Хэрэглэгч:Timur/Ноорог/Тэнгэрийн механик

Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. It is distinguished from astrodynamics, which is the study of the creation of artificial satellite orbits.

Түүх

Although modern analytic celestial mechanics starts 400 years ago with Isaac Newton, prior studies addressing the problem of planetary positions are known going back perhaps 3,000 or more years.

Classical Greek writers speculated widely regarding celestial motions, and presented many geometrical mechanisms to model the motions of the planets. Their models employed combinations of uniform circular motion and were centered on the earth. An independent philosophical tradition was concerned with the physical causes of such circular motions. An extraordinary figure among the ancient Greek astronomers is Aristarchus of Samos (310 BC - c.230 BC), who suggested a heliocentric model of the universe and attempted to measure Earth's distance from the Sun.

Клаудиус Птолемей

Claudius Ptolemy was an ancient astronomer and astrologer in early Imperial Roman times who wrote several books on astronomy. The most significant of these was the Almagest, which remained the most important book on predictive geometrical astronomy for some 1400 years. Ptolemy selected the best of the astronomical principles of his Greek predecessors, especially Hipparchus, and appears to have combined them either directly or indirectly with data and parameters obtained from the Babylonians. Although Ptolemy relied mainly on the work of Hipparchus, he introduced at least one idea, the equant, which appears to be his own, and which greatly improved the accuracy of the predicted positions of the planets. Although his model was extremely accurate, it relied solely on geometrical constructions rather than on physical causes; Ptolemy did not use celestial mechanics.

Иоганн Кеплер

Johannes Kepler was the first to closely integrate the predictive geometrical astronomy, which had been dominant from Ptolemy to Copernicus, with physical concepts to produce a New Astronomy, Based upon Causes, or Celestial Physics.... His work led to the modern laws of planetary orbits, which he developed using his physical principles and the planetary observations made by Tycho Brahe. Kepler's model greatly improved the accuracy of predictions of planetary motion, years before Isaac Newton had even developed his law of gravitation.

See Kepler's laws of planetary motion and the Keplerian problem for a detailed treatment of how his laws of planetary motion can be used.

Исаак Ньютон

Isaac Newton is credited with introducing the idea that the motion of objects in the heavens, such as planets, the Sun, and the Moon, and the motion of objects on the ground, like cannon balls and falling apples, could be described by the same set of physical laws. In this sense he unified celestial and terrestrial dynamics. Using Newton's law of gravitation, proving Kepler's Laws for the case of a circular orbit is simple. Elliptical orbits involve more complex calculations, which Newton included in his Principia.

Жозеф-Луй Лагранж

After Newton, Lagrange attempted to solve the three-body problem, analyzed the stability of planetary orbits, and discovered the existence of the Lagrangian points. Lagrange also reformulated the principles of classical mechanics, emphasizing energy more than force and developing a method to use a single polar coordinate equation to describe any orbit, even those that are parabolic and hyperbolic. This is useful for calculating the behaviour of planets and comets and such. More recently, it has also become useful to calculate spacecraft trajectories.

Альберт Эйнштейн

After Einstein explained the anomalous precession of Mercury's perihelion, astronomers recognized that Newtonian mechanics did not provide the highest accuracy. Today, we have binary pulsars whose orbits not only require the use of General Relativity for their explanation, but whose evolution proves the existence of gravitational radiation, a discovery that led to a Nobel prize.

Бодлогуудын жишээ

Celestial motion without additional forces such as thrust of a rocket, is governed by gravitational acceleration of masses due to other masses. A simplification is the n-body problem, where we assume n spherically symmetric masses, and integration of the accelerations reduces to summation.

Examples:

• 4-body problem: spaceflight to Mars (for parts of the flight the influence of one or two bodies is very small, so that there we have a 2- or 3-body problem; see also the patched conic approximation)
• 3-body problem:
  • quasi-satellite
  • spaceflight to, and stay at a Lagrangian point

In the case that n=2 (two-body problem), the situation is much simpler than for larger n. Various explicit formulas apply, where in the more general case typically only numerical solutions are possible. It is a useful simplification that is often approximately valid.

Examples:

• a binary star, e.g. Alpha Centauri (approx. the same mass)
• a binary asteroid, e.g. 90 Antiope (approx. the same mass)

A further simplification is based on "standard assumptions in astrodynamics", which include that one body, the orbiting body, is much smaller than the other, the central body. This is also often approximately valid.

Examples:

• Solar system orbiting the center of the Milky Way
• a planet orbiting the Sun
• a moon orbiting a planet
• a spacecraft orbiting Earth, a moon, or a planet (in the latter cases the approximation only applies after arrival at that orbit)

Either instead of, or on top of the previous simplification, we may assume circular orbits, making distance and orbital speeds, and potential and kinetic energies constant in time. Notable examples where the eccentricity is high and hence this does not apply are:

• the orbit of the dwarf planet Pluto, ecc. = 0.2488
• the orbit of Mercury, ecc. = 0.2056
• Hohmann transfer orbit
• Gemini 11 flight
• suborbital flights

Of course, in each example, to obtain more accuracy a less simplified version of the problem can be considered.

Хөндөлтийн онол

Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem.

Мөн үзэх

• Astrometry is a part of astronomy that deals with the positions of stars and other celestial bodies, their distances and movements.
• Astrodynamics is the study and creation of orbits, especially those of artificial satellites.
• Orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity.
• Orbital elements are the parameters needed to specify a Newtonian two-body orbit uniquely.
• Osculating orbit is the gravitational Keplerian orbit about a central body that an object would have if other perturbations were not present.
• Satellite is an object that orbits another object (known as its primary). The term is often used to describe an artificial satellite (as opposed to natural satellites, or moons). The common noun moon (not capitalized) is used to mean any natural satellite of the other planets.
• Celestial navigation is a position fixing technique that was the first system devised to help sailors locate themselves on a featureless ocean.
• VSOP82 and VSOP87 are two versions of a mathematical theory for the orbits and positions of the major planets to the highest possible accuracy.

Гадны линкүүд

• Calvert, James B. (2003-03-28). "Celestial Mechanics" (English хэлээр). University of Denver. Татаж авсан: 2006-08-21.{{cite web}}: CS1 maint: unrecognized language (link)

Research

• Marshall Hampton's research page: Central configurations in the n-body problem

Artwork

• Celestial Mechanics is a Planetarium Artwork created by D. S. Hessels and G. Dunne

Course notes

• Professor Tatum's course notes at the University of Victoria

Ном хэвлэл

• Asger Aaboe, Episodes from the Early History of Astronomy, 2001, Springer-Verlag, ISBN 0-387-95136-9
• Forest R. Moulton, Introduction to Celestial Mechanics, 1984, Dover, ISBN 0-486-64687-4
• John E.Prussing, Bruce A.Conway, Orbital Mechanics, 1993, Oxford Univ.Press
• William M. Smart, Celestial Mechanics, 1961, John Wiley. (Hard to find, but a classic)
• J. M. A. Danby, Fundamentals of Celestial Mechanics, 1992, Willmann-Bell.