Orbital inclination change
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Orbital inclination change is an
In general, inclination changes can take a very large amount of delta-v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This is typically achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize any inclination change required over the duration of the spacecraft life. Planetary flybys are the most efficient way to achieve large inclination changes, but they are only effective for interplanetary missions..
Efficiency
The simplest way to perform a plane change is to perform a burn around one of the two crossing points of the initial and final planes. The delta-v required is the vector change in velocity between the two planes at that point.
However, maximum efficiency of inclination changes are achieved at
For the most efficient example mentioned above, targeting an inclination at
For Hohmann transfer orbits, the initial orbit and the final orbit are 180 degrees apart. Because the transfer orbital plane has to include the central body, such as the Sun, and the initial and final nodes, this can require two 90 degree plane changes to reach and leave the transfer plane. In such cases it is often more efficient to use a broken plane maneuver where an additional burn is done so that plane change only occurs at the intersection of the initial and final orbital planes, rather than at the ends.[2]
Inclination entangled with other orbital elements
An important subtlety of performing an inclination change is that Keplerian orbital
Calculation
In a pure inclination change, only the inclination of the orbit is changed while all other orbital characteristics (radius, shape, etc.) remains the same as before. Delta-v () required for an inclination change () can be calculated as follows:
- is the orbital eccentricity
- is the argument of periapsis
- is the true anomaly
- is the mean motion
- is the semi-major axis
For more complicated maneuvers which may involve a combination of change in inclination and orbital radius, the delta-v is the
According to the law of cosines, the minimum Delta-v () required for any such combined maneuver can be calculated with the following equation [3]
Here and are the initial and target velocities.
Circular orbit inclination change
Where both orbits are circular (i.e. ) and have the same radius the Delta-v () required for an inclination change () can be calculated using:
Other ways to change inclination
Some other ways to change inclination that do not require burning propellant (or help reduce the amount of propellant required) include
- aerodynamic lift (for bodies within an atmosphere, such as the Earth)
- solar sails
Transits of other bodies such as the Moon can also be done.
None of these methods will change the delta-V required, they are simply alternate means of achieving the same end result and, ideally, will reduce propellant usage.
See also
References
- ^ a b Braeunig, Robert A. "Basics of Space Flight: Orbital Mechanics". Archived from the original on 2012-02-04. Retrieved 2008-07-16.
- ^ Abilleira, Fernando. Broken-Plane Maneuver Applications for Earth to Mars Trajectories (PDF) (Report). Retrieved November 13, 2022.
- ^ Owens, Steve; Macdonald, Malcolm (2013). "Hohmann Spiral Transfer With Inclination Change Performed By Low-Thrust System" (PDF). Advances in the Astronautical Sciences. 148: 719. Retrieved 3 April 2020.