Question

Define binding energy and obtain an expression for binding energy of a satellite revolving in a circular orbit round the earth.

Answer 1

Let mass of satellite is m and r is the radius of the circular orbit. satellite moves in circumference of circular orbit around the earth.

now, at equilibrium condition,
centripetal force = gravitational force
$\frac{mv^2}{r}=\frac{GMm}{r^2}$

or, $mv^2=\frac{GMm}{r}$

or, $\frac{1}{2}mv^2=\frac{GM}{2r}$

or, $K.E=\frac{GM}{2r}$.......(1)

now , potential energy between satellite and the earth is given by $P.E=-\frac{GMm}{r}$
[ here negative sign indicates force acts between satellite and earth is attractive]

so, $T.E=P.E+K.E$

or, $T.E=\frac{-GMm}{r}+\frac{GMm}{2r}$

or, $T.E=-\frac{GMm}{2r}$

or, $E_r=-\frac{GMm}{2r}$
here negative sign indicates that the satellite is bound to the earth by attractive force and cannot leave it on its own. To move the satellite to infinity , we have to supply energy from outside to satellite - planet system.
so, binding energy of a satellite revolving in a circular orbit round the earth is $E=\frac{GMm}{2r}$

Answer 2

Explanation:

the bonding energy are obtained for the satellite revolving in the circulation orbit around the earth its known as binding energy