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Depending on their relative masses and velocities, the path of the smaller will be a circle, or more likely, an ellipse.

An old model for this is to consider a canon mounted at the top of the globe.

Firing a shell at moderate velocities, it will fall to Earth quite soon.

At a much higher velocity it will have sufficient energy to make a circle round the globe.

At higher velocities again, it will form an ellipse.

Eventually we reach escape velocity, where the shell just continues on a giant ellipse - really, an escape.

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