orbit is the mirror image of the raise maneuver; both burns are made retrograde. Altitude change by bi-elliptic transfer A slightly more complicated altitude change maneuver is the bi-elliptic transfer, which consists of two half-elliptic orbits; the first, posigrade burn sends the spacecraft into an arbitrarily high apoapsis chosen at some point away from the central body. At this point a second burn modifies the periapsis to match the radius of the final desired orbit, where a third, retrograde burn is performed to inject the spacecraft into the desired orbit. While this takes a longer transfer time, a bi-elliptic transfer can require less total propellant than the Hohmann transfer when the ratio of initial and target orbit radii is 12 or greater. Burn 1 (posigrade): Burn 2 (posigrade or retrograde), to match periapsis to the target orbit's altitude: Burn 3 (retrograde): Change of plane Plane change maneuvers can be performed alone or in conjunction with other orbit adjustments. For a pure rotation plane change maneuver, consisting only of a change in the inclination of the orbit, the specific angular momentum, h, of the initial and final orbits are equal in magnitude but not in direction. Therefore, the change in specific angular momentum can be written as: where h is the specific angular momentum before the plane change, and Δi is the desired change in the inclination angle. From this it can be shown that the required delta-v is: From the definition of h, this can also be written as: where v is the magnitude of velocity before plane change and φ is the flight path angle. Using the small-angle approximation, this becomes: The total delta-v for a combined maneuver can be calculated by a vector addition of the pure rotation delta-v and the delta-v for the other planned orbital change. Translunar flight Vehicles sent on lunar or planetary missions are generally not launched by direct injection to departure trajectory, but first put into a low Earth parking orbit; this allows the flexibility of a bigger launch window and more time for checking that the vehicle is in proper condition for the flight. Escape velocity is not required for flight to the Moon; rather the vehicle's apogee is raised high enough to take it through a point where it enters the Moon's gravitational sphere of influence (SOI). This is defined as the distance from a satellite at which its gravitational pull