Hohmann Transfer Calculator

Hohmann transfer calculator lets you find the best fuel-efficient transfers between two circular orbits.

Total delta-v3,856.58 m/stwo burns: 2,399.35 m/s to leave and 1,457.23 m/s to arrive

First burn2,399.35 m/sprograde, raising the far side

Second burn1,457.23 m/sprograde, circularising at the top

Transfer time5.289 hourshalf the period of the transfer ellipse — you arrive exactly opposite where you left

Transfer semi-major axis24,464 km

Starting circular speed7,672.6 m/s

Target circular speed3,074.92 m/sSLOWER than where you started — a higher orbit is a slower one, so raising your orbit costs energy while reducing your speed

Phase angle at departure100.428°how far ahead the target must be when you burn, so that it arrives when you do

Why two burns and not onea single burn cannot do itone burn changes the shape of an orbit but leaves it passing through the point where you burned — you always come back. Raising the other side takes a second burn at the far end

Synodic period2.1353 yearshow often the two line up again — 1/T_syn is the DIFFERENCE of the two orbital rates, which is why it is always longer than either period

Launch windows per decade4.683transfers can only start when the alignment comes round

The formula

Δv = √(GM/r₁)(√(2r₂/(r₁+r₂)) − 1); 1/T_syn = |1/T₁ − 1/T₂|

A higher orbit is a slower orbit

The most counter-intuitive fact in orbital mechanics is that raising your orbit leaves you moving more slowly. Geostationary orbit is travelled at about 3.07 km/s against the space station's 7.67 km/s, yet getting there costs nearly 4 km/s of delta-v. The energy goes into climbing the gravity well, and the higher orbit needs less speed to stay in it.

Why two burns

A single burn changes an orbit's shape but leaves it passing through the point where you burned — you always come back to it. Raising the far side takes one burn; making the new orbit circular takes a second at the far end. That is the Hohmann transfer, and for most ratios of radii it is the cheapest two-burn route there is.

Waiting for the window

Because you arrive exactly opposite where you left, the target has to be at the right place when you depart. That alignment recurs at the synodic period, whose reciprocal is the DIFFERENCE of the two orbital rates — which is why it is always longer than either period, and why Mars launch windows come round only about every 26 months.