Physics · Gravitation · NEET
Speed only gives kinetic energy, which is always positive: KE = +GMm/2r. But the satellite also sits deep inside Earth's gravity well, so its potential energy is negative: PE = -GMm/r. The negative PE is bigger in size than the positive KE, so when you add them (E = KE + PE = -GMm/2r), the total comes out negative. A positive speed does not force the total energy to be positive.
No. Negative total energy means the satellite is bound to Earth - it cannot escape to infinity, but it stays in a stable circular orbit at fixed radius r. Falling down would need it to lose energy (become even more negative). A steady orbit keeps E constant at -GMm/2r. Negative energy is about being trapped, not about crashing.
Energy is negative only because of the chosen zero level. In gravitation we set PE = 0 at infinity (very far away). Any point closer than infinity then has negative PE. Since the satellite is at a finite distance r, its PE is negative, and this makes the total energy negative. It is a comparison to the escape point, not a strange physical quantity.
For a circular orbit, gravity supplies the centripetal force: GMm/r^2 = mv^2/r, so mv^2 = GMm/r. Then KE = 1/2 mv^2 = +GMm/2r and PE = -GMm/r. Comparing sizes, |PE| = 2 x KE. This is called the virial relation for a 1/r force. It is why E = KE + PE = GMm/2r - GMm/r = -GMm/2r.
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 M is Earth's mass, m the satellite mass and r the orbit radius (r = R + h). It equals half the potential energy and the negative of the kinetic energy: E = PE/2 = -KE.
Yes. Any object in a closed (bound) orbit around Earth has negative total energy. Zero total energy means it just barely escapes to infinity, and positive total energy means it flies away as a free body. Negative means trapped in orbit.
KE = +GMm/2r, PE = -GMm/r, and E = KE + PE = -GMm/2r. So PE = -2 KE and E = -KE. In size, PE is twice KE and total energy equals KE but with a minus sign.
NEET repeatedly tests the sign and the formula E = -GMm/2r (for example NEET 2016). Students lose easy marks by taking PE as positive. Knowing E = -KE = PE/2 lets you answer orbit-energy and binding-energy questions in seconds.
