Obtain an expression for total energy of a satellite revolving in circular orbit around a planet .

Explanation

Gravitational P.E. at a point above the surface of the earth at a distance r = R + h is given by P.E. = `(-GM m)/(r)` where 'M' is mass of the earth and m is the mass of the satellite .
kinetic energy of satellite = `(1)/(2) (GMm)/(r)`
Total energy of satellite = E = PE + KE
Hence E = `(-GMm)/(r) + (1)/(2) (GMm)/(r)`
i.e., `E = - (1)/(2) (GMm)/(r)`
The `-ve` sign indicates that the satellite is bounded to the earth .