is defined by the angle between ecliptic North and the vector normal to the orbit plane, (i.e. the angular momentum vector). This means that inclination is always positive and is entangled with other orbital elements primarily the argument of periapsis which is in turn connected to the longitude of the ascending node. This can result in two very different orbits with precisely the same inclination. 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: where: 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 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 () required for any such combined maneuver can be calculated with the following equation 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: where is the orbital velocity and has the same units as . 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 Inclination Orbital inclination Orbital maneuver References Astrodynamics Orbital maneuvers