Apollo missions (13 through 17). Lunar orbit insertion In the Apollo program, the retrograde lunar orbit insertion burn was performed at an altitude of approximately on the far side of the Moon. This became the pericynthion of the initial orbits, with an apocynthion on the order of . The delta v was approximately . Two orbits later, the orbit was circularized at . For each mission, the flight dynamics officer prepared 10 lunar orbit insertion solutions so the one could be chosen with the optimum (minimum) fuel burn and best met the mission requirements; this was uploaded to the spacecraft computer and had to be executed and monitored by the astronauts on the lunar far side, while they were out of radio contact with Earth. Interplanetary flight In order to completely leave one planet's gravitational field to reach another, a hyperbolic trajectory relative to the departure planet is necessary, with excess velocity added to (or subtracted from) the departure planet's orbital velocity around the Sun. The desired heliocentric transfer orbit to a superior planet will have its perihelion at the departure planet, requiring the hyperbolic excess velocity to be applied in the posigrade direction, when the spacecraft is away from the Sun. To an inferior planet destination, aphelion will be at the departure planet, and the excess velocity is applied in the retrograde direction when the spacecraft is toward the Sun. For accurate mission calculations, the orbital elements of the planets must be obtained from an ephemeris, such as that published by NASA's Jet Propulsion Laboratory. Simplifying assumptions For the purpose of preliminary mission analysis and feasibility studies, certain simplified assumptions may be made to enable delta-v calculation with very small error: All the planets' orbits except Mercury have very small eccentricity, and therefore may be assumed to be circular at a constant orbital speed and mean distance from the Sun. All the planets' orbits (except Mercury) are nearly coplanar, with very small inclination to the ecliptic (3.39 degrees or less; Mercury's inclination is 7.00 degrees). The perturbating effects of the other planets' gravity is negligible. The spacecraft will spend most of its flight time under only the gravitational influence of the Sun, except for brief periods when it is in the sphere of influence of the departure and destination planets. Since interplanetary spacecraft spend a large period of time in heliocentric orbit between the planets, which are at relatively