Aviation Calcs

Hohmann transfer

Hohmann Transfer Calculator

The two-impulse Hohmann transfer between coplanar circular orbits: a burn into a transfer ellipse that is tangent at both ends, then a second burn to circularize. The page reports each delta-v, the total, the transfer time of flight, and the ellipse’s periapsis and apoapsis speeds. Earth is the default body. A 300 km LEO to GEO transfer is about 3.9 km/s.

Earth radius

Choose “GEO” to use the circular radius whose period is one sidereal day (about 42,164 km). The first and second orbits can be in either order — an inward transfer has the same total |Δv|.

Total Δv

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The Hohmann transfer

Walter Hohmann’s 1925 coplanar transfer uses an ellipse that is tangent to two circular orbits of radii r1 and r2. The semi-major axis of the transfer is at = (r1 + r2)/2. The two impulsive burns are the differences between the circular speeds and the vis-viva speeds on the ellipse at each tangency:

vc = √(μ/r),   v = √(μ (2/r − 1/at))
Δv1 = |v(r1) − vc(r1)|,   Δv2 = |vc(r2) − v(r2)|

Time of flight is half the transfer period: t = π √(at³ / μ).

LEO to GEO, about 3.9 km/s

From a 300 km circular orbit about the WGS-84 equator to a geosynchronous circular orbit (period = one sidereal day), the ideal two-burn total is about 3.9 km/s. A 200 km starting orbit is a little more; a 400 km starting orbit is a little less. This is the classic first estimate before plane-change and finite-burn penalties are added.

Sources

Hohmann (1925); Vallado, Fundamentals of Astrodynamics and Applications; Curtis, Orbital Mechanics for Engineering Students; Bate, Mueller and White, Fundamentals of Astrodynamics. Circular speeds themselves are on the orbital velocity calculator.

Frequently asked questions

Why is LEO-to-GEO quoted as about 3.9 km/s?

That is the ideal two-impulse Hohmann total from a low circular Earth orbit (a few hundred kilometres) to a geosynchronous circular orbit, using Earth’s μ. It is not a launch-from-the-ground figure, and it does not include inclination change.

Does the order of the orbits matter?

The total of the absolute values of the two burns is the same going out or coming in. Each burn simply changes sign.

Is a Hohmann always the cheapest two-burn transfer?

Among impulsive coplanar transfers between circular orbits, yes, when the radius ratio is not extreme. For very large ratios, a bi-elliptic transfer can use less delta-v, at the cost of a much longer time of flight.