Hohmann Transfer Orbit - inclination change

Description

In orbital mechanics, the Hohmann transfer orbit is an elliptical orbit used to transfer between two circular orbits of different radii in the same plane.

The orbital maneuver to perform the Hohmann transfer uses two engine impulses, one to move a spacecraft onto the transfer orbit and a second to move off it. This maneuver was named after Walter Hohmann, the German scientist who published a description of it in his 1925 book Die Erreichbarkeit der Himmelskörper (“The Accessibility of Celestial Bodies”) Hohmann was influenced in part by the German science fiction author Kurd Lasswitz and his 1897 book Two Planets.

Vis viva (Latin for “live force”) is a term from the history of mechanics, and it survives in this sole context. It represents the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done.

This formula shows the required change of velocity during a perpendicular impulsive maneuver performed passing the equatorial plane which changes only the inclination i.