1. Three-Body Trajectory Model and Spiral Transfer Matching
March 5, 2009
[Andrew Damon] [Mission Ops] 1

2. Three-Body Gravity Model
Much more accurate than patched two body model
Gravity effects of Earth and moon are always taken into account
Important Result: We will not need a separate circularization scheme!!
Time of flights will be on the order of 1 year to desired lunar orbit
Spiral Out ~ 290 days
Spiral In ~ 60 days
[Andrew Damon] [Mission Ops] 2

3. Approximate Data for Trajectory Match
All scenarios based on 400 km Earth parking orbit and 50 km lunar circular orbit
Total TOF set to 350 days
Sizing will be iterative procedure with propulsion group (Brad)
Important to match masses at end of outbound spiral and beginning of inbound spiral
ΔV to match up outbound and inbound spirals is not yet optimized
Payload
Thrust (mN)
Mass flow (mg/s)
Preliminary ΔV at Match (m/s)
Added Prop Mass (kg)
100 g
120
5.60
220
4.80
10 kg
189
249
6.25
[Andrew Damon] [Mission Ops] 3

4. [Andrew Damon] [Mission Ops]
Backup Slides
10 kg payload case
[Andrew Damon] [Mission Ops] 4

5. 100g case - Zoomed in to match point:
[Andrew Damon] [Mission Ops] 5

6. 10 kg case - Zoomed in to match point:
[Andrew Damon] [Mission Ops] 6

7. [Andrew Damon] [Mission Ops]
A Big Thanks to:
Dan Grebow and
Marty Ozimek
Their help with the orbit mechanics of the 3-body problem was invaluable. They spent several hours checking over our code and also lent us class notes from Prof. Howell’s AAE 632.
[Andrew Damon] [Mission Ops] 7