Question

A 15,000 kg satellite is orbiting at 800 km above the Earth’s surface. What is the potential energy of the satellite?

Answer 1

Answer:

$-8.34\times 10^{11}\ \text{J}$

Explanation:

m = Mass of satellite = 15000 kg

h = Distance above Earth = 800 km

R = Radius of Earth = 6371 km

M = Mass of Earth = $5.972\times 10^{24}\ \text{kg}$

G = Gravitational constant = $6.674\times 10^{-11}\ \text{Nm}^2/\text{kg}^2$

Potential energy is given by

$U=-\dfrac{GMm}{R+h}\\\Rightarrow U=-\dfrac{6.674\times 10^{-11}\times 5.972\times 10^{24}\times 15000}{(6371+800)\times 10^3}\\\Rightarrow U=-8.34\times 10^{11}\ \text{J}$

The potential energy of the satellite is $-8.34\times 10^{11}\ \text{J}$.