Orbit of Jupiter's Moon

[magnusen]

Hello,

 

I do not understand how to solve the following problem. Help is greatly appreciated!

 

From Earth, we see the orbit of Jupiter's largest moon, Ganymede, almost edge-on. At some point an observer would see it disappear behind Jupiter (enter Jupiter's shadow) and at some later time re-emerge on the other side of Jupiter. How long does it take for Ganymede to enter (or re-emerge from) Jupiter's shadow? Assume that the shadow has a sharp edge. (Hint: draw a picture of Jupiter showing Ganymede in orbit around it. Use a perspective in which the orbit is seen "edge on." How long does it tale Ganymede to completely disappear from view as it moves behind Jupiter, or equivalently, how long does it take to completely reappear as it emerges on the other side? The period of Ganymede is P = 7.155 days. Its diameter is D = 5262 km. The radius of its orbit is R = 1,070,000 km. Given that it travels a distance C = 2 pi R, in a time P, how long does it take to travel a distance D, equal to its diameter? That will be the time it takes to move completely into (or out of) Jupiter's shadow.)

Edited November 20, 2011 by magnusen

[swansont]

Can you draw a picture of what is happening?

[Janus]

For Ganymede to complete its orbit behind Jupiter it takes; deleted.

 

It is extremely poor netiquette to just give the answer to someone asking for help with what appears to be a homework question; The idea is to help them solve the problem for themselves, not just do it for them.

 

It is even worse netiquette to give them the wrong answer.

Edited November 20, 2011 by swansont
deleted answer in quote