The trajectory is computed of a vehicle from the Earth to the planet Mars or the planet Venus by deriving the equations of motion under the assumption that the motion of the vehicle is influenced only by the gravitational fields of the Earth, Moon, Sun, Venus, Mars and Jupiter. The problem consists of three phases. During the first phase the influence of the Earth-Moon system is greater than that of the Sun or of the other planets. Consequently a geocentric coordinate system is used. During the second phase the influence of the Sun is predominant. Consequently a heliocentric coordinate system is used. Finally, during the third phase, the target planet Mars or Venus has the greatest influence on the motion of the vehicle and so a planetocentric coordinate system is used. The geocentric coordinate system used is a right handed rectangular coordinate system with the positive x-axis in the direction of the vernal equinox and the positive z-axis in the direction of the north celestial pole, that is, the coordinate system is what astronomers call the equatorial coordinate system. Subsequent systems are chosen so that the new axes are parallel to the old and so the transformations consist merely of translations as changes in coordinates are made.