Delta-v budgets and Hohmann transfer orbits
How a two-burn transfer works, why delta-v is the currency of spaceflight, and where the Hohmann ideal stops matching reality.
Delta-v is the budget of a mission
Every manoeuvre in space costs a change in velocity, called delta-v, and a rocket carries only a fixed supply set by its fuel and engines. Planners add up the delta-v for each burn, from launch to insertion to station keeping, to build a budget the vehicle must fit inside. Because the rocket equation makes fuel grow exponentially with delta-v, saving even a few hundred metres per second can be the difference between a workable design and an impossible one. That is why the efficient Hohmann transfer sits at the heart of most trajectory planning.
The two burns of a Hohmann transfer
The manoeuvre uses an ellipse that is tangent to the starting orbit at one end and the target orbit at the other. The first burn adds speed to lift the low point of the orbit into that ellipse, then the craft coasts halfway around with the engines off. At the far side it is moving too slowly for the higher circular orbit, so a second burn adds the missing speed to circularise. This calculator reports each burn separately along with the total, because the two are rarely equal and the departure burn is often the larger one.
Reading the transfer time
The coast between burns is exactly half of one lap around the transfer ellipse, so the tool computes t = pi times the square root of a cubed over mu, where a is the average of the two radii. Short hops like low orbit to geostationary take hours, while an interplanetary Earth to Mars transfer stretches to roughly 259 days on the numbers here. That long coast is why launch windows matter: the destination has to be at the right point in its own orbit when the spacecraft arrives.
Where the ideal breaks down
A pure Hohmann transfer assumes both orbits share a plane, both are circular, the burns are instantaneous and only one body pulls on the craft. Real missions rarely get all of that. Changing orbital plane costs extra delta-v, real engines burn over minutes rather than instants, and near a planet you must account for its atmosphere and oblateness. For very large radius ratios a three-burn bi-elliptic transfer can even beat the Hohmann, so use this result as a clean baseline and layer the corrections your specific trajectory needs.