Celestial mechanics

The celestial mechanics describes as a branch of astronomy, the movement of astronomical objects due to physical theories or mathematical modeling. Thus, the description of planetary motion Kepler's laws is a mathematical modeling, which was established theoretically by Newtonian mechanics in the sequence. The term astrodynamics is sometimes used interchangeably, but specifically referred to the motion of artificial bodies in the gravitational field. A separate sub-region, both through special interest as well as its complexity, is the moon theory, which deals with the motion of the moon. Creating tabular overviews of the movement of astronomical objects is called ephemeris.

History

At the beginning of celestial mechanics is the study of the classical problem of predicting the motion of the planets, which originally also sun and moon were counted. The first, subjects derive regularities from already quite precise observations of these movements were, from the 3rd millennium BC, the inhabitants of Mesopotamia, whose observations are handed in later cuneiform texts of the Babylonians and Assyrians, such as the Venus tablets of Ammi - saduqa. For their findings include the discovery of regularity in the occurrence of solar and lunar eclipses, known as the Saros cycle today. The Egyptians, in turn, was also successful in the 3rd millennium BC by observing the heliacal sunrises of Sirius a determination of the length of the tropical year 365.25 days, which in the modern era lasted until the introduction of the Gregorian calendar.

Was the next big step to the Greek. Due to development of mathematical methods and models By using geometric methods specific Eratosthenes in the 3rd century BC, the circumference of the Earth with 252,000 stadia or 50 times the distance from Alexandria and Aswan, ie 41,750 km, what the actual value ( 40,075 km at the equator ) is very close came. Hipparchus in the 2nd century BC calculated the distance of the moon with 30 Earth radii ( = 382260 km ), which is also almost coincides with today's measured average distance of 385,000 km. In addition, Hipparchus discovered based on the comparison with older measurements, the precession of the equinoxes, a phenomenon which is caused by a wobble of Earth's axis over the course of about 25,000 years.

Middle of the 2nd century the astronomical knowledge of the ancient world by Claudius Ptolemy summarized in his Mathematike syntaxis, better known under the title Almagest. This work contains the description of a worldview with a stationary earth at the center to the move to loop orbits the planet. These orbits occur by the planets move in small circles, the epicycles, the centers of the epicycles in turn run on larger circles, the deferent. This model of the world was until the time of Copernicus, so for around 1400 years, based on all practical calculations of planetary locations.

Through the work of Nicolaus Copernicus Commentariolus, already at the beginning of the 16th century, the Copernican revolution was a revolution in world view, initiated. But based on the Ptolemaic model table works were still used for the calculation of ephemerides and horoscopes. Even were the Copernican world model, as well as the Ptolemaic model, the motion of the planets on circular orbits based. That changed only by Johannes Kepler, who in his study of the orbit of Mars came from the very precise observations of Tycho Brahe to the conclusion that the planets do not move on circles, but in ellipses in one focus, the Sun is, now known as the first law of Kepler.

The jump to the physical theory, in which the kepler Bahn movements of simple statements about the acting forces between bodies would have be derived mathematically was for but not yet completed. The only succeeded Isaac Newton, who in his 1687 published work Philosophiae Naturalis Principia Mathematica ( " Mathematical Principles of Natural Philosophy " ), not only the mechanism of action of gravitation formulated, but also by the development of calculus ( which he called fluxions ) the tools and utilities provided with which resulting from the law of gravity movements were calculated. The Prinzipia Mathematica remained until the end of the 18th century authoritative standard work on celestial mechanics and physics at all.

As a result, Newton's tools have been applied, developed and refined. Thus was the beginning of the 18th century, Edmond Halley through the study of cometary orbits arrive at the conclusion that a number of previously observed comets no individual phenomena, but the periodic appearance are one and the same comet, namely the eponymous Halley 's comet, whose re- emergence he predicted success for the turn of 1758/1759. In the further development and refinement of the sky mechanical instruments that went hand in hand with the progress of mathematics, the mathematician Euler, Clairaut, and d' Alembert made ​​significant contributions through their work on the three-body problem, the perturbation theory and the lunar theory. In summary, the findings were that time in the Traité de mécanique céleste monumental work of Pierre -Simon Laplace.

The next big step was in connection with the discovery of the dwarf planet Ceres. The object was discovered by Giuseppe Piazzi on January 1, 1801 and followed a few weeks, then disappeared behind the Sun and then could not be recovered despite great efforts. Starting in September, then devoted himself to Carl Friedrich Gauss the problem, where he pursued a new approach of path computation, namely without any assumptions about shape and position of the web to make to find that Kepler ellipse that best corresponded to the present observations. These extreme value problem of the minimization of errors is now known as the method of least squares and finds numerous applications outside of celestial mechanics. Because of Gauss ' calculations Ceres could then be recovered by Franz Xaver von Zach in December 1801.

Another advance sky mechanical methods resulted from initially unexplained deviations in the position of 1781 discovered the planet Uranus from the predetermined path. After first preparing the quality of older observations cast doubt considered deviations from Newton 's law of gravitation and potential interference was examined by a hypothetical moon of Uranus, sat down in 1840 the view through that only interference from a previously undiscovered planet would the observations in a satisfactory manner can explain. It now turned a complex problem of " inverse " perturbation theory, had to be in the closed from the observed disturbances on the position of the disturbing body. Almost simultaneously to Urbain Le Verrier and John Couch Adams made ​​to its solution, and came in 1845 to the first results, but at first no attention was paid. Only when George Biddell Airy, Astronomer Royal at the time in Greenwich, stood out the similarity of the results of Le Verrier and Adams, prompted the search. Meanwhile, however, Le Verrier had the German astronomer Johann Gottfried Galle contacted and asked him to look after the presumed planet at the calculated position. Bile was then practically on 23 September 1846 a first attempt uncharted star find, which soon turned out by its movement when the newly discovered planet Neptune.

The next big step was found to be the beginning of the 20th century, again for unexplained deviations, this time in the orbit of the planet Mercury, it was in fact found that the perihelion of Mercury minimal (43 " per century ) changed, which is not going through the motions and masses of the sun and the known planets could be explained. The attempt in the usual way to connect to an unknown planet that we provisionally named the volcano and would have to move very close to the sun, but failed. Only by Albert Einstein's general theory of relativity the perihelion of Mercury could be fully explained by the mass of the Sun caused by the curvature of space. In the following decades the observation accuracy was improved so that now relativistic corrections are also involved in the movements of all the other bodies of the solar system.

The celestial mechanics of the presence finally is characterized by both new opportunities and new problems. New opportunities arose on the one hand by the use of computers, and thus a tremendous increase in available computing power. Problems that would previously have required years of computing, can now be solved in minutes utmost precision. The increase in orders of magnitude performance of modern telescopes and the availability of instruments in space do today completely new celestial mechanics phenomena visible, for example exoplanets and their orbits. Issues that were previously untreatable at best basic idea of ​​how the question of the stability of the solar system, the dynamics of the evolution of planetary systems and the origin and collisions of entire galaxies can be simulated by suitably powerful computer today.

Classical texts

• Nicolaus Copernicus De revolutionibus orbium Coelestium 1543
• Johannes Kepler 's Astronomia nova aitiologetos seu Physica coelestis 1609 and Rudolphine Tables 1627
• Isaac Newton Philosophiae Naturalis Principia Mathematica in 1687
• Edmond Halley Astronomiae Cometicae Synopsis 1705
• Pierre-Simon Laplace 's Traité de mécanique céleste 1798-1825
• Carl Friedrich Gauss Theoria motus corporum Coelestium in sectionibus conicis solem ambientium ( " theory of motion of celestial bodies that orbit the sun in conic sections " ) 1809
• Henri Poincaré Les methodes nouvelles de la mecanique celeste 1892-1899
• Carl Charlier The mechanics of the sky 1902-1907