Question

A satellite orbits the earth in a circle of radius 6570km find the speed of the satellite and time taken to complete one revolution

Answer 1

a)

$$v=\sqrt{\dfrac{GM_E}{R}},$$ $$v=\sqrt{\dfrac{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot5.97\cdot10^{24}\ kg}{6.57\cdot10^6\ m}}=7785\ \dfrac{m}{s}.$$

b)

$$\dfrac{T^2}{R^3}=\dfrac{4\pi^2}{GM_E},$$ $$T=\sqrt{\dfrac{4\pi^2R^3}{GM_E}},$$ $$T=\sqrt{\dfrac{4\pi^2\cdot(6.57\cdot10^6\ m)^3}{6.67\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot5.97\cdot10^{24}\ kg}}=5302\ s\cdot\dfrac{1\ h}{3600\ s}=1.47\ h.$$