Editing Orbital inclination change (section)

== 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]] (<math>\Delta v_i</math>) required for an inclination change (<math>\Delta i</math>) can be calculated as follows:
<math display="block">\Delta v_i = {2\sin(\frac{\Delta{i}}{2})(1+e\cos(f))na \over {\sqrt{1-e^2}\cos(\omega+f)}}</math>
where:
*<math>e\,</math> is the [[orbital eccentricity]]
*<math>\omega\,</math> is the [[argument of periapsis]]
*<math>f\,</math> is the [[true anomaly]]
*<math>n\,</math> is the [[mean motion]]
*<math>a\,</math> 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 [[vector subtraction|vector difference]] between the velocity vectors of the initial orbit and the desired orbit at the transfer point.  These types of combined maneuvers are commonplace, as it is more efficient to perform multiple orbital maneuvers at the same time if these maneuvers have to be done at the same location.

According to the [[law of cosines]], the minimum [[Delta-v]] (<math>\Delta{v}\,</math>) required for any such combined maneuver can be calculated with the following equation <ref>{{cite journal |last1=Owens |first1=Steve |last2=Macdonald |first2=Malcolm |date=2013 |title=Hohmann Spiral Transfer With Inclination Change Performed By Low-Thrust System |url=https://pure.strath.ac.uk/ws/portalfiles/portal/22210390/Owens_S_Macdonald_M_Pure_Hohmann_spiral_transfer_with_inclination_change_performed_by_low_thrust_system_Feb_2013.pdf | journal=Advances in the Astronautical Sciences |volume=148 |pages=719 |access-date=3 April 2020}}</ref>
<math display="block">\Delta v = \sqrt{V_1^2 + V_2^2 - 2 V_1 V_2 cos(\Delta i)}</math>

Here <math>V_1</math> and <math>V_2</math> are the initial and target velocities.