Hohmann Transfer Calculator

A Hohmann transfer is a two-impulse maneuver between two circular, coplanar orbits around the same central body. The spacecraft first enters an elliptical transfer orbit tangent to the initial circle. After coasting for half of that ellipse, it performs a second burn at the opposite apsis to match the destination circle. Under the ideal two-body assumptions, this method is usually the lowest-delta-v two-burn transfer when the orbital radius ratio is not extremely large. The calculator treats the entered values as radii measured from the center of the attracting body, not altitudes above its surface. It multiplies central-body mass by the gravitational constant to obtain the standard gravitational parameter. Circular speed at each radius is the square root of that parameter divided by radius. The transfer ellipse has a semimajor axis equal to the average of the two circular radii. The vis-viva equation gives transfer-orbit speed at periapsis and apoapsis. For an outward transfer, the first prograde burn increases speed from the inner circular speed to transfer periapsis speed. The second prograde burn raises transfer apoapsis speed to the outer circular speed. Their differences are the two ideal delta-v values displayed, and their sum is the ideal mission total. Transfer time is half the ellipse period, calculated as pi times the square root of semimajor axis cubed divided by the gravitational parameter. This ideal result excludes many operational requirements. Real burns take time, propulsion systems lose performance, orbital planes may differ, gravity from other bodies perturbs the path, and launch windows constrain departure geometry. Transfers between planets are more accurately modeled with heliocentric departure and arrival velocities connected to planet-centered escape and capture trajectories. A direct Earth-to-Moon example is similarly simplified because the Moon's moving gravity field is not represented by a single Earth-centered circular destination. Use consistent center-to-center radii and a mass appropriate to the central body. Delta-v describes velocity change, not propellant directly; convert it to propellant with the rocket equation and an engine-specific exhaust velocity or specific impulse. Reserve margins for navigation correction, finite-burn loss, attitude control, station keeping, and uncertainty. Mission-critical trajectory planning requires high-fidelity ephemerides, numerical propagation, launch-window analysis, and professional flight-dynamics review rather than this idealized estimate.