Physics
posted by Dan on .
Speed of Asteroids With the same Radius?
Two spherical asteroids have the same radius R . Asteroid 1 has mass M and asteroid 2 has mass 2M. The two asteroids are released from rest with distance 10R between their centers. What is the speed of each asteroid just before they collide?
Hint: You will need to use two conservation laws.
Enter your answers separated by a comma. Express your answers in terms of the variables M, R, and appropriate constants.

momentum is conserved.
0=Mv+2M*V
or v of the smaller=2V of larger
conservation of energy
PE=final KE
GM*2M/R^2= 1/2 Mv^2+ 1/2 (2M)V^2
2GM^2/R^2=1/2 M (4V^2 + V^2)
4GM/R^2=5V^2 that leads to the speed of the larger, and the speed of the smaller is twice that. 
What is the gravitational force between two identical 5000kg asteroids whose centers of mass are separated by 100 m?