Orbital Energy Calculator

About this calculator

The specific orbital energy (ε = −μ/2a) of a two-body orbit is the sum of kinetic and potential energy per unit mass, where μ is the standard gravitational parameter (GM) of the central body and a is the orbit's semi-major axis. Because ε depends only on a — not on eccentricity or where the orbiting body currently sits along its path — it stays constant throughout the orbit under the vis-viva relation, which is exactly what makes it useful: it's a conserved quantity you can check against at any point.

This calculator takes the central body's mass and the orbit's semi-major axis, computes μ, and returns the specific orbital energy, along with whether the orbit is bound (negative ε), parabolic (ε = 0) or hyperbolic (positive ε, an escape trajectory). Aerospace engineering students, mission planners sanity-checking transfer orbits, and astronomy enthusiasts modeling satellite or planetary motion use it to verify orbit classification and cross-check vis-viva calculations without deriving the energy equation from scratch each time.