Physics · Gravitation · NEET
No. Escape energy sends the satellite to infinity with zero speed, so its final total energy is 0. Launch-into-orbit energy leaves the satellite in a bound orbit, so its final total energy is still negative (−GMm/2r). Launching into an orbit always needs less energy than fully escaping, because you do not have to climb all the way to zero energy.
The satellite is not starting from rest at infinity — it starts sitting on Earth's surface, where it already has potential energy −GMm/R. Minimum energy is only the extra amount you must add. So E_needed = E_final − E_initial = E_orbit − E_surface. Subtracting a negative number makes the result larger and positive, which is correct.
In the standard NEET model we ignore Earth's rotation, so the satellite on the surface is treated as at rest with kinetic energy = 0. Its total energy on the surface is just its potential energy, E_surface = −GMm/R. This keeps the calculation clean and is what the 2024 NEET question expects.
Altitude means height above the surface. If altitude = 2R, the orbit radius from Earth's centre is r = R + 2R = 3R. Then E_orbit = −GMm/(2 × 3R) = −GMm/6R and E_surface = −GMm/R, so E_needed = −GMm/6R − (−GMm/R) = 5GMm/6R. This is the exact NEET 2024 answer.
Binding energy is the energy needed to remove an already-orbiting satellite from its orbit to infinity: it equals +GMm/2r. Launch energy starts from the ground, not from orbit. So launch energy = binding-energy step plus the extra energy to first lift the satellite off the surface into the orbit.
The minimum energy required to launch a satellite of mass m from the surface of the earth (mass M, radius R) into a circular orbit at an altitude 2R from the surface is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
E_needed = E_orbit − E_surface = (−GMm/2r) − (−GMm/R) = GMm/R − GMm/2r, where R is Earth's radius and r is the orbit radius from Earth's centre. Always add the altitude to R to get r.
Put r = R: E_needed = GMm/R − GMm/2R = GMm/2R. So the minimum energy to just place a satellite in a low orbit near the surface is GMm/2R, which equals the orbital kinetic energy there.
E_orbit and E_surface are both negative, but E_orbit (a smaller negative, closer to zero) is larger than E_surface. So E_orbit − E_surface is positive. A positive value makes sense because you must supply energy to lift and speed up the satellite.
No. For NEET the satellite is taken as at rest on the surface (KE = 0). Earth's spin gives a small real-world boost but is ignored in the standard formula, so E_surface = −GMm/R.
Escape energy from the surface is GMm/R (final energy = 0). Launch-into-orbit energy is always less than this, because the satellite ends in a bound orbit with negative energy, not at infinity.
