Question

A satellite of mass 500 kg moves around the earth in a circular orbit with speed 30 ms–1, the PE
of the satellite in its orbit is

Answer 1

Given that,

Mass of a satellite, m = 500 kg

Speed of satellite in a circular orbit, v = 30 m/s

To find,

The potential energy of the satellite in its orbit.

Solution,

The sum of kinetic and potential energy equals total energy. So,

$TE=\dfrac{GmM}{r}+\dfrac{1}{2}mv^2$

We know that, $PE=\dfrac{GmM}{r}$

Also, $v=\sqrt{\dfrac{GM}{r}}$

So,

$PE=mv^2$

Put the values of m and v in above formula we get,

$PE=500\times (30)^2\\\\PE=450000\ J\\\\PE=450\ kJ$

So, the potential energy of the satellite in its orbit is 450 kJ.