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A satellite of mass 5M is in a circular orbit around the Earth. At a point in its orbit it suddenly splits into two parts: a piece of mass M and a piece of mass 4M. The mass M continues along the same circular orbit but moving in the opposite direction (same speed, reversed). What is the nature of the orbit of the 4M piece immediately after the explosion?

1. In a circular orbit
2. unbound
3. elliptical orbit
4. data is insufficient to determine the nature of the orbit.

Correct answer: unbound

Solution

Momentum conservation fixes the 4M fragment's speed at 1.5v. The escape speed at the orbit radius is sqrt(2)*v approx 1.414v. Since 1.5v exceeds the escape speed, the fragment has positive total energy and is unbound (escapes on a hyperbolic trajectory).

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