Question

A satellite orbits a planet at 9000 m/s at a distance r. The satellite moves to an orbit that is r/2. What is the new orbital speed of the satellite

Answer 1

$$v=\sqrt{\frac{GM}{r}}\\v'=\sqrt{\frac{2GM}{r}}=\sqrt{2}v\\v'=\sqrt{2}\cdot9000=12728\frac{m}{s}$$