Question

Define binding energy of a satellite. Obtain an expression for the binding energy of a satellite revolving around the earth at a certain altitude.

Answer 1

The minimum amount of energy required for a satellite to escape from earth's gravitational influence is called as Binding Energy of a satellite. r is a radius of orbit i.e. Radius of earth + height at which satellite is orbiting the earth

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

now, at equilibrium condition,

centripetal force = gravitational force

mV²/r = GMm/ r2

mV² = GMm/ r

½ mV² = GMm/ 2r

KE = GMm/ 2r

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

PE = - GMm/ r

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

TE = KE+PE

TE = GMm/ 2r + - GMm/ r

TE = - GMm/2r

E_r = - GMm/ r

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, so, the binding energy of a satellite revolving in a circular orbit around the earth is