Orbit
An orbit is the path followed by a celestial body moving in a gravitational field. When a single object, such as a planet, is moving freely in a gravitational field of a massive body, such as a star, the orbit is in the shape of a conic section, that is, elliptical, parabolic, or hyperbolic. Most orbits are elliptical.
The exact path and position of an object in space can be determined by taking into account seven orbital elements. These elements deal with the mathematical relationships between the two bodies. To determine the orbit of a celestial body, it must be observed and precise measurements taken at least three times. However, at least 20 precise observations, covering at least one full revolution, are needed for accurate orbital elements to be determined. If two bodies that move in elliptical orbits around their common center of mass (for example, the Sun and Jupiter) were alone in an otherwise empty universe, we would expect that their orbits would remain constant. However, the solar system consists of the Sun, eight major planets, and an enormous number of much smaller bodies all orbiting around the solar system's center of mass. The masses of these objects all influence the orbits of each other in small and large ways.
Perturbation theory
The Sun's gravitational attraction is the main force acting on each planet, but there are much weaker gravitational forces between the planets, which produce perturbations of their elliptical orbits; these make small changes in a planet's orbital elements with time. The planets which perturb the Earth's orbit most are Venus, Jupiter, and Saturn. These planets and the sun also perturb the moon's orbit around the Earth--Moon system's center of mass. The use of mathematical series for the orbital elements as functions of time can accurately describe perturbations of the orbits of solar system bodies for limited time intervals. For longer intervals, the series must be recalculated.
Today, astronomers use high-speed computers to figure orbits in multiple body systems such as the solar system. The computers can be programmed to make allowances for the important perturbations on all the orbits of the member bodies. Such calculations have now been made for the Sun and the major planets over time intervals of up to several tens of millions of years.
As accurately as these calculations can be made, however, the behavior of celestial bodies over long periods of time cannot always be determined. For example, the perturbation method has so far been unable to determine the stability either of the orbits of individual bodies or of the solar system as a whole for the estimated age of the solar system. Studies of the evolution of the Earth-Moon system indicate that the Moon's orbit may become unstable, which will make it possible for the Moon to escape into an independent orbit around the Sun. Recent astronomers have also used the theory of chaos to explain irregular orbits.
The orbits of artificial satellites of the Earth or other bodies with atmospheres whose orbits come close to their surfaces are very complicated. The orbits of these satellites are influenced by atmospheric drag, which tends to bring the satellite down into the lower atmosphere, where it is either vaporized by atmospheric friction or falls to the planet's surface. In addition, the shape of Earth and many other bodies is not perfectly spherical. The bulge that forms at the equator, due to the planet's spinning motion, causes a stronger gravitational attraction. When the satellite passes by the equator, it may be slowed enough to pull it to earth.
Types of orbits
A synchronous orbit around a celestial body is a nearly circular orbit in which the body's period of revolution equals its rotation period. This way, the same hemisphere of the satellite is always facing the object of its orbit. This orbit is called a geosynchronous orbit for the Earth where, with its sidereal rotation period of 23 hours 56 minutes 4 seconds, the geosynchronous orbit is 21,480 miles (35,800 km) above the equator on the Earth's surface. A satellite in a synchronous orbit will seem to remain fixed above the same place on the body's equator. But perturbations will cause synchronous satellites to drift away from this fixed place above the body's equator. Thus, frequent corrections to their orbits are needed to keep geosynchronous satellites in their assigned places. They are very useful for communications and making global meteorological observations. Hence, the vicinity of the geosynchronous orbit is now crowded with artificial satellites.
The Space Age has greatly increased the importance of hyperbolic orbits. The orbits of spacecraft flybys past planets, their satellites, and other solar system bodies are hyperbolae. Other recent flybys have been made past Comet Halley in March 1986 by three spacecraft, and past the asteroids 951 Gaspra in October 1991 and 243 Ida in August 1993; both flybys were made by the Galileo spacecraft enroute to Jupiter. Although accurate masses could not be found for these small bodies from the hyperbolic flyby orbits, all of them were extensively imaged.
Orbits of double and multiple stars
The orbits of double stars, where the sizes of the orbits have been determined, provide the only information we have about the masses of stars other than the Sun. Close doublestars will become decidedly non-spherical because of tidal distortion and/or rapid rotation, which produces effects analogous to those described above for close artificial planetary satellites. Also, such stars often have gas streaming from their tidal and equatorial bulges, which can transfer mass from one star to the other, or can even eject it completely out of the system. Such effects are suspected to be present in close doublestars where their period of revolution is found to be changing.
Multiple stars with three (triple) or more (multiple) members have very complicated orbits for their member stars, and require many perturbing effects to be considered. The investigation of the orbits of double and multiple stars is important for solving many problems in astrophysics, stellar structure, and stellar evolution.
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