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Notes_KFR%20BP - K FR 1 Example Free-Return Trajectories...

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Unformatted text preview: K FR 1 Example: Free-Return Trajectories Consider circumlunar trajectories Assume coplanar orbits Sun off Moon’s orbit circular Note: patched-conic approach less accurate in this problem than for interplanetary If has no gravity 1. Jump to ellipse from parking orbit 2. At , with no Δv , remains on transfer ellipse 3. Returns to ⊕ at radius of parking orbit does possess gravity 1. Passage through local field of Changes velocity magnitude and direction wrt ⊕ 2. No return to ⊕ unless Δv to return to transfer ellipse K FR 2 Consider: 1. make transfer ellipse larger 2. Δv still tangential (most efficient) 3. apogee ≥ r 4. reach sooner at different angle If pass vr+ = −vr− vθ = + vθ + − such that end up on same traj for ⊕ return K FR 3 Vector Diagram Same relative velocity equation: − v − = v∞ / + v Flyby angle determined by value of v∞ and rp K FR 4 Notes: 1. Early Apollo flights free-return Typical 3-day outbound leg Pass ahead of so s/c could enter 3-day return leg if failure occurs Apollo 11 (for landing) 3 day out; 2.5 day return (if insertion did not occur would not return to vicinity of Earth) 2. Apollo 17 altered its initial free-return translunar trajectory to get a more precise landing rp / = 1849 (111 altitude) / passed ahead rp = 111 altitude Entered lunar orbit — ra = 314 3. Apollo 13 Had made a mid-course correction to leave free-return path landing before experiencing failure that aborted Lunar module engines used after explosion to modify trajectory and return to ⊕ Apollo 13 same trajectory / failure enroute to / lunar module descent engines did fire Lunar approach: vr = +.244 vθ = 0 ...
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