Editing Hohmann transfer orbit (section)

== Application to interplanetary travel ==

When used to move a spacecraft from orbiting one planet to orbiting another, the [[Oberth effect]] allows to use less delta-''v'' than the sum of the delta-''v'' for separate manoeuvres to escape the first planet, followed by a Hohmann transfer to the second planet, followed by insertion into an orbit around the other planet.

For example, consider a spacecraft travelling from [[Earth]] to [[Mars]]. At the beginning of its journey, the spacecraft will already have a certain velocity and kinetic energy associated with its orbit around Earth. During the burn the rocket engine applies its delta-''v'', but the kinetic energy increases as a square law, until it is sufficient to [[escape velocity|escape the planet's gravitational potential]], and then burns more so as to gain enough energy to get into the Hohmann transfer orbit (around the [[Sun]]). Because the rocket engine is able to make use of the initial kinetic energy of the propellant, far less delta-''v'' is required over and above that needed to reach escape velocity, and the optimum situation is when the transfer burn is made at minimum altitude (low [[periapsis]]) above the planet. The delta-''v'' needed is only 3.6&nbsp;km/s, only about 0.4&nbsp;km/s more than needed to escape Earth, even though this results in the spacecraft going 2.9&nbsp;km/s faster than the Earth as it heads off for Mars (see table below).

At the other end, the spacecraft must decelerate for the [[gravity of Mars]] to capture it. This capture burn should optimally be done at low altitude to also make best use of the Oberth effect. Therefore, relatively small amounts of thrust at either end of the trip are needed to arrange the transfer compared to the free space situation.

However, with any Hohmann transfer, the alignment of the two planets in their orbits is crucial – the destination planet and the spacecraft must arrive at the same point in their respective orbits around the Sun at the same time.  This requirement for alignment gives rise to the concept of [[launch window]]s.

The term lunar transfer orbit (LTO) is used for the [[Moon]].

It is possible to apply the formula given above to calculate the Δv in km/s needed to enter a Hohmann transfer orbit to arrive at various destinations from Earth (assuming circular orbits for the planets). In this table, the column labeled "Δv to enter Hohmann orbit from Earth's orbit" gives the change from Earth's velocity to the velocity needed to get on a Hohmann ellipse whose other end will be at the desired distance from the Sun. The column labeled "LEO height" gives the velocity needed (in a non-rotating frame of reference centered on the earth) when 300&nbsp;km above the Earth's surface. This is obtained by adding to the specific kinetic energy the square of the [[escape velocity]] (10.9&nbsp;km/s) from this height. The column "LEO" is simply the previous speed minus the LEO orbital speed of 7.73&nbsp;km/s.

{|style="text-align:left;" class="wikitable"
|-
! rowspan="2" | Destination
! rowspan="2" | Orbital<br />radius<br />([[astronomical unit|AU]])
! colspan="3" | Δ''v'' (km/s) to enter Hohmann orbit from
|-
! Earth's orbit
! LEO height
! LEO
|-
| [[Sun]]
|align=center|0
|align=center| 29.8
|align=center| 31.7
|align=center| 24.0
|-
|[[Mercury (planet)|Mercury]]
|align=center| 0.39
|align=center| 7.5
|align=center| 13.3
|align=center| 5.5
|-
|[[Venus]]
|align=center| 0.72
|align=center| 2.5
|align=center| 11.2
|align=center| 3.5
|-
|[[Mars]]
|align=center| 1.52
|align=center| 2.9
|align=center| 11.3
|align=center| 3.6
|-
|[[Jupiter]]
|align=center| 5.2
|align=center| 8.8
|align=center| 14.0
|align=center| 6.3
|-
|[[Saturn]]
|align=center| 9.54
|align=center| 10.3
|align=center| 15.0
|align=center| 7.3
|-
|[[Uranus]]
|align=center| 19.19
|align=center| 11.3
|align=center| 15.7
|align=center| 8.0
|-
|[[Neptune]]
|align=center| 30.07
|align=center| 11.7
|align=center| 16.0
|align=center| 8.2
|-
|[[Pluto]]
|align=center| 39.48
|align=center| 11.8
|align=center| 16.1
|align=center| 8.4
|-
|[[Infinity]]
|align=center| ∞
|align=center| 12.3
|align=center| 16.5
|align=center| 8.8
|-
|}

Note that in most cases, Δ''v'' from LEO is less than the Δ''v'' to enter Hohmann orbit from Earth's orbit.

To get to the Sun, it is actually not necessary to use a Δ''v'' of 24&nbsp;km/s. One can use 8.8&nbsp;km/s to go very far away from the Sun, then use a negligible Δ''v'' to bring the angular momentum to zero, and then fall into the Sun. This can be considered a sequence of two Hohmann transfers, one up and one down. Also, the table does not give the values that would apply when using the Moon for a [[gravity assist]]. There are also possibilities of using one planet, like Venus which is the easiest to get to, to assist getting to other planets or the Sun.