Orbit & Hohmann Transfer Calculator

Three two-body calculations in one place. For an orbit given by its periapsis and apoapsis altitudes it returns the semi-major axis, eccentricity, period, the speeds at periapsis and apoapsis, the escape speed at periapsis, the specific orbital energy and the angular momentum. For a Hohmann transfer between two circular orbits it gives each of the two burns, the total Δv, the transfer time and the transfer ellipse, plus the phase angle the target must lead by at departure for a rendezvous. And from a period it finds the circular orbit that has it — a sidereal day of 23 h 56 min 4.09 s puts a satellite at the familiar geostationary altitude of 35,786 km. The Earth, Moon, Mars, Venus, Jupiter and Sun come with standard gravitational parameters (IERS for the Earth, JPL DE440 for the rest); any other body can be entered as its μ and radius. The closed forms are checked by numerically integrating the equations of motion, which reproduces the periods, speeds and transfer times to a part in a hundred million. What the model leaves out is as important: it is the ideal two-body problem, with no atmospheric drag, no J2 oblateness (which precesses real Earth orbits by degrees per day), no third-body pull and instantaneous burns — so it is the textbook answer and a good first estimate, not a mission plan. A Hohmann transfer is the cheapest two-burn option only when the orbits' radius ratio is below about 11.94; beyond that a bi-elliptic transfer can use less Δv.