Physics · Gravitation · NEET
Kinetic energy is always positive. KE = (1/2)mv^2 and both mass and v^2 are positive, so KE = +GMm/2r. Only the potential energy (PE = -GMm/r) and the total energy (E = -GMm/2r) are negative for a bound satellite. Never write KE with a minus sign.
We set PE = 0 at infinity. As the satellite is brought from infinity closer to Earth, gravity does positive work, so the stored PE becomes negative: PE = -GMm/r. Kinetic energy comes from actual motion, so it is always positive. This is why the total E = KE + PE ends up negative overall.
KE = +GMm/2r, PE = -GMm/r, E = -GMm/2r. Dividing by GMm/2r gives KE : PE : E = +1 : -2 : -1. Two quick facts follow: PE = -2 KE and E = -KE. NTA loves testing these relations, so memorise them.
Yes to both. E = -GMm/2r is directly proportional to satellite mass m and inversely proportional to orbit radius r. A heavier satellite has more negative energy; a satellite in a higher (larger r) orbit has less negative energy, meaning it is less tightly bound to Earth.
r is always the distance from the centre of the Earth, not the height above the surface. If a satellite orbits at height h, then r = R + h, where R is Earth's radius. A common exam mistake is putting r = h. Always convert height to r = R + h first.
A satellite of mass m orbits the earth (radius R) at height h. In terms of g0 (surface gravity), the total energy of the satellite is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
E = -GMm/2r, where G is the gravitational constant, M is Earth's mass, m is the satellite's mass, and r = R + h is the orbit radius from Earth's centre. Using GM = gR^2, it can also be written E = -mgR^2 / 2(R+h).
They are equal in size but opposite in sign: E = -KE. Since KE = GMm/2r and E = -GMm/2r, the total energy is exactly the negative of the kinetic energy. Also PE = 2E = -2KE.
E = -GMm/2r becomes less negative (closer to zero) as r increases. So a satellite in a higher orbit has greater (less negative) total energy and is more weakly bound. Raising a satellite to a higher orbit requires adding energy.
A negative total energy means the satellite is bound to Earth and cannot escape on its own. To free it (send it to infinity where E = 0), you must add energy equal to its binding energy, GMm/2r. This is covered in the next concept, why total energy is negative.
