Name: Gravitational Potential Energy
Uploaded: 2019-07-19
Duration: 9 min 10 s
Description: The energy possessed by a body because of its position in a gravitational field is known as Gravitational Potential Energy. Let’s learn about it in detail in...

Question

Explain the meaning of binding energy of a satellite and derive the formula.

Accepted Answer

Binding energy can be defined as the minimum energy recquired to be supplied to it order to free the satellite from the gravitational influnce of the planet.

Consider a satellite of mass $m_{s}$ revolving around a planet of mass $M_{p}$ with speed $V$ at a distance $r$ from the centre of the planet. The kinetic energy $K . E$ and potential energy $P . E$ is given by

$K . E . = \frac{1}{2} m_{s} V^{2} P . E = - \frac{{GM}_{p} m_{s}}{r}$

The satellite gets the necessary centripetal force from the gravitational force. That is

$\frac{m_{s} V^{2}}{r} = \frac{{GM}_{p} m_{s}}{r^{2}}$

$m_{s} V^{2} = \frac{{GM}_{p} m_{s}}{r^{}}$

Subsituting the value of ${v_{o}}^{2}$ in eqs. (2) we get

$K = \frac{1}{2} \frac{{GM}_{e}}{r}$

The total energy of the satellite is

$E = P . E + K . E = - \frac{{GM}_{e} m}{r} + \frac{1}{2} \frac{{GM}_{e} m}{r} E = - \frac{1}{2} \frac{{GM}_{e}}{r}$

We see the total energy of the satellite is negative, which is numerically same as the binding of the satellite towards the earth. The energy just equal and opposite sign is the binding energy of the satellite. So the binding energy of the satellite becomes $= \frac{1}{2} \frac{{GM}_{e}}{r}$

Explain the meaning of binding energy of a satellite and derive the formula.

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