Celestial Mechanics

Ceres, the first asteroid or minor planets, was discovered to orbit the Sun between the orbits of liars and Jupiter in 1801. Thousands of other asteroids have been discovered in that part of interplanetary space, which is now called the Main asteroid Belt.

Daniel Kirkwood (1815-1895) noticed in 1866 that the periods of revolution of the asteroids around the Sun did not form a continuous distribution over the Main Asteroid Belt but showed gaps (now known as Kirkwood's gaps) at periods corresponding to 1/2, 1/3, and 2/5 Jupiter's period of revolution (11.86 sidereal years). This phenomenon can be explained by the fact that, if an asteroid is in one of Kirkwood's gaps, then every second, third, or fifth revolution around the Sun, it will experience a perturbation by Jupiter of the same direction and magnitude; over the course of millions of years, these perturbations move asteroids out of the Kirkwood's gaps. This is a resonance effect of planetary perturbations, and it is only one of several resonance phenomena found in the solar system.

Ratios between the periods of revolution of several planets around the Sun are another resonance phenomenon that is poorly understood. The periods of revolution of Venus, Earth, and Mars around the Sun are nearly in the ratio is 5:8:15. The periods of revolution of Jupiter and Saturn are nearly in a 2:5 ratio, and for Uranus, Neptune, and Pluto they are nearly in a 1:2:3 ratio. The 2:3 ratio between the periods of revolution of Neptune and Pluto makes Pluto's orbit more stable. Due to the ellipticity of its orbit, near perihelion (the point on its orbit closest to the Sun) Pluto comes closer to the Sun than Neptune. Pluto last reached perihelion in September 1989; it has been closer to the Sun than Neptune since 1979 and will continue to be closer until 1998, when it will resume its usual place as the Sun's most distant known planet. However, Neptune will be the Sun's most distant known planet from 1995 to 1998! Recent calculations showed that, because of the 2:3 ratio of the orbital periods, the orientation of Pluto's orbit, and of the positions of Neptune and Pluto in their orbits, Neptune and Pluto have never been closer than 2,500,000,000 km in the last 10,000,000 years. Without the 2:3 ratio of their orbital periods, Pluto probably would have had a close encounter with Neptune which could have ejected Pluto and Charon into separate orbits around the Sun that are drastically different from the systems present orbit.

Jupiter's inner three Gallean satellite, Io, Europa, and Ganymede, have orbital periods of revolution around Jupiter that are nearly in the ratio 1:2:4. Five of Saturn's closest satellites, Pandora, Mimas, Enceladus, Tethys, and Dione, have orbital periods of revolution around Saturn that are nearly in the ratio 4:6:9:12:18. Resonance effects produced by some of these satellites, especially the 1.2 resonance with Mimas' period of revolution around Saturn, seem to have produced the Cassini Division between Saturn's A and B rings, which is analogous to the 1:2 Kirkwood's gap in the Main Asteroid Belt. A 3:4 orbital period resonance seems to exist between Saturn's largest satellite Titan and its next satellite out Hyperion.

Other resonances between the satellites and ring systems of Jupiter, Uranus, and Neptune are not clear because these ring systems are far less developed than that of Saturn.