# What is the momentum of the asteroid before the collision? What is the total momentum of the satellite-asteroid system before the collision? What is the speed of the asteroid-satellite system after the collision?

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A 1040 kg satellite is orbiting the Earth at a speed of 8250 m/s relative to the Earth at an altitude of 2100 km. A 500 kg asteroid flying at a speed of 12375 m/s is also orbiting the Earth at an altitude of 2100 km in the same direction as the satellite. The two objects collide and end up stuck together.

A 1040 kg satellite is orbiting the Earth at a speed of 8250 m/s relative to the Earth at an altitude of 2100 km. A 500 kg asteroid flying at a speed of 12375 m/s is also orbiting the Earth at an altitude of 2100 km in the same direction as the satellite. The two objects collide and end up stuck together.

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#### Explanation

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Momentum = mass * velocity. It is conserved, so the total momentum of the system will remain the same before and after the collision.

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Velocity has a direction, so the result will be different for bodies on the same trajectory or in opposite ones. In this case the momentum of each body will be additive to make up the system momentum.

The final system velocity will be the weighted average of the two bodies and their velocities.

M1 * V1 + M2 * V2 = System Momentum

System Velocity = System Momentum/System Mass

V_sys = (M1 * V1 + M2 * V2)/(M1 + M2)

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