When does Phobos collide with Mars?

[PeroK]

Could you explain it with more details?

This thread is 70 posts long and you've made no progress. I'm sorry that I'm not able to help you.

 

[PMNIMG]

You said

I highly recommend using Kepler's third law. It gives you a quick way to get a good approximation. The answer will be the time to fall to the centre of a planet, and not to its surface. The difference should be small if the object falls from far enough away.

Please explain about this

 

[PeterDonis]

so, it is (b). About Phobos

In that case, every single post that has been made so far in this thread is irrelevant to your question. That includes all the posts you have asked people to explain. Kepler's Third Law is irrelevant. The free fall time from the altitude of Phobos is irrelevant. The equations you wrote in the OP are irrelevant.

The reason Phobos will eventually hit Mars as described in option b) is tidal effects. So you need to go find the relevant equations for tidal effects for a satellite like Phobos whose orbital period is less than the period of rotation of the planet it is orbiting. Once you do that, you can start a new homework help thread based on those equations.

In the meantime, this thread is closed.