A large celebratory ride is being planned to open in the year 2100, on the 50th anniversary of establishing the Moon Colony. The ride will give the visitors an extended view of the Colony from the capsule while it soars in orbit overhead. One of the early sketches shows the cylindrical capsule in which the visitors will ride. The capsule leaves the platform, rolls without slipping down a slope, and enters a low altitude circular lunar orbit at the bottom. The eventual capture and return of the capsule is yet in the planning stages.
The exact mass distribution of the outer capsule is as yet a matter of design. For the following questions, assume the moment of inertia of the capsule is I = k. Ih.c, where k represents the relative distribution of mass and Ih.c is the moment of inertial for a hollow cylindrical shell.
a. Find a relationship for the minimum height H necessary to ensure that the speed of the capsule is sufficient to enter orbit once it reaches the surface. Your answer should only include the variables given above (i.e. R, d or K) or other universal constants.
b. The financiers of the new ride want the capsule to be a hollow cylindrical shell, such that the sides can remain open for a maximum viewing experience, Given your solution to part (a), why is this a problem?
