celestial mechanics - History of celestial mechanics, Examples of problems

The study of the motions of celestial objects in gravitational fields. Founded by Isaac Newton, it deals with satellite and planetary motion within the Solar System, using Newtonian gravitational theory.

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Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects.

History of celestial mechanics

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 years.

Ancient civilizations

The Ancient Babylonians had no mechanistic theories regarding celestial motions, but recognized repeating patterns in the motion of the sun, moon, and planets.

Imperial Chinese astrologers also observed and tabulated positions of planets and guest stars which can refer to either a comet or a nova.

The Classical Greek writers speculated widely regarding celestial motions, and presented many mechanisms for the motions of the planets.

Claudius Ptolemy

Claudius Ptolemy was an ancient astronomer and astrologer in early Imperial Roman times who wrote a book on astronomy now called the Almagest.

Johannes Kepler

Johannes Kepler was the first to develop the modern laws of planetary orbits, which he did by carefully analyzing the planetary observations made by Tycho Brahe.

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.

Isaac Newton

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.

Using Newton's law of gravitation, proving Kepler's Laws for the case of a circular orbit is simple.

Albert Einstein

After Einstein explained the anomalous precession of Mercury's perihelion, astronomers recognized that Newtonian mechanics did not provide the highest accuracy.

Examples of problems

Celestial motion without additional forces such as thrust of a rocket, is governed by gravitational acceleration of masses due to other masses.

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. 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.

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. = 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.

Perturbation theory

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.