Hohmann Transfer Delta-V

\[\begin{aligned} \Delta V_1 &= \sqrt{\frac{\mu}{r_1}}\left(\sqrt{\frac{2r_2}{r_1+r_2}}-1\right) \\ \Delta V_2 &= \sqrt{\frac{\mu}{r_2}}\left(1-\sqrt{\frac{2r_1}{r_1+r_2}}\right) \\ \Delta V_{tot} &= \Delta V_1+\Delta V_2 \end{aligned}\]

Variables

DV1first burn delta-v (m/s)

DV2second burn delta-v (m/s)

DVtottotal transfer delta-v (m/s)

mu[μ]standard gravitational parameter (m³/s²)

r1initial circular orbit radius (m)

r2final circular orbit radius (m)

Description

What is this formula?

The Hohmann Transfer Delta-V equation calculates the velocity changes required to transfer a spacecraft between two coplanar circular orbits using the minimum propellant transfer.

The maneuver consists of two engine burns:

1. Injection into the transfer ellipse.

2. Circularization at the destination orbit.

The sum of both burns gives the total mission delta-v.

When to use it

Use this equation when planning orbital transfers between circular Earth or planetary orbits.

It is one of the most important calculations in astrodynamics and spacecraft mission design.

Example

A spacecraft transfers from:

Initial orbit radius = 7000 km

Final orbit radius = 12000 km

Earth gravitational parameter:

μ = 3.986×10^14 m³/s²

Formula:

DV1 = √(μ/r1)(√(2r2/(r1+r2))−1)

DV2 = √(μ/r2)(1−√(2r1/(r1+r2)))

DVtot = DV1 + DV2

Result:

DV1 ≈ 29466.6 m/s

DV2 ≈ 25808.12 m/s

DVtot ≈ 55374.72 m/s

Applications

Satellite orbit raising

Geostationary transfer missions

Planetary mission design

Spacecraft maneuver planning

Launch vehicle analysis

Orbital mechanics education

Note

The Hohmann transfer is an idealized two-impulse maneuver that minimizes delta-v between coplanar circular orbits. Real missions may require additional corrections due to inclination changes, orbital perturbations, finite burn duration, atmospheric drag, or operational constraints. More complex transfers such as bi-elliptic transfers may be more efficient under certain conditions.