Question

You will need to use the Momentum Principle to do the first part of this problem, and the Energy Principle to do the second part. A satellite of mass 4500 kg orbits the Earth in a circular orbit of radius of 9.3 106 m (this is above the Earth's atmosphere).The mass of the Earth is 6.0 1024 kg.
1. What is the speed of the satellite? (m/s)
2. What is the minimum amount of energy required to move the satellite from this orbit to a location very far away from the Earth?

Answer 1

Answer

given,

Mass of satellite, m = 4500 kg

Mass of the earth, M = 6 x 10²⁴ Kg

Earth circular orbit radius, R = 9.3 x 10⁶ m

a) To find the speed of the satellite

   we need to equate the gravitation force between earth and satellite with the centripetal force.

$\dfrac{GMm}{R^2}=\dfrac{mV^2}{R}$

$V = \sqrt{\dfrac{GM}{R}}$

$V = \sqrt{\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}}{9.3\times 10^6}}$

   V = 6559.89 m/s

b) Minimum amount of energy of satellite

    $E = \dfrac{GMm}{r}-\dfrac{1}{2}mv^2$

    $E =\dfrac{6.67\times 10^{-11}\times 6\times 10^{24}\times 4500}{9.3\times 10^6}}-\dfrac{1}{2}\times 4500\times 6559.89^2$

           E = 9.68 x 10¹⁰ J

Minimum amount of energy require to move satellite is equal to E = 9.68 x 10¹⁰ J