# Physics

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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.

• Physics -

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.

• Physics -

What is the gravitational force between two identical 5000kg asteroids whose centers of mass are separated by 100 m?

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