Question

A satellite orbits Earth 5.00x102 km above its surface. What is its period? The radius of Earth is 6.38x106 m and Earth has a mass of 5.97x1024 kg. Assume (G = 6.67x10-11 N•m2/kg2). a. 94.6 h or 340560 s b. 1.43 h or 5148 s c. 1.58 h or 5682 s d. 15.7 h or 56520 s

Answer 1

Given:

The radius of the orbit is,

$\begin{gathered} r=5.00\times10^2\operatorname{km} \\ =5.00\times10^5m \end{gathered}$

The radius of the Earth is,

$R=6.38\times10^6m$

The mass of the Earth is,

$M=5.97\times10^{24}\operatorname{kg}$

The gravitational constant is,

$G=6.67\times10^{-11}N.m^{2^{}}.kg^{-2}$

The time period of the satellite is,

$\begin{gathered} T=2\pi\sqrt[]{\frac{(R+h)^3}{GM}} \\ =2\pi\sqrt[]{\frac{(5.00\times10^5+6.38\times10^6)^3}{6.67\times10^{-11}\times5.97\times10^{24}}} \\ =5682\text{ s} \\ =1.58\text{ h} \end{gathered}$

Hence the option c is correct.