Q.Derive an expression for energy of a satellite.

A satellite's total mechanical energy is the sum of its kinetic energy and its gravitational potential energy, and for any bound orbit this sum always works out to be negative -- the mathematical fingerprint of being permanently bound to the central body.

Derivation. For a satellite of mass $M_s$ at height $h$ (orbital radius $R_e+h$), the potential energy is $U=-\dfrac{GM_sM_e}{R_e+h}$, and using the orbital speed $v=\sqrt{GM_e/(R_e+h)}$, the kinetic energy is

Notice that the kinetic energy is exactly half the magnitude of the potential energy -- so $K.E.<|U|$, i.e. kinetic energy is always less than the (magnitude of the) potential energy for a circular orbit. Adding them gives the total energy

$E=K.E.+U=\frac12\frac{GM_sM_e}{R_e+h}-\frac{GM_sM_e}{R_e+h}=-\frac12\frac{GM_sM_e}{R_e+h}.$ …