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Three-Body Trajectory Model and Spiral Transfer Matching

This document presents a comprehensive model for three-body trajectories crucial for lunar missions, focusing on the integration of Earth and Moon gravitational effects for enhanced accuracy. Unlike traditional patched two-body models, this approach eliminates the need for a separate circularization scheme, allowing for efficient mission planning. We discuss time-of-flight estimates around 350 days, specific to a 400 km Earth orbit and a 50 km lunar orbit, while iteratively sizing propulsive metrics to ensure optimal performance. Special acknowledgments are made to contributors for their invaluable support.

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Three-Body Trajectory Model and Spiral Transfer Matching

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  1. March 5, 2009 [Andrew Damon] [Mission Ops] Three-Body Trajectory Model and Spiral Transfer Matching 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 [Andrew Damon] [Mission Ops] 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 3

  4. 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 Grebowand 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. 7

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