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Gravity-Assist Navigation

By means of a close flyby of a planet, it is possible to increase a spacecraft's orbital velocity far beyond the capability of its propulsion system. Although this may seem like getting something for nothing, in fact the spacecraft is taking some orbital energy from the planet - but only a tiny fraction. Except for minuscule dissipative forces on the spacecraft and planet, including effects of gravitational radiation, the total energy and angular momentum of the solar system are conserved during the gravity assist.

The earliest studies of the gravity-assist problem considered the orbital perturbations of comets making close approaches to Jupiter. In the 1890s F. Tisserand pointed out that the orbital elements of a comet could be radically different before and after the close approach. However, using an integral discovered by Carl Gustav Jacob Jacobi (1804-1851), he also showed that a combination of the semimajor axis a, the eccentricity e, and the inclination