Hohmann Transfer Calculator

Calculate transfer velocities, burn delta-v, orbital periods, transfer time, eccentricity, and energy from central-body mass and orbital radii. Hohmann Transfer Calculator supports mission planners, astronomers, students, and spacecraft engineers analyzing efficient two-impulse orbital transfers.

Highlights

  • Calculate efficient two-impulse Hohmann transfers between circular orbits.
  • Determine initial and final orbital velocities with flexible unit conversions.
  • Find transfer-orbit eccentricity, semi-major axis, and spacecraft velocities.
  • Calculate burn delta-v requirements, including initial, final, and total delta-v.
  • Estimate transfer time, orbital periods, and specific orbital energy.

Table of Contents

  1. How Hohmann Transfer Calculator Works?
  2. Practical Use Cases
  3. Accuracy and Limitations
  4. Quick Examples
  5. Frequently Asked Questions (FAQs)
  6. Cite This Calculator

How Hohmann Transfer Calculator Works?

The Hohmann Transfer Calculator models an ideal two-impulse transfer between two circular, coplanar orbits around a central astronomical body. It uses the body's mass to determine the standard gravitational parameter, μ = GM, where G is the gravitational constant and M is the central body mass. The initial and final orbit radii are measured from the body's center.

μ=GM

For an outward transfer, the circular velocity at each orbit is found from the vis-viva relationship. The transfer ellipse has its periapsis at the initial orbit and its apoapsis at the final orbit.

vc=μr

The transfer semi-major axis and eccentricity are calculated from the two circular-orbit radii:

a=r1+r22,e=r2−r1r2+r1

Using the vis-viva equation, the spacecraft velocities at the transfer ellipse's periapsis and apoapsis are:

v=μ(2r−1a)

The first burn changes the initial circular velocity to the transfer periapsis velocity. The second burn changes the transfer apoapsis velocity to the final circular velocity. For an outward transfer, the burn magnitudes are:

Δv1=vp,t−vc,1,Δv2=vc,2−va,t

The total delta-v is the sum of the two burn magnitudes. Transfer time is half the period of the elliptical transfer orbit, while each circular-orbit period is calculated independently:

ttransfer=πa3μ,T=2πr3μ

Finally, the transfer orbit's specific orbital energy depends on its semi-major axis:

ε=−μ2a

OutputMeaning
Initial and final orbital velocityVelocity required for circular motion at each specified radius.
Transfer semi-major axis and eccentricitySize and shape of the elliptical transfer orbit.
Transfer periapsis and apoapsis velocitySpacecraft speed at the two ends of the transfer ellipse.
Initial, final, and total delta-vIdealized impulse requirements for the two burns.
Transfer time and orbital periodsTime of flight on the transfer ellipse and full periods of the circular orbits.
Specific orbital energyOrbital energy per unit spacecraft mass on the transfer ellipse.

For an inward transfer, the same orbital relationships apply, but the burn directions reverse; the calculator reports delta-v as impulse magnitudes.

Practical Use Cases

Mission planners can estimate the ideal departure burn, circularization burn, total delta-v, and time of flight when evaluating transfers between low and high circular orbits.

Astronomers can compare orbital-transfer requirements around different central bodies by entering the relevant body mass and orbital radii, then examining velocity, eccentricity, energy, and period outputs.

Students can use the calculator to connect the gravitational parameter, circular velocity, vis-viva equation, elliptical-orbit geometry, orbital period, and delta-v calculations in one worked model.

Spacecraft engineers can perform preliminary propulsion sizing and trajectory checks using the two-impulse idealization before applying higher-fidelity models that include finite burns, perturbations, and spacecraft-specific constraints.

Accuracy and Limitations

The calculator is accurate for the ideal two-body Hohmann-transfer equations when both input orbits are circular, coplanar, and centered on the same spherical central body, with burns treated as instantaneous impulses. It assumes the supplied central-body mass determines the entire gravitational field and excludes atmospheric drag, oblateness and other perturbations, third-body gravity, plane changes, finite-thrust gravity losses, launch-site effects, and propellant-mass changes. The transfer-time result is the time along exactly half of the ideal elliptical transfer orbit, and the delta-v values are theoretical impulse magnitudes rather than a complete mission budget. For a conventional outward transfer, the final radius should exceed the initial radius; reverse transfers require interpreting the burn directions accordingly.

Quick Examples

Example #1: Earth LEO to GEO

Models an efficient two-burn transfer from a low Earth orbit to geostationary orbit.

Example #2: Mars Parking Orbit to High Orbit

Analyzes a Hohmann transfer from a low Mars orbit to a higher operational orbit.

Example #3: Earth Orbit to Mars Orbit

Estimates transfer requirements for a spacecraft traveling from Earth's orbit to Mars's average solar orbit.

Frequently Asked Questions

A Hohmann transfer is a fuel-efficient two-burn maneuver that moves a spacecraft between two circular, coplanar orbits using an elliptical transfer orbit.

The first burn places the spacecraft onto the transfer ellipse, while the second burn changes its velocity to match the destination circular orbit.

The transfer takes half the period of the elliptical transfer orbit. For transfers between larger orbital radii, the travel time is generally longer.

The required delta-v depends mainly on the central body's mass and the initial and final orbital radii. Larger changes in orbital radius typically require more total delta-v.

Students, astronomers, mission planners, and spacecraft engineers use Hohmann transfers to study orbital mechanics and estimate efficient spacecraft maneuvers.

Cite This Calculator