Orbit
Orbit
Orbits of double and multiple stars
An orbit, in physics, 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.
German astronomer and mathematician Johannes Kepler (1571–1630) first studied orbits when he developed his three laws of planetary motion. At the time, he discovered that celestial bodies in the solar system have elliptical orbits rather than the generally accepted circular orbits. Kepler also discovered that these objects vary in their speeds within their orbits, rather than moving with a constant speed. He also formulated the equality: the cube of the distance from a planet to the sun (measured in astronomical units, the mean distance from the Earth to the sun) is equal to the square of the orbital period of that planet (measured in Earth years). English physicist and mathematician Sir Isaac Newton (1642–1727) showed that Kepler’s orbital laws were valid when he applied them to his theory of gravitation. These two mathematicians helped to develop the theories and equations behind how orbits are studied and calculated today.
The exact path and position of an object in space can be determined by taking into account seven orbital elements (epoch, orbital inclination, right ascension of ascending node, argument of perigee, eccentricity, mean motion, and mean anomaly). These elements deal with the mathematical relationships between the two bodies. To determine the orbit of a celestial body, the orbit must be observed and precise measurements taken of it 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, scientists 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 that 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. Recently, 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 the 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 the Earth’s surface.
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 mi (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. However, 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. These satellites 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 en route to Jupiter. Although accurate masses could not be found for these small bodies from the hyperbolic flyby orbits, all of them were extensively imaged.
Later, a pair of space missions launched in 1999 and 2004 are helping scientists reach a better understanding of the physics of comets. NASA’s Stardust mission, launched in 1999, captured dust from the tail of short-period Comet Wild (pronounced vilt) 2 in 2004, and returned the samples to Earth on January 15, 2006. Thousands of samples—most sample grains embedded in the Stardust aerogel were smaller than the width of a human hair—have been distributed to about 150 scientists around the world for analysis.
In February 2003, the European Space Agency’s Rosetta mission—originally scheduled to rendezvous with Comet Wirtanen on its trip around the sun—was postponed due to launch failures suffered by Europe’s Ariane 5 rocket. In March 2003, ESA scientists retasked the Rosetta mission spacecraft to rendezvous with 67P/Churyumov-Gerasimenko. With a launch in February 2004 (from Kourou in French Guiana), it should rendezvous with the comet in 2014. During its six-month stay near the comet, Rosetta will move closer to the comet’s nucleus until it is only 12 to 15 mi (20 to 25 km) away. It will then map the comet and send a probe to the surface for a landing. The larger size of 67P/Churyumov-Gerasimenko—thus, a stronger gravitational field—poses some problems for the lander that will require recalculation of the landing
KEY TERMS
Drag —A frictional force on a moving body that is produced by a fluid (air, water, etc.) through which the body moves. Drag slows the body and dissipates its energy of motion (kinetic energy).
impact stress on the lander legs. For its remaining mission at the comet, Rosetta will observe the comet as it races toward the sun. After completing its mission to the comet, the Rosetta will be redirected to a voyage of the outer solar system.
Orbits of double and multiple stars
The orbits of double stars, where the sizes of the orbits have been determined, provide the only information scientists have about the masses of stars other than the sun. Close double stars 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. In addition, 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 double stars 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.
See also Celestial mechanics; Geocentric theory; Heliocentric theory; Kepler’s laws.
Frederick West