Physics · Gravitation · NEET
Binding energy is always POSITIVE. It is the energy you must ADD to the satellite to just free it. The total energy of the orbiting satellite is negative (E = -GMm/2r), and binding energy is the magnitude of that negative energy: BE = -E = +GMm/2r. A negative total energy is the sign that the satellite is bound; the positive binding energy is how much you pay to unbind it.
They are equal in size but opposite in sign. Total energy E = -GMm/2r (negative, tells you the satellite is trapped). Binding energy = |E| = +GMm/2r (positive, the energy needed to escape to infinity with zero final speed). In one line: Binding Energy = -(Total Energy). If a question gives you total energy as -X, the binding energy is +X.
Yes, numerically. For a circular orbit, KE = +GMm/2r and total energy E = -GMm/2r, so binding energy = |E| = GMm/2r = KE. So the binding energy of an orbiting satellite exactly equals its kinetic energy in orbit. But be careful: this equality holds only in circular orbit; it does not mean binding energy and KE are the same concept.
GMm/r is the potential energy magnitude at radius r (that would be the binding energy for a body sitting at rest at r). But a satellite is already MOVING with orbital kinetic energy KE = +GMm/2r. That orbital motion already supplies half the energy needed to escape. So you only need to add the remaining GMm/2r. Total energy = KE + PE = GMm/2r + (-GMm/r) = -GMm/2r, giving binding energy GMm/2r.
Use GM = gR^2, where g is surface gravity and R is Earth's radius. Substitute into BE = GMm/2r to get BE = mgR^2/2r. For a satellite at height h, r = R + h, so BE = mgR^2 / [2(R+h)]. For a satellite skimming the surface (h = 0, r = R), this simplifies to BE = mgR/2.
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.
It is the minimum extra energy needed to remove the satellite from its orbit and take it to infinity with zero speed. BE = GMm/2r = |total energy|.
Put r = R (Earth's radius): BE = GMm/2R = mgR/2, since GM = gR^2. This is the smallest orbit, so it needs the most binding energy per unit total energy compared to higher orbits.
BE = GMm/2r decreases as r increases. A satellite in a higher orbit is more loosely bound, so less extra energy is needed to free it. As r tends to infinity, binding energy tends to zero.
For an orbiting satellite, binding energy IS the energy to escape from that orbit: BE = GMm/2r. But 'escape energy from the surface' is different (GMm/R for a body at rest on the surface). Always check whether the body is orbiting or at rest.
Negative total energy means the satellite does not have enough energy to reach infinity (where PE = 0, KE >= 0, so E >= 0). Being short of that zero by GMm/2r is exactly the binding energy you must supply.
