Question

A satellite is projected near the surface of Earth so that it has a certain speed that can orbit the Earth. Calculate the speed of the satellite and the time for 1 complete rotation around the Earth. (Given, ME = 6 x 1024 kg, RE = 6.38 x 106 m, G = 6.67 x 10-11 Nm2kg-2)

Answer 1

(i) the speed of the satellite

$$v=\sqrt{G\frac{M_E}{r_E}}\\ =\sqrt{6.67*10^{-11}*\frac{6*10^{24}}{6.38*10^6}}=7920\;\rm m/s$$

(ii) the period of rotation

$$T=\frac{2\pi r_E}{v}\\ =\frac{6.28*6.38*10^6}{7920}=5059\:\rm s=84\: min$$