|
The apsis (Greek ἁψίς), plural apsides (; Greek: ἁψίδες) is an extreme point in an object's orbit. The word comes via Latin from Greek from the word apse.〔http://dictionary.reference.com/browse/apsis〕 For elliptic orbits about a larger body, there are two apsides, named with the prefixes ''peri-'' () and ''ap-'', or ''apo-'', () added to a description of the thing being orbited. * For a body orbiting the Sun the point of least distance is the perihelion () and the point of greatest distance is the aphelion ();〔This is the pronunciation given in the Oxford English Dictionary () and other major English dictionaries, and is based on the usual pronunciation of scientific words derived from Greek. However, the pronunciation is often met, and is based on the misunderstanding that the elements ἀπό + ἥλιος remain separate.〕 * The terms become periastron and apastron when discussing orbits around other stars. * For any satellite of Earth including the Moon the point of least distance is the perigee () and greatest distance the apogee. * For any orbits around a center of mass, there are the terms pericenter and apocenter. Periapsis and apoapsis (or apapsis) are equivalent alternatives. A straight line connecting the pericenter and apocenter is the ''line of apsides''. This is the major axis of the ellipse, its greatest diameter. For a two-body system the center of mass of the system lies on this line at one of the two foci of the ellipse. When one body is sufficiently larger than the other it may be taken to be at this focus. However whether or not this is the case, both bodies are in similar elliptical orbits each having one focus at the system's center of mass, with their respective lines of apsides being of length inversely proportional to their masses. Historically, in geocentric systems, apsides were measured from the center of the Earth. However, in the case of the Moon, the center of mass of the Earth–Moon system, or Earth–Moon barycenter, as the common focus of both the Moon's and Earth's orbits about each other, is about 74% of the way from Earth's center to its surface. In orbital mechanics, the apsis technically refers to the distance measured between the centers of mass of the central and orbiting body. However, in the case of spacecraft, the family of terms are commonly used to describe the orbital altitude of the spacecraft from the surface of the central body (assuming a constant, standard reference radius). ==Mathematical formulae== These formulae characterize the pericenter and apocenter of an orbit: * Pericenter: maximum speed at minimum (pericenter) distance * Apocenter: minimum speed at maximum (apocenter) distance while, in accordance with Kepler's laws of planetary motion (based on the conservation of angular momentum) and the conservation of energy, these two quantities are constant for a given orbit: * specific relative angular momentum * specific orbital energy where: * is the semi-major axis, equal to * is the standard gravitational parameter * is the eccentricity, defined as Note that for conversion from heights above the surface to distances between an orbit and its primary, the radius of the central body has to be added, and conversely. The arithmetic mean of the two limiting distances is the length of the semi-major axis . The geometric mean of the two distances is the length of the semi-minor axis . The geometric mean of the two limiting speeds is which is the speed of a body in a circular orbit whose radius is . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Apsis」の詳細全文を読む スポンサード リンク
|