024   6.0x106   10.4  Earth   6.0x1024   6.4x106   11.2  Moon   7.36x1022   1.7x106   2.6  Mars   6.4x1023   3.4x106   5.0  Jupiter   1.9x1027   7.1x107   59.7  Saturn   5.7x1026   6.0x107   35.5  Uranus   8.7x1025   2.6x107   21.3  Neptune   1.0x1026   2.5x107   23.5  

24  

planet

planetesape R

GMv

2=

Mo1ons  to  consider  

25  

1)  Orbital  mo1on  of  the  Earth  2)  Orbital  mo1on  of  Mars  3)  Launch  of  spacecrae  off  Earth  4)  Escape  of  spacecraC  from  Earth    5)  Orbital  mo1on  of  the  spacecrae  6)  Capture  of  spacecrae  by  Mars  

We  also  need  enough  energy  to  get  into  transfer  orbit  

Two  velocity  requirements  for  gehng  into  transfer  orbit:  1.  Spacecrae  must  change  it’s  velocity  to  get  into  Low  Earth  

Orbit  (LEO).    Note  that  this  change  in  velocity  is  less  than  the  escape  velocity  of  the  Earth.  

2.  Spacecrae  also  needs  an  addi#onal  change  in  velocity  to  get  into  the  transfer  orbit    

The  spacecrae  accelerates  (remember  that  accelera#on  is  the  change  in  velocity  over  #me)  to  these  veloci1es  using  propulsion  

But  what  is  this  addi#onal  change  in  velocity  to  get  into  the  transfer  orbit?    

   

26  

Mo1ons  to  consider  

27  

1)  Orbital  mo1on  of  the  Earth  2)  Orbital  mo1on  of  Mars  3)  Launch  of  spacecrae  off  Earth  4)  Escape  of  spacecrae  from  Earth    5)  Orbital  mo8on  of  the  spacecraC  6)  Capture  of  spacecrae  by  Mars  

Hohmann  Transfer  

1.5  AU   1.0  AU  

Kepler’s  and  Newton’s  laws  provide  a  way  to  calculate  the  path  between  to  bodies  in  the  solar  system.  

What  is  the  semimajor  axis  of  this  orbit?  

2a  =  1.5  AU  +  1  AU  =  2.5  AU    

a  =  1.25  AU  

Hohmann  Transfer:    transfer  orbit  that  requires  the  minimum  energy  (usually)  

28  

Mars’  orbit  

Earth’s  orbit  

spacecrae’s  orbit  

Hohmann  Transfer  

1.5  AU   1.0  AU  

Kepler’s  and  Newton’s  laws  provide  a  way  to  calculate  the  path  between  to  bodies  in  the  solar  system.  

What  is  the  semimajor  axis  of  this  orbit?  

a  =  1.25  AU  

Hohmann  Transfer:    transfer  orbit  that  requires  the  minimum  energy  (usually)  

What  is  the  1me  required?  

Kepler’s  3rd  Law:  P2  =  a3  

P  =  (a3)1/2    P  =  (1.253)1/2    =  1.4  yrs  

Travel  1me  =  0.7  years  =  8.4  months   29  

Mars’  orbit  

Earth’s  orbit  

spacecrae’s  orbit  

Earth–Mars  (Hohmann)  Transfer  Orbit:  How  much  change  in  velocity  is  needed?  

For a circular orbit

Transfer orbit is actually elliptical so velocity depends on location in orbit (this results from conservation of energy and Kepler’s 2nd law regarding equal areas in equal times)

Pavorbitπ2

=

30  

1.5  AU   1.0  AU  

Mars’  orbit  

Earth’s  orbit  

spacecrae’s  orbit  

V1  V2  

Earth–Mars  Transfer  Orbit:  How  much  change  in  velocity  is  needed?  

•  We can calculate this.

•  Our satellite must leave going 0.8 km/sec faster than Earth and arrive at Mars going 2.4 km/sec slower than Mars.

V1 = 30.6 km/sec

V2 = 21.8 km/sec

•  Recall that the Earth and Mars are moving at 29.8 km/sec and 24.2 km/sec.

31  

1.5  AU   1.0  AU  

Mars’  orbit  

Earth’s  orbit  

spacecrae’s  orbit  

V1  V2