Question

Another nice physics question.

Answer 1

A space vehicle is approaching a planet with a speed \(v\) and is a long way out (treat it as infinity). The trajectory would miss the centre of the planet by distance \(R\) if it continued in a straight line. If the planet has a mass \(m\) and a distance \(r\), what is the smallest value of \(R\) in order that the resulting orbit will just miss the surface?

Answer 2

So I'll try using conservation of energy here probably.