Apsis

An apsis (Greek ἁψίς, gen. ἁψῖδος), plural apsides (; Greek: ἁψῖδες), is the point of greatest or least distance of a body from one of the foci of its elliptical orbit. In modern celestial mechanics this focus is also the center of attraction, which is usually the center of mass of the system. Historically, in geocentric systems, apsides were measured from the center of the Earth.

The point of closest approach (the point at which two bodies are the closest) is called the periapsis or pericentre, from Greek , peri, around, and κέντρον. The point of farthest excursion is called the apoapsis (, apó, "from", apocentre or apapsis [from , ap-, before an unaspirated, or , aph-, before an aspirated vowel, respectively]), (the latter term, although etymologically more correct, is much less used). A straight line drawn through the periapsis and apoapsis is the line of apsides. This is the major axis of the ellipse, the line through the longest part of the ellipse.

Derivative terms are used to identify the body being orbited. The most common are perigee () and apogee (), referring to orbits around the Earth (Greek , gê, "earth"), and perihelion () and aphelion (), referring to orbits around the Sun (Greek , hēlios, "sun"). During the Apollo program, the terms pericynthion and apocynthion were used when referring to the Moon.

Mathematical formulas

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:

where:

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 $a$. The geometric mean of the two distances is the length of the semi-minor axis $b$.

The geometric mean of the two limiting speeds is $\backslash sqrt\{-2\backslash epsilon\}$, the speed corresponding to a kinetic energy which, at any position of the orbit, added to the existing kinetic energy, would allow the orbiting body to escape (the square root of the product of the two speeds is the local escape velocity).

Terminology

Various related terms are used for other celestial objects. The '-gee', '-helion' and '-astron' and '-galacticon' forms are frequently used in the astronomical literature, while the other listed forms are occasionally used, although '-saturnium' has very rarely been used in the last 50 years. The '-gee' form is commonly (although incorrectly) used as a generic 'closest approach to planet' term instead of specifically applying to the Earth. The term peri/apomelasma (from the Greek root) was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon (from the Latin) appeared in the scientific literature in 2002.

Since "peri" and "apo" are Greek, it is considered by some purists more correct to use the Greek form for the body, giving forms such as '-zene' for Jupiter and '-krone' for Saturn. The daunting prospect of having to maintain a different word for every orbitable body in the solar system (and beyond) is the main reason why the generic '-apsis' has become the almost universal norm in cases other than the Sun and Earth.

The perihelion and aphelion of the Earth

Currently, the annual perihelion happens at about 14 days after the December Solstice, thus making January 4 the average date of perihelion. The perihelion that currently occurs in early January places the Earth at a distance of about 147,098,070 kilometers (about 91,402,500 miles) from the sun, which can also be expressed as about 0.98329 astronomical units (AU). (The eccentricity of the orbit also varies slowly over many millennia.)

Likewise, the annual aphelion that currently occurs in early July happens about 14 days after the June Solstice. At this time, the distance of the aphelion is currently about about 152,097,700 kilometers (94,509,130 miles), which can also be expressed as about 1.01671 AU.

On a very long time scale, the dates of the perihelion and of the aphelion progress through the seasons, and they make one complete cycle in 22,000 to 26,000 years. There is a corresponding movement of the position of the stars as seen from Earth that is called the precession of the orbit. (This is not the precession of the axis.)

A common thing that astronomers do is to express the timing of perihelion relative to the vernal equinox not in terms of days and hours, but rather as an angle of orbital displacement, the so-called longitude of the periapsis. For the orbit of the Earth, this is called the longitude of perihelion, and in the year 2000 was about 282.895 degrees. By the year 2010, this had advanced by a small fraction of a degree to about 283.067 degrees.

The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:

Planetary perihelion and aphelion

The following chart shows the range of distances of the planets, dwarf planets and Halley's Comet from the Sun.

The images below show the perihelion and aphelion points of the inner and outer planets.

See also

Notes and references

External links

Category:Celestial mechanics Category:Astrodynamics Category:Earth