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# Orbital inclination change

Orbital inclination change is a orbital maneuver aimed at changing inclination of orbiting body's orbit. This maneuver requires a change in the orbital velocity vector (delta v) at the orbital nodes (i.e. the point where the initial and desired orbits intersect).

Maximum efficiency of inclination change is achieved at apoapsis where orbital velocity $v\,$ is the lowest. In general, inclination changes require the most delta v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This can sometimes be achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize the inclination change required.

## 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 ($\Delta{v_i}\,$) required for a pure inclination change ($\Delta{i}\,$) can be calculated as follows:

$\Delta{v_i}=2v{sin{\Delta{i}\over{2}}}$

where:

• $v\,$ is orbiting body's velocity at orbital position where maneuver takes place.

For more complicated manuvers which may involve a combination of change in inclination and orbital radius, the amount of delta v is the vector differnece between the velocity vectors of the initial orbit and the desired orbit at the transfer point.