What is a Hohmann transfer?

A Hohmann transfer is an elliptical orbit used to move a spacecraft between two circular orbits in the same plane. It uses two engine burns: one to raise the orbit's apogee to the target orbit and another to circularize at the target. It is the most fuel-efficient transfer for coplanar circular orbits when the ratio of radii is less than about 11.94.

What is the gravitational parameter (μ)?

The gravitational parameter (μ) is the product of the gravitational constant (G) and the mass of the central body (M). For Earth, μ ≈ 398,600 km³/s². You must enter the correct μ for the central body you are orbiting, as it directly affects the calculated velocities and transfer time.

Physics

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Hohmann Transfer Calculator.

Calculate the ideal two-burn delta-v and transfer time between two coplanar circular orbits.

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02 / ANSWER

Ideal two-body Hohmann transfer: both orbits are coplanar and circular, burns are impulsive, and μ = G×M is supplied by you. No atmosphere, inclination change, or perturbation is modeled.

Gravitational parameter μ

Initial circular-orbit radius

Target circular-orbit radius

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FAQs

What assumptions does the Hohmann transfer calculator use?

It models a coplanar two-body transfer between circular orbits with impulsive burns. You enter the gravitational parameter, and atmospheric drag, inclination changes, and perturbations are excluded.

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Cite this calculator

Canonical URL: https://mathify.one/en/physics/hohmann-transfer

Cite as: Mathify. (n.d.). Hohmann Transfer Calculator. https://mathify.one/en/physics/hohmann-transfer

Use Cases

Educational tool for astrodynamics

Understand the mechanics of Hohmann transfers by experimenting with different orbit radii and gravitational parameters. See how delta-v and transfer time change with orbit size.

Example: Compare transfers around Earth vs. Mars by changing μ.

Frequently Asked Questions

What is a Hohmann transfer?: A Hohmann transfer is an elliptical orbit used to move a spacecraft between two circular orbits in the same plane. It uses two engine burns: one to raise the orbit's apogee to the target orbit and another to circularize at the target. It is the most fuel-efficient transfer for coplanar circular orbits when the ratio of radii is less than about 11.94.
What is the gravitational parameter (μ)?: The gravitational parameter (μ) is the product of the gravitational constant (G) and the mass of the central body (M). For Earth, μ ≈ 398,600 km³/s². You must enter the correct μ for the central body you are orbiting, as it directly affects the calculated velocities and transfer time.

Tips & Common Mistakes

Tips

Ensure you use consistent units for radius and gravitational parameter. For example, if radii are in kilometers, use μ in km³/s².
The transfer time is half the period of the elliptical transfer orbit. The calculator computes this using the semi-major axis of the transfer ellipse.
For large radius ratios (greater than about 11.94), a bi-elliptic transfer may be more efficient, but this calculator only handles the standard Hohmann transfer.
Remember that the delta-v values are ideal and assume instantaneous burns; real missions have additional losses due to gravity and atmospheric drag.

Common Mistakes to Avoid

Using the wrong gravitational parameter for the central body. For example, using Earth's μ when orbiting the Moon will give incorrect results.
Mixing units, such as entering radii in kilometers but μ in m³/s², leading to wildly inaccurate delta-v and time values.
Assuming the transfer time is the full orbital period of the transfer ellipse; it is actually half the period.

Last updated: August 13, 2026