orbit

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Orbit

Perturbation theory

Types of orbits

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 (15711630) 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 (16421727) showed that Keplers 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 systems center of mass. The masses of these objects all influence the orbits of each other in small and large ways.

Perturbation theory

The suns 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 planets orbital elements with time. The planets that perturb the Earths orbit most are Venus, Jupiter, and Saturn. These planets and the sun also perturb the moons orbit around the Earth-moon systems 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 moons 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 planets 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 planets spinning motion, causes a stronger gravitational attraction. When the satellite passes by the equator, it may be slowed enough to pull it to the Earths surface.

Types of orbits

A synchronous orbit around a celestial body is a nearly circular orbit in which the bodys 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 Earths surface. A satellite in a synchronous orbit will seem to remain fixed above the same place on the bodys equator. However, perturbations will cause synchronous satellites to drift away from this fixed place above the bodys 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. NASAs 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 samplesmost sample grains embedded in the Stardust aerogel were smaller than the width of a human hairhave been distributed to about 150 scientists around the world for analysis.

In February 2003, the European Space Agencys Rosetta missionoriginally scheduled to rendezvous with Comet Wirtanen on its trip around the sunwas postponed due to launch failures suffered by Europes 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 comets 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-Gerasimenkothus, a stronger gravitational fieldposes 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.

Frederick West

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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 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. 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 .

Frederick West

KEY TERMS

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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).

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Orbit

An orbit is the path a celestial object follows when moving under the control of another's gravity. This gravitational effect is evident throughout the universe: satellites orbit planets, planets orbit stars, stars orbit the cores of galaxies, and galaxies revolve in clusters.

Without gravity, celestial objects would hurtle off in all directions. Gravity pulls those objects into circular and elliptical (oval-shaped) orbits. Indeed, gravity was responsible for the clumping together of dust and gas shortly after the beginning of the universe, which led to the formation of stars and galaxies.

Kepler's laws and planetary motion

Since ancient times, astronomers have been attempting to understand the patterns in which planets travel throughout the solar system and the forces that propel them. One such astronomer was the German Johannes Kepler (15711630). In 1595, he discovered that the planets formed ellipses in space. In 1609, he published his first two laws of planetary motion. The first law states that a planet travels around the Sun on an elliptical path. The second law states that a planet moves faster on its orbit when it is closer to the Sun and slower when it is farther away.

Ten years later, Kepler added a third law of planetary motion. This law makes it possible to calculate a planet's relative distance from the Sun knowing its period of revolution. Specifically, the law states that the cube of the planet's average distance from the Sun is equal to the square of the time it takes that planet to complete its orbit.

Scientists now know that Kepler's planetary laws also describe the motion of stars, moons, and human-made satellites.

Newton's laws

More than 60 years after Kepler published his third law, English physicist Isaac Newton (16421727) developed his three laws of motion and his law of universal gravitation. Newton was the first to apply the notion of gravity to orbiting bodies in space. He explained that gravity was the force that made planets remain in their orbits instead of falling away in a straight line. Planetary motion is the result of movement along a straight line combined with the gravitational pull of the Sun.

Newton discovered three laws of motion, which explained interactions between objects. The first is that a moving body tends to remain in motion and a resting body tends to remain at rest unless acted upon by an outside force. The second states that any change in the acceleration of an object is proportional to, and in the same direction as, the force acting on it. (Proportional means corresponding, or having the same ratio.) In addition, the effects of that force will be inversely proportional (opposite) to the mass of the object; that is, when affected by the same force, a heavier object will move slower than a lighter object. Newton's third law states that for every action there is an equal and opposite reaction.

Newton used these laws to develop the law of universal gravitation. This law states that the gravitational force between any two objects depends on the mass of each object and the distance between them. The greater each object's mass, the stronger the pull, but the greater the distance between them, the weaker the pull. The strength of the gravitational force, in turn, directly affects the speed and shape of an object's orbit. As strength increases, so does the orbital speed and the tightness of the orbit.

Newton also added to Kepler's elliptical orbit theory. Newton found that the orbits of objects going around the Sun could be shaped as circles, ellipses, parabolas, or hyperbolas. As a result of his work, the orbits of the planets and their satellites could be calculated very precisely. Scientists used Newton's laws to predict new astronomical events. Comets and planets were eventually predicted and discovered through Newtonian or celestial mechanicsthe scientific study of the influence of gravity on the motions of celestial bodies.

Einstein revises Newton's laws

In the early 1900s, German-born American physicist Albert Einstein (18791955) presented a revolutionary explanation for how gravity works. Whereas Newton viewed space as flat and time as constant (progressing at a constant ratenot slowing down or speeding up), Einstein described space as curved and time as relative (it can slow down or speed up).

According to Einstein, gravity is actually the curvature of space around the mass of an object. As a lighter object (like a planet) approaches a heavier object (like the Sun) in space, the lighter object follows the lines of curved space, which draws it near the heavier object. To understand this concept, imagine space as a huge stretched sheet. If you were to place a large heavy ball on the sheet, it would cause the sheet to sag. Now imagine a marble rolling toward the ball. Rather than traveling in a straight line, the marble would follow the curves in the sheet caused by the ball's depression.

Einstein's ideas did not prove Newton wrong. Einstein merely showed that Newtonian mechanics work more accurately when gravity is weak. Near stars and black holes (single points of infinite mass and gravity that are the remains of massive stars), where there are powerful gravitational fields, only Einstein's theory holds up. Still, for most practical purposes, Newton's laws continue to describe planetary motions well.

[See also Celestial mechanics; Moon; Satellite; Solar system; Star; Sun ]

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orbit, in astronomy, path in space described by a body revolving about a second body where the motion of the orbiting bodies is dominated by their mutual gravitational attraction. Within the solar system, planets, dwarf planets, asteroids, and comets orbit the sun and satellites orbit the planets and other bodies.

Planetary Orbits

From earliest times, astronomers assumed that the orbits in which the planets moved were circular; yet the numerous catalogs of measurements compiled especially during the 16th cent. did not fit this theory. At the beginning of the 17th cent., Johannes Kepler stated three laws of planetary motion that explained the observed data: the orbit of each planet is an ellipse with the sun at one focus; the speed of a planet varies in such a way that an imaginary line drawn from the planet to the sun sweeps out equal areas in equal amounts of time; and the ratio of the squares of the periods of revolution of any two planets is equal to the ratio of the cubes of their average distances from the sun. The orbits of the solar planets, while elliptical, are almost circular; on the other hand, the orbits of many of the extrasolar planets discovered during the 1990s are highly elliptical.

After the laws of planetary motion were established, astronomers developed the means of determining the size, shape, and relative position in space of a planet's orbit. The size and shape of an orbit are specified by its semimajor axis and by its eccentricity. The semimajor axis is a length equal to half the greatest diameter of the orbit. The eccentricity is the distance of the sun from the center of the orbit divided by the length of the orbit's semimajor axis; this value is a measure of how elliptical the orbit is. The position of the orbit in space, relative to the earth, is determined by three factors: (1) the inclination, or tilt, of the plane of the planet's orbit to the plane of the earth's orbit (the ecliptic); (2) the longitude of the planet's ascending node (the point where the planet cuts the ecliptic moving from south to north); and (3) the longitude of the planet's perihelion point (point at which it is nearest the sun; see apsis).

These quantities, which determine the size, shape, and position of a planet's orbit, are known as the orbital elements. If only the sun influenced the planet in its orbit, then by knowing the orbital elements plus its position at some particular time, one could calculate its position at any later time. However, the gravitational attractions of bodies other than the sun cause perturbations in the planet's motions that can make the orbit shift, or precess, in space or can cause the planet to wobble slightly. Once these perturbations have been calculated one can closely determine its position for any future date over long periods of time. Modern methods for computing the orbit of a planet or other body have been refined from methods developed by Newton, Laplace, and Gauss, in which all the needed quantities are acquired from three separate observations of the planet's apparent position.

Nonplanetary Orbits

The laws of planetary orbits also apply to the orbits of comets, natural satellites, artificial satellites, and space probes. The orbits of comets are very elongated; some are long ellipses, some are nearly parabolic (see parabola), and some may be hyperbolic. When the orbit of a newly discovered comet is calculated, it is first assumed to be a parabola and then corrected to its actual shape when more measured positions are obtained. Natural satellites that are close to their primaries tend to have nearly circular orbits in the same plane as that of the planet's equator, while more distant satellites may have quite eccentric orbits with large inclinations to the planet's equatorial plane. Because of the moon's proximity to the earth and its large relative mass, the earth-moon system is sometimes considered a double planet. It is the center of the earth-moon system, rather than the center of the earth itself, that describes an elliptical orbit around the sun in accordance with Kepler's laws. All of the planets and most of the satellites in the solar system move in the same direction in their orbits, counterclockwise as viewed from the north celestial pole; some satellites, probably captured asteroids, have retrograde motion, i.e., they revolve in a clockwise direction.

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or·bit / ˈôrbit/ • n. 1. the curved path of a celestial object or spacecraft around a star, planet, or moon, esp. a periodic elliptical revolution. ∎  one complete circuit around an orbited body. ∎  the state of being on or moving in such a course: the earth is in orbit around the sun. ∎  the path of an electron around an atomic nucleus. 2. a sphere of activity, interest, or application: he moved into the orbit of two great anticommunist socialists of the 1940s and 1950s. 3. Anat. the cavity in the skull of a vertebrate that contains the eye; the eye socket. ∎  the area around the eye of a bird or other animal. • v. (-bit·ed, -bit·ing) [tr.] (of a celestial object or spacecraft) move in orbit around (a star, planet, or moon): Mercury orbits the Sun. ∎  [intr.] fly or move around in a circle: the mobile's disks spun and orbited slowly. ∎  put (a satellite) into orbit. PHRASES: into orbit inf. into a state of heightened performance, activity, anger, or excitement: his goal sent the fans into orbit.

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orbitacquit, admit, backlit, bedsit, befit, bit, Brit, Britt, chit, commit, demit, dit, emit, fit, flit, frit, git, grit, hit, intermit, it, kit, knit, legit, lickety-split, lit, manumit, mishit, mitt, nit, omit, outsit, outwit, permit, pit, Pitt, pretermit, quit, remit, retrofit, shit, sit, skit, slit, snit, spit, split, sprit, squit, submit, tit, transmit, twit, whit, wit, writ, zit •albeit, howbeit •poet •bluet, cruet, intuit, suet, Yuit •Inuit • floruit • Jesuit •Babbitt, cohabit, habit, rabbet, rabbit •ambit, gambit •jackrabbit • barbet • Nesbit • rarebit •adhibit, exhibit, gibbet, inhibit, prohibit •titbit (US tidbit) • flibbertigibbet •Cobbett, gobbet, hobbit, obit, probit •orbit • Tobit •cubit, two-bit •hatchet, latchet, ratchet •Pritchett •crotchet, rochet

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orbit
1. The bony socket of the eye.

2. The path described by a body moving around another under gravitational attraction. See EQUATORIAL ORBIT; GEOSTATIONARY ORBIT; GEOSYNCHRONOUS ORBIT; POLAR ORBIT; and SUN-SYNCHRONOUS ORBIT.

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orbit Path of a celestial body in a gravitational field. The path is usually a closed one about the focus of the system to which it belongs, as with those of the planets around the Sun. Most celestial orbits are elliptical, although the eccentricity can vary greatly. It is rare for an orbit to be parabolic or hyperbolic.

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orbit eye-socket XVI; path of a heavenly body XVII. — L. orbita wheel-track, course, path (of the moon), in medL. eye-cavity, sb. use of fem. of orbitus circular, f. orbis, orb- ORB.

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orbit (or-bit) n. the cavity in the skull that contains the eye. It is formed from parts of the frontal, sphenoid, zygomatic, lacrimal, ethmoid, palatine, and maxillary bones.