Lesson 10 of 11 · 6 min
Energy of an orbiting satellite
NCERT §7.10
Kavya reads that a 200 kg weather satellite at 400 km has negative total energy. How can a moving machine, with plenty of kinetic energy, have less than zero energy in total?
The lesson in notes
In short
In a circular orbit of radius r = R_E + h, kinetic energy K = G M_E m / 2r (positive).
Potential energy, with zero at infinity, is U = −G M_E m / r: negative and twice the kinetic energy in size.
Total energy E = K + U = −G M_E m / 2r, negative, and equal to −K.
Negative total energy means the satellite is bound: it cannot reach infinity. Zero or positive total energy would mean escape.
In an elliptical orbit K and U change from point to point, but the total energy stays constant and negative.
Moving a 400 kg satellite from orbit radius 2R_E to 4R_E needs ΔE = G M_E m / 8R_E = m g R_E / 8 ≈ 3.13 × 10⁹ J. Its kinetic energy falls by 3.13 × 10⁹ J and its potential energy rises by 6.25 × 10⁹ J.
To send an orbiting satellite out of the earth's influence you must supply only G M_E m / 2r, which is less than for a body at rest at the same height.