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Part of a series on
Astrodynamics
Orbital mechanics
Orbital elements Apsis Argument of periapsis Eccentricity Inclination Mean anomaly Orbital nodes Semi-major axis True anomaly
Types of two-body orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit Radial orbit Decaying orbit
Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period Orbital velocity Surface gravity Specific orbital energy Vis-viva equation
Celestial mechanics
Gravitational influences Barycenter Hill sphere Perturbations Sphere of influence
N-body orbits Lagrangian points (Halo orbits) Lissajous orbits Lyapunov orbits
Engineering and efficiency
Preflight engineering Mass ratio Payload fraction Propellant mass fraction Tsiolkovsky rocket equation
Efficiency measures Gravity assist Oberth effect
Propulsive maneuvers Orbital maneuver Orbit insertion
v t e

In astronautics, the Hohmann transfer orbit (/ˈhoʊmən/) is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. For example, a Hohmann transfer could be used to raise a satellite's orbit from low Earth orbit to geostationary orbit. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits. The maneuver uses two impulsive engine burns: the first establishes the transfer orbit, and the second adjusts the orbit to match the target.

The Hohmann maneuver often uses the lowest possible amount of impulse (which consumes a proportional amount of delta-v, and hence propellant) to accomplish the transfer, but requires a relatively longer travel time than higher-impulse transfers. In some cases where one orbit is much larger than the other, a bi-elliptic transfer can use even less impulse, at the cost of even greater travel time.

The maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper (The Attainability of Celestial Bodies).^[1] Hohmann was influenced in part by the German science fiction author Kurd Lasswitz and his 1897 book Two Planets.

When used for traveling between celestial bodies, a Hohmann transfer orbit requires that the starting and destination points be at particular locations in their orbits relative to each other. Space missions using a Hohmann transfer must wait for this required alignment to occur, which opens a launch window. For a mission between Earth and Mars, for example, these launch windows occur every 26 months. A Hohmann transfer orbit also determines a fixed time required to travel between the starting and destination points; for an Earth-Mars journey this travel time is about 9 months. When transfer is performed between orbits close to celestial bodies with significant gravitation, much less delta-v is usually required, as the Oberth effect may be employed for the burns.

They are also often used for these situations, but low-energy transfers which take into account the thrust limitations of real engines, and take advantage of the gravity wells of both planets can be more fuel efficient.^[2][3][4]

Example

The diagram shows a Hohmann transfer orbit to bring a spacecraft from a lower circular orbit into a higher one. It is an elliptic orbit that is tangential both to the lower circular orbit the spacecraft is to leave (cyan, labeled 1 on diagram) and the higher circular orbit that it is to reach (red, labeled 3 on diagram). The transfer orbit (yellow, labeled 2 on diagram) is initiated by firing the spacecraft's engine to add energy and raise the apogee. When the spacecraft reaches apogee, a second engine firing adds energy to raise the perigee, putting the spacecraft in the larger circular orbit.

Due to the reversibility of orbits, a similar Hohmann transfer orbit can be used to bring a spacecraft from a higher orbit into a lower one; in this case, the spacecraft's engine is fired in the opposite direction to its current path, slowing the spacecraft and lowering its perigee to that of the elliptical transfer orbit. The engine is then fired again at the lower distance to slow the spacecraft into the lower circular orbit. The Hohmann transfer orbit is based on two instantaneous velocity changes. Extra fuel is required to compensate for the fact that the bursts take time; this is minimized by using high-thrust engines to minimize the duration of the bursts. For transfers in Earth orbit, the two burns are labelled the perigee burn and the apogee burn (or apogee kick^[5]); more generally, they are labelled periapsis and apoapsis burns. Alternately, the second burn to circularize the orbit may be referred to as a circularization burn.

Type I and Type II

An ideal Hohmann transfer orbit transfers between two circular orbits in the same plane and traverses exactly 180° around the primary. In the real world, the destination orbit may not be circular, and may not be coplanar with the initial orbit. Real world transfer orbits may traverse slightly more, or slightly less, than 180° around the primary. An orbit which traverses less than 180° around the primary is called a "Type I" Hohmann transfer, while an orbit which traverses more than 180° is called a "Type II" Hohmann transfer.^[6][7]

Transfer orbits can go more than 360° around the primary. These multiple-revolution transfers are sometimes referred to as Type III and Type IV, where a Type III is a Type I plus 360°, and a Type IV is a Type II plus 360°.^[8]

Uses

A Hohmann transfer orbit can be used to transfer an object's orbit toward another object, as long as they co-orbit a more massive body. In the context of Earth and the Solar System, this includes any object which orbits the Sun. An example of where a Hohmann transfer orbit could be used is to bring an asteroid, orbiting the Sun, into contact with the Earth.^[9]

Calculation

For a small body orbiting another much larger body, such as a satellite orbiting Earth, the total energy of the smaller body is the sum of its kinetic energy and potential energy, and this total energy also equals half the potential at the average distance ${\displaystyle a}$ (the semi-major axis):

Solving this equation for velocity results in the vis-viva equation,

where:

• ${\displaystyle v}$ is the speed of an orbiting body,
• ${\displaystyle \mu =GM}$ is the standard gravitational parameter of the primary body, assuming ${\displaystyle M+m}$ is not significantly bigger than ${\displaystyle M}$ (which makes ${\displaystyle v_{M}\ll v}$), (for Earth, this is μ~3.986E14 m³ s⁻²)
• ${\displaystyle r}$ is the distance of the orbiting body from the primary focus,
• ${\displaystyle a}$ is the semi-major axis of the body's orbit.

Therefore, the delta-v (Δv) required for the Hohmann transfer can be computed as follows, under the assumption of instantaneous impulses:

to enter the elliptical orbit at ${\displaystyle r=r_{1}}$ from the ${\displaystyle r_{1}}$ circular orbit, where ${\displaystyle r_{2}}$ is the aphelion of the resulting elliptical orbit, and to leave the elliptical orbit at ${\displaystyle r=r_{2}}$ to the ${\displaystyle r_{2}}$ circular orbit, where ${\displaystyle r_{1}}$ and ${\displaystyle r_{2}}$ are respectively the radii of the departure and arrival circular orbits; the smaller (greater) of ${\displaystyle r_{1}}$ and ${\displaystyle r_{2}}$ corresponds to the periapsis distance (apoapsis distance) of the Hohmann elliptical transfer orbit. Typically, ${\displaystyle \mu }$ is given in units of m³/s², as such be sure to use meters, not kilometers, for ${\displaystyle r_{1}}$ and ${\displaystyle r_{2}}$. The total ${\displaystyle \Delta v}$ is then:

Whether moving into a higher or lower orbit, by Kepler's third law, the time taken to transfer between the orbits is