Speed of the meteoroid as it passes close to earth

[mavid]

A meteoroid, heading for Earth, has speed 2.94 km/s as it crosses the Moon's orbit, but misses the Earth by 5000 km. What is its speed at its closest point?

No idea what equations to use at all (my physics prof. is crazy about planetary motion and such). Please, give me any suggestions that ou might have. Thank you in advance.

 

[nasu]

I would suggest conservation of energy. There is kinetic energy and gravitational potential energy of the asteroid-earth system.

 

[mavid]

I would suggest conservation of energy. There is kinetic energy and gravitational potential energy of the asteroid-earth system.

ok. I aasume then:
K+U= ?
We had not covered such type of problems in the class. I'd appreciate little bit more information about how I set equations in order to derive a correct answer.

 

[nasu]

I don't know what you mean by "this type of problem".
If you don;t know about mechanical energy is hard to believe that you are studying planetary motion.

Conservation of energy means that you write the expressions for total energy in two states of interest and then you equate these expressions.
For your problem, the two states can be
1. The meteoroid at a distance from Earth equal to the distance Earth-Moon.
2. The meteoroid at 5000 km from Earth.

Write the energies (kinetic and potential) for these two states and equate them.

 

[mavid]

I figured it out. Thank u for help. And the problem was selected by a professor since he is into planetary motion. We hadn't done anything like that in class, but he likes to "try" us :)