Question

The space shuttle in a 300km high orbit wants to capture a smaller satellite for repairs. What are speeds of the shuttle and the satellite in this orbit?

Answer 1

To solve this, we must equate the centripetal force of the shuttle and satellite due to its circular orbit, with the force due to earths gravity. Thus \[F_{s}=F_{g}\] and hence \[\frac{m_{s}v^{2}}{r}=\frac{GM_{E}m_{s}}{r^2}\] where \(M_{E}\) is the mass of the Earth, \(m_{s}\) is the mass of the space shuttle or satellite, and \(r \) is the distance from the centre of the earth. \(G\)is the gravitational constant This then simplifies to \[v^{2}=\frac{GM_{E}}{r}\]since the mass of the shuttle/satellite cancels. This means that the mass of the orbiting object is not important in determining the speed of orbit, and that only the mass of the earth and height of orbit is important.