Specific Orbital Energy Calculator

Specific orbital energy (epsilon) is the total mechanical energy per unit mass of an orbiting body: the sum of its kinetic and potential energy per unit mass. For a bound elliptical orbit, epsilon = -GM/(2a), where G is the gravitational constant, M is the central body mass, and a is the semi-major axis of the orbit.

A negative total energy means the object is bound to the gravitational field and cannot escape. Zero energy means it is at the escape boundary (parabolic trajectory). Positive energy means it is on a hyperbolic escape trajectory. This parallels atomic orbital energy levels, which are also negative for bound electrons.

The vis-viva equation relates orbital speed v at any point in the orbit to the distance r from the central body: v² = GM(2/r - 1/a). At periapsis (closest approach) speed is highest; at apoapsis (farthest point) speed is lowest. Specific orbital energy epsilon = -GM/(2a) is constant throughout the orbit.

For a low Earth orbit (a = 6,571 km = 6.571 x 10^6 m) with GM = 3.986 x 10^14 m³/s², epsilon = -30.3 MJ/kg. For a geostationary orbit (a = 42,164 km), epsilon = -4.72 MJ/kg. The closer the orbit, the more negative (more tightly bound) the energy.

Specific orbital energy is conserved in Keplerian orbits (no drag or thrust). Knowing epsilon allows calculation of the semi-major axis for any orbit. Changing epsilon by firing a rocket changes the orbit. Delta-v calculations for orbital maneuvers (like Hohmann transfers) rely on this relationship.