Question: A lunar module (LM) lifts off from the lunar surface and flies a powered trajectory to its burnout point at 30 km altitude. The velocity

A lunar module (LM) lifts off from the lunar surface and flies a powered trajectory to its burnout point at 30 km altitude. The velocity vector of the LM is parallel to the lunar surface at burnout. It then coasts halfway around the moon, where it must climb and rendezvous with the Apollo command module (CM) in a 250-km circular orbit. Note: μmoon = 4902.8 km3/s2, rmoon = 1740 km.

a) Calculate vp, the burnout speed of the LM (km/s).

b) Calculate vCM, the CM circular orbit speed (km/s).

c) Calculate va, the LM orbit speed when it reaches the CM (km/s).

d) Calculate the ∆v required to match speeds at the rendezvous with the CM (km/s).

e) Calculate tcoast, the required coast time for the LM to reach the CM (seconds).

f) In order to assure a rendezvous, it is desirable that the LM and CM arrive at the rendezvous point together. Where must the CM be in relation to the LM at burnout? Cite your answer as a time differential and an angle differential of the CM ahead of, or behind the LM burnout point. This sets the “launch window” for the LM takeoff.

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