During the Apollo missions, while the astronauts were on the Moon with the lunar module (L...

During the Apollo missions, while the astronauts were on the Moon with the lunar module (LM), the command module (CM) would fly in a circular orbit around the Moon at an altitude of 60 mi. After the astronauts were done exploring the Moon, the LM would launch from the Moon’s surface (at L) and undergo powered flight until burnout at P, which occurred when the LM was approximately 15 mi above the surface of the Moon with its velocity υbo parallel to the surface of the Moon (i.e., at periapsis). It would then fly under the influence of the Moon’s gravity until reaching apoapsis A, at which point it would rendezvous with the CM. The radius of the Moon is 1079 mi, and its mass is 0.0123 times that of the Earth.

(a) Determine the required speed υbo at burnout P.

(b) What is the change in speed ΔvLM required of the LM at the rendezvous point A?

(c) Determine the time it takes the LM to travel from P to A.

(d) In terms of the angle θ, where should the CM be when the LM reaches P so that they can rendezvous at A?

Assume that the changes in speed are impulsive; that is, they occur instantaneously.

Figure P5.110