Question

A spacecraft moves in a circular orbit around the moon at a speed of 1200 m s^-1 . What is the mean distance above the surface the moon? Given the mass and radius of the moon are M 7.7 10²² kg and r 1.7 10⁶ m respectively and G 6.67 10¹¹ Nm²kg².

Answer 1

$$v=\sqrt{\frac{GM}{R+h}}\\ 1200=\sqrt{\frac{(6.67\cdot10^{-11})(7.7\cdot10^{22})}{1.7\cdot10^6+h}}\\h=1.9\cdot10^6\ m$$