Hohmann Transfer Calculator
Find the delta-v for a Hohmann transfer between circular Earth orbits.
A Hohmann transfer is the most fuel-efficient two-burn path between circular orbits.
How the Math Works
The Hohmann Transfer Calculator computes delta-v using two velocity changes (burns) to move a spacecraft between circular orbits. The first burn accelerates the spacecraft into an elliptical transfer orbit, with its semi-major axis calculated as the average of the initial and target orbital radii. Using the vis-viva equation (v = √[μ(2/r - 1/a)]), we find the velocities at the initial orbit edge (r1) and the apogee of the transfer orbit (r2). The delta-v for the first burn is the difference between these velocities. The second burn circularizes the orbit at the target radius by matching its velocity to the new orbital speed. Total delta-v is the sum of both burns' magnitudes.
Practical Applications
To use this calculator, input the radii of your starting and target circular orbits (e.g., 6,678 km for low Earth orbit and 42,164 km for geostationary orbit). The tool will output the required delta-v for each burn and the total needed. This is critical for mission planning, as minimizing delta-v reduces fuel consumption, which directly impacts spacecraft mass and launch costs. Engineers use these calculations to design efficient trajectories for satellite deployments, interplanetary missions, or orbital maneuvers, ensuring optimal use of limited propulsion resources.
Day-to-Day Use
While you may not calculate orbital transfers daily, this math underpins the satellites that power your GPS, weather forecasts, and global communications. By optimizing fuel efficiency through Hohmann transfers, spacecraft can reach their destinations faster and carry more instruments or data. This means more accurate navigation apps, better weather warnings, and uninterrupted internet services. Without these calculations, satellites might fail to achieve proper orbits, leading to degraded performance or premature mission failure, affecting everything from emergency response to streaming entertainment.
Worked example
LEO (6771 km) to GEO (42164 km) → about 3935 m/s total.
FAQ
Is it always cheapest?
For coplanar circular orbits, yes — though slower than higher-energy transfers.