How this calculator works
A Hohmann transfer joins two circular, coplanar orbits with a half-ellipse and two instantaneous tangential burns. This model supports both inward and outward transfers. The reported burns are magnitudes, while the direction label distinguishes prograde from retrograde. Rocket-equation propellant assumes the same specific impulse at both burns and no staging. Plane changes, finite burn duration and launch-window phasing are excluded.
Formula
at = (r1+r2)/2; vt(r) = sqrt[mu(2/r-1/at)]; delta-v1 = |vt(r1)-sqrt(mu/r1)|; delta-v2 = |sqrt(mu/r2)-vt(r2)|; coast = pi sqrt(at³/mu). Propellant = m0[1-exp(-total delta-v/(g0 Isp))].
Worked example
For mu = 1 and circular radii 1 m and 3 m, transfer semi-major axis is 2 m and eccentricity is 0.5. Coast time is 8.885766 s and total burn magnitude is 0.393847 m/s.
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Frequently asked questions
Can the transfer go inward?
Yes. Both burns then reduce the velocity in the local prograde direction.
Does minimum delta-v always mean Hohmann?
No. Other constraints and large radius ratios can make other transfers preferable.
Are the radius inputs altitudes?
Choose the convention explicitly. Altitudes are increased by the supplied primary radius before calculation.