Orbit Determination Calculator

Given only perigee and apogee altitude, this calculator reconstructs a satellite's full orbital geometry using two classical relations: the semi-major axis is simply the average of the perigee and apogee radii (measured from Earth's center, not the surface), and eccentricity falls out of their difference divided by their sum — 0 for a perfect circle, approaching 1 for a highly stretched ellipse. From the semi-major axis, Kepler's third law gives the orbital period directly, using Earth's gravitational parameter (GM = 398,600.44 km³/s²) with no dependence on the orbit's shape, only its size. Velocity at perigee and apogee comes from the vis-viva equation, which explains why an elliptical orbit's speed isn't constant: the spacecraft moves fastest at perigee (closest approach) and slowest at apogee (farthest point), trading kinetic for potential energy as it climbs and falls, while specific orbital energy stays constant and negative — confirming the orbit is gravitationally bound rather than escaping.

A key simplification here: the period calculation ignores J2 perturbation, the bulge in Earth's gravity from its oblateness that measurably shifts real orbital planes and nodal periods over time, so the reported nodal period is really just the two-body Keplerian period restated, not a true ground-track-repeat figure. For a circular orbit, set perigee and apogee altitude equal; leaving them different builds an elliptical orbit, and it's easy to accidentally enter an apogee lower than perigee — this calculator prevents that by clamping apogee altitude to never fall below the perigee value you entered.