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

now, at equilibrium condition,
centripetal force = gravitational force

`"mv"^2/"r" = "GMm"/"r"^2`

or `"mv"^2 = "GMm"/"r"`

or, `1/2 "mv"^2 = "GM"/"2r"`

or K.E. = `"GMm"/"2r"`     ....(1)

now , potential energy between satellite and the earth is given by 

P.E. = -`"GMm"/"r"`

[here negative sign indicates force acts between satellite and earth is attractive]

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

or, T.E = -`"GMm"/"r" + "GMm"/"2r"`

or, T.E = `-"GMm"/"2r"`

or E_r = `-"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 = `"GMm"/"2r"`