Hohmann Transfer

Author: Tianjiang Shuo
Website: https://cislunarspace.cn

Definition

The Hohmann transfer is a two-impulse, minimum-energy, coplanar circular orbit transfer scheme proposed by the German engineer Hohmann. The transfer orbit is an ellipse tangent to the initial orbit at perigee and tangent to the final orbit at apogee. The spacecraft applies two velocity impulses along the direction of motion at the tangent points to complete the transfer.

Core Elements

Transfer Process

At perigee $A$ of the initial orbit, the spacecraft applies a prograde impulse $\Delta v_1$ to enter the transfer ellipse. At apogee $B$ , a second impulse $\Delta v_2$ is applied to enter the final circular orbit.

Velocity Impulse Computation

The semi-major axis of the transfer orbit:

a_E = \frac{r_1 + r_2}{2}

The two velocity impulses:

\begin{cases} \Delta v_1 = v_{c1}\left(\sqrt{\frac{2r_2}{r_1 + r_2}} - 1\right) \\ \Delta v_2 = v_{c2}\left(1 - \sqrt{\frac{2r_1}{r_1 + r_2}}\right) \end{cases}

where $v_{c1} = \sqrt{\mu/r_1}$ and $v_{c2} = \sqrt{\mu/r_2}$ .

Transfer Time

T = \frac{\pi}{\sqrt{\mu}} \left(\frac{r_1 + r_2}{2}\right)^{3/2}

Hohmann Rendezvous

When the chaser spacecraft rendezvous with the target at apogee, the angular lead of the target over the chaser is:

\theta_H = \pi\left[1 - \left(\frac{r_1 + r_2}{2r_2}\right)^{3/2}\right]

If the initial phase angle does not satisfy this condition, the chaser must wait in the initial orbit to eliminate the discrepancy.

Application Value

The Hohmann transfer is the most classical orbital transfer scheme. For coplanar circular transfers, it is the most energy-efficient option when $r_2/r_1 < 11.94$ . It is widely used in geostationary satellite insertion, space station orbit transfers, preliminary interplanetary trajectory design, and other missions.

References

郑伟, 安雪滢, 周祥, 何睿智. 空天飞行力学[M]. 国防科技大学, 2026.
贾沛然, 陈克俊, 等. 远程火箭弹道学[M]. 国防科技大学出版社.