Apsis

As apse ( Greek " curvature ", plural apses ) is called the two main peaks on the elliptical orbit of a celestial body. Apoapsis is the point with the greatest distance to the main body and the least with the periapsis. Since the ellipse has exactly two main peaks, the term is usually used in the plural.

• 2.1 eccentricity and apse distance
• 2.2 apses and apsides
• 2.3 Railway ellipses and barycenter
• 2.4 perturbations

• 3.1 perihelion of the Earth-Moon center of gravity
• 3.2 perihelion of Erdmittelpunkts

Word origin and derived terms

Apse is the Greek word for " buckle, bow" and is derived from the term apse architecture, apo- and peri- are the prefixes " far" and " close ".

Main body: Ap (O) -, peri-

For the main body of the sun, earth, moon and stars have the apses own names, which are derived from the corresponding Greek:

• Hel - to helios " sun ": The perihelion is the next sun, the aphelion (pronounced " Ap - hel " or " Afel ") of sonnenfernste point of an orbit around the sun. The earth has its perihelion passage to January 3 ( January 2 to 5, depending on the time after the last leap year) at 147.099 million kilometers, and its aphelion passage about July 5 ( 3 -6 July. ) at 152.096 million kilometers.

• - gäum to ge or gaia "earth"; see also perigee: perigee and apogee are the erdnächste or erdfernste point. For the moon differ by the markedly elliptical shape of the lunar orbit (eccentricity 0.055 ), the two distances by more than 13 percent. They amount to 356 410 and 406,740 km and the semi-major axis of 384,405 km ( for the difference see above, center of mass ).
• Artificial Satellites: For artificial satellites called the vestibules as well as the natural Earth's moon. If you give it as a height above the Earth's surface, their difference is of course more than at geocentric distances. For example, changing a 300 km high circular orbit at an eccentricity of only 0.001, the two heights change at about 235 and 365 km. Russian synchronized satellites may even have values ​​from 500 to 80,000 km, and a so-called transition to the Moon even more extreme. To obtain stable satellite orbits, the perigee must be at least 200 km high due to the braking effect of the high atmosphere.

• - selenium to selene "moon ": perilune and Aposelen denote the moon or the next mondfernsten point in the path of the moon orbiting body (English is Perilune or Apolune usual ). For example, the third Lunar Orbiter (1967 ) initially had a perilune of 210 km altitude and a Aposelen from 1790 km. After 4 days, the railway was converted to 45 and 1850 km, to attract more high-resolution photos.

• - astron "star": periastron and Apoastron: The point on the orbit of a double star partner, on which it is removed at the next or most of his companions.

• - galaktikum to galaxy " Milky Way ": Perigalaktikum and Apogalaktikum are the points on the orbit of a star around the center of the Milky Way system on which it is removed from the closest or farthest.

• - jovum to Latin Jupiter: Jupiter only when one says Perijovum and Apojovum (English Peri, Apojove, from the Latin genitive Iovis for Jupiter ).

• - ares to Greek Ares: When Mars and the vestibules Periares and Apares hot after the Greek name of the planet and War God.

• More Planets: Consequently, would attach it to Peri - or apo- the Greek name of the other planets. However, as these are often not known, but is mostly paraphrased here. The definition for exoplanets in its orbit around its central star is analogous.

Other terms

Pericentre and Apozentrum (Latin centrum " axis point " ) specially designate points in a multi-body system and refer to its center of gravity, specifically the barycenter. An example is the point on the orbit of a partner in a binary star system where this is away from the center of mass of the system at the next or the furthest. If, in a general context of celestial mechanics the apses of a path the speech without a certain central body is to be specified, then they can also be referred to as the pericentre and Apozentrum, but also as Perifokus and Apofokus (Latin focus " focal point ").

The distance between system barycenter and apse is the apse distance ( Apsidendistanz ), or apse distance, so perihelion ( perihelion distance, often only briefly " perihelion " ), Apheldistanz ( Aphelabstand, " aphelion " ), Perizentrumsdistanz etc. It should be noted that " Periapsisdistanz " ( " Periapsisabstand " ) sometimes referred to as a path element the angle argument of periapsis.

The line connecting the two vestibules is the line of apsides.

Basics

Eccentricity and apse distance

The relationship between ( numerical ) eccentricity and apse distances is

Apses and apsides

The straight line through the two apses apsides is called. It corresponds to the major axis of the ellipse. For the path computation half the size of apsides is often expressed as " semi-major axis " or " average distance ".

Railway and Ellipses barycenter

If you look closer orbit data and the two Apsidendistanzen averages, sometimes striking that this average distance is different from the semi-major axis. When the main body is not substantially greater than the second, the effect of the barycenter is it made ​​clear. For it is not the center of the main body is the focus of the orbital ellipse, but the barycenter as the common center of gravity of the celestial bodies.

In the Earth-Moon system is the barycenter ( the Earth-Moon barycenter) nearly 5000 km outside of Geozentrum, ie in the region of the moon facing the Earth's mantle. The center of the earth, therefore, monthly describes an ellipse of 10,000 km in diameter.

For double stars ( see below), this effect is even much larger and can often even be detected astrometrisch. For example, a periodic change in location of the bright star Sirius was found already in 1800, but until 1862 his small companion detected optically.

In the detection of exoplanets with the radial velocity method, this effect is exploited from the radial component of motion of the host star close to the barycenter of mass and orbital period of the planet.

During the passage of a body through its periapsis it has its greatest speed rail because he up there - will revert to the Gravizentrum - due to the decreasing orbital radius; during its passage through the apoapsis its lowest rotational speed, because it moves away to get there from Gravizentrum. The angular velocity ( apparent velocity ) in circulation center varies even more, because in addition to the rushed through in the same time slot arc and the distance shortened (the radius ) - this effect is striking about in observing the daily motion of the moon or a satellite.

Perturbations

In the absence of gravity influences the other heavenly bodies and neglecting relativistic effects, a line of apses would always have the same orientation in space. Since the orbiting body is, however, usually exposed to such interference, the line of apsides is not fixed, but slowly rotates in the direction of the orbiting celestial body. This process is called Apsidendrehung. Assigns the orbit of a celestial body to an appreciable Apsidendrehung, so between his anomalistic orbital period (return to the same apse ) and its sidereal orbital period must be distinguished (return to the same position relative to the fixed star background).

The interference from other celestial bodies can not only cause the Apsidendrehung even minor short-term deformation of an orbit. The largest and the smallest distance between these deformed sheet from the main body will be in slightly different locations are as the vestibules of the unperturbed orbit. This affects both the timing of Apsidendurchläufe and the apse distances concerned.

Perihelion and Apheldurchgang Earth

The earth has over moonless planet on the peculiarity that it is not the center of the Earth, which orbits the sun on a Keplerian ellipse, but the focus of the Earth- Moon system. While this focus is still within the earth - in about 1700 km depth - but about 4670 km from the center of the earth. While the focus of the Kepler ellipse follows the center of the earth orbits the center of gravity at an average distance of about 4670 km, and performs a sinuous line to the Kepler ellipse.

Perihelion of the Earth-Moon center of gravity

The focus of the perihelion passes each in mean time intervals of one anomalistic year, ie 365 days, and a good six hours. At the end of a calendar year of 365 days, the focus therefore needs another six hours to reach the perihelion again. Therefore, each perihelion place at a later to about six hours time occur until after four years of a leap advances the perihelion again one day (compare similar patterns at the beginning of all seasons. ) However, since the leap year scheme adapted to the calendar the tropical year, and not synchronize with the longer by about 25 minutes anomalistic year, the perihelion moves over the long term through the calendar.

The table shows the annual accruing late and jumping back after a leap year ( bold) are clearly visible. The remaining deviations from a strict regularity are due to the gravitational influences of the other planets, which deform the Earth's orbit slightly, so that the exact position of the sun next point always moves a little back and forth.

Perihelion of Erdmittelpunkts

The center of the earth performs the aforementioned shaft line to the Kepler ellipse around the center of gravity. The smallest distance of the sun Erdmittelpunkts therefore arises during passage through the perihelion of the gravity path nearest waves " tal ". Those described above, caused by the leap year cycle and the planetary disturbances fluctuations in the Perihelzeiten the center of gravity is superimposed as in the Perihelzeiten of Erdmittelpunkts an additional significant variation.

If the center-of- perihelion approximately along with a new or full moon, so the impact on the Perihelzeiten of Erdmittelpunkts are low. If the center-of- perihelion with a first quarter together, the earth, the sun -side half of its orbit begins at this point to the center of gravity, so it is just about the sun to approach further and thus has not yet reached its own point nearest the Sun. In this case, the Mittelpunktsperihel is particularly evident late against the Schwerpunktsperihel. Conversely, the Mittelpunktsperihel is temporally precede the Schwerpunktsperihel the last quarter. The thus effected displacement may be more than one day.

The extreme Perihelzeiten for the period from 1980 to 2020 January 1, 1989 23h CET and January 5, 2020 9 am CET (see Figure Extreme perihelion positions). Due to the slow drift of the perihelion along the Earth's orbit is also the Perihelzeitpunkte will shift to later calendar data. Around the year 1600 the perihelion fell on 26 to 28 December. Around the year 2500 it will drop to around the 10 to 13 January.

The conditions described for the perihelion apply mutatis mutandis to the Apheldurchgänge of gravity and center of the Earth. The following table lists perihelion and Apheldurchgänge of Erdmittelpunkts.