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A satellite of mass M moves in a circular orbit of radius R about the Earth's centre. A meteorite of the same mass M, falling toward Earth, strikes the satellite and sticks to it (perfectly inelastic collision). Just before impact, the satellite and the meteorite have equal speeds. What is the subsequent motion of the combined body?

1. in a circular orbit of a different radius
2. in the same circular orbit of radius R
3. in an elliptical orbit
4. such that it escapes to infinity

Correct answer: in an elliptical orbit

Solution

Momentum conservation gives the combined body a velocity that is partly radial and reduced in magnitude. Its energy is still negative (bound) but it no longer satisfies the circular-orbit condition, so it follows an ellipse.

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