Hohmann Transfer Calculator
Calculate delta-v requirements for a Hohmann transfer orbit between two circular orbits. Enter values for instant results with step-by-step formulas.
Formula
delta-v_total = |v_periapsis - v1| + |v2 - v_apoapsis|
Where v1 and v2 are circular orbit velocities at r1 and r2, v_periapsis and v_apoapsis are velocities on the transfer ellipse at closest and farthest points, computed using the vis-viva equation: v = sqrt(mu * (2/r - 1/a)).
Worked Examples
Example 1: LEO to Geostationary Orbit
Problem: Calculate the delta-v for a Hohmann transfer from a 300 km LEO (r = 6,678 km) to geostationary orbit (r = 42,164 km) around Earth (mu = 398,600 km^3/s^2).
Solution: v1 = sqrt(398600/6678) = 7.726 km/s\nv2 = sqrt(398600/42164) = 3.075 km/s\na_transfer = (6678+42164)/2 = 24421 km\nv_periapsis = sqrt(398600*(2/6678-1/24421)) = 10.252 km/s\nv_apoapsis = sqrt(398600*(2/42164-1/24421)) = 1.621 km/s\ndV1 = 10.252-7.726 = 2.526 km/s\ndV2 = 3.075-1.621 = 1.454 km/s\nTotal = 3.980 km/s
Result: Total delta-v: 3.980 km/s | Transfer time: ~5.3 hours
Example 2: Earth to Mars Hohmann Transfer
Problem: Calculate the heliocentric Hohmann transfer from Earth orbit (r = 149,598,023 km) to Mars orbit (r = 227,939,366 km) with Sun mu = 1.327e11 km^3/s^2.
Solution: v_Earth = sqrt(1.327e11/149598023) = 29.78 km/s\nv_Mars = sqrt(1.327e11/227939366) = 24.13 km/s\na_transfer = (149598023+227939366)/2 = 188768694.5 km\nv_departure = sqrt(mu*(2/r1-1/a)) = 32.73 km/s\nv_arrival = sqrt(mu*(2/r2-1/a)) = 21.48 km/s\ndV1 = 32.73-29.78 = 2.95 km/s\ndV2 = 24.13-21.48 = 2.65 km/s
Result: Total delta-v: ~5.60 km/s | Transfer time: ~259 days
Frequently Asked Questions
What is a Hohmann transfer orbit and why is it important?
A Hohmann transfer orbit is the most fuel-efficient two-impulse maneuver to move a spacecraft between two circular orbits in the same plane. Named after Walter Hohmann who proposed it in 1925, this transfer uses an elliptical orbit that is tangent to both the inner and outer circular orbits. The spacecraft fires its engines at periapsis to enter the transfer ellipse and again at apoapsis to circularize into the target orbit. While it requires the least delta-v of any two-burn transfer, it takes the longest time. This trade-off between fuel efficiency and transfer time makes it fundamental to mission planning for satellite deployment, interplanetary travel, and orbital rendezvous.
What does delta-v mean and how is it calculated for a Hohmann transfer?
Delta-v (change in velocity) is the key metric for orbital maneuvers, representing how much a spacecraft must change its velocity to perform a specific maneuver. For a Hohmann transfer, two delta-v burns are needed. The first burn at periapsis accelerates the spacecraft from its circular orbit velocity to the transfer ellipse velocity. The second burn at apoapsis accelerates it from the ellipse velocity to the target circular orbit velocity. The total delta-v is the sum of both burns. Delta-v directly determines fuel requirements through the Tsiolkovsky rocket equation, making it the primary measure of maneuver cost in astrodynamics. Lower delta-v means less fuel needed.
How long does a Hohmann transfer take compared to other methods?
A Hohmann transfer takes exactly half the orbital period of the transfer ellipse, calculated as pi times the square root of the semi-major axis cubed divided by the gravitational parameter. For a LEO to GEO transfer, this is approximately 5.3 hours. For an Earth-to-Mars heliocentric transfer, it takes about 259 days. While the Hohmann transfer is the slowest two-burn option, it uses the minimum delta-v. Faster alternatives include bi-elliptic transfers for very large orbit ratio changes, and direct high-energy transfers that trade fuel for speed. Spacecraft with continuous low-thrust propulsion like ion engines use spiral trajectories instead.
When is a bi-elliptic transfer more efficient than a Hohmann transfer?
A bi-elliptic transfer becomes more fuel-efficient than a Hohmann transfer when the ratio of the outer orbit radius to the inner orbit radius exceeds approximately 11.94. In a bi-elliptic transfer, the spacecraft first enters a highly elliptical orbit that goes far beyond the target orbit, then performs a second burn at apoapsis to adjust, and a third burn to circularize at the target orbit. Despite requiring three burns and taking much longer, the total delta-v can be less than the Hohmann two-burn approach for large orbit ratio changes. This scenario is relatively rare in practical applications but important for theoretical understanding of orbital mechanics optimization.
Can Hohmann transfers be used for interplanetary travel?
Yes, Hohmann transfers are the foundational concept for interplanetary mission planning. For travel between planets, the two circular orbits represent the planetary orbits around the Sun, and the gravitational parameter is that of the Sun. The transfer ellipse connects the departure planet orbit to the arrival planet orbit. Real interplanetary missions use patched conic approximations that combine the Hohmann heliocentric transfer with hyperbolic escape and capture trajectories at each planet. Launch windows for Hohmann transfers occur at specific intervals called synodic periods when the planets are properly aligned. Most Mars missions use near-Hohmann trajectories, though gravity assists can reduce fuel requirements further.
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