Meteor Passing a Planet. Sample UC Berkeley Final question

[berzerkeley]

Homework Statement

A meteor is approaching a planet of mass M and radius R with speed while it is far away. If there were
no gravity, it would miss the center of the planet by a distance b. Gravity makes the meteor barely graze
the planets surface as it passes. Find in terms of other given quantities and gravitational constant G.

Homework Equations

Force of Gravity=GMm/r^2
Gravitational Potential Energy=-GMm/r

The Attempt at a Solution

I tried work and energy
I also tried an acceleration method
but I really have no idea

 

[ehild]

What is the question?

It is a good idea to use conservation of energy, but there is an other quantity conserved during planetary motion.

ehild