Apsis



An apsis (ἁψίς; plural apsides, Greek: ἁψίδες) is an extreme point in an object's orbit. The word comes via Latin from Greek and is cognate with apse. For elliptic orbits about a larger body, there are two apsides, named with the prefixes peri-  and ap-, or apo-  added to a reference to 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.
 * 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 objects in Lunar orbit, the point of least distance is the pericynthion and the greatest distance the apocynthion.
 * 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 refer to 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 $$ v_\mathrm{per} = \sqrt{ \tfrac{(1+e)\mu}{(1-e)a} } \,$$ at minimum (pericenter) distance $$r_\mathrm{per}=(1-e)a\!\,$$
 * Apocenter: minimum speed $$ v_\mathrm{ap} = \sqrt{ \tfrac{(1-e)\mu}{(1+e)a} } \,$$ at maximum (apocenter) distance $$r_\mathrm{ap}=(1+e)a\!\,$$

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 $$h = \sqrt{(1-e^2)\mu a}$$
 * specific orbital energy $$\varepsilon=-\frac{\mu}{2a}$$

where:
 * a is the semi-major axis, equal to $$\frac{r_\mathrm{per}+r_\mathrm{ap}}{2}$$
 * μ is the standard gravitational parameter
 * e is the eccentricity, defined as
 * $$e=\frac{r_\mathrm{ap}-r_\mathrm{per}}{r_\mathrm{ap}+r_\mathrm{per}}=1-\frac{2}{\frac{r_\mathrm{ap}}{r_\mathrm{per}}+1}$$

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
 * $$\sqrt{-2\varepsilon}=\sqrt{\frac{\mu}{a}}$$

which is the speed of a body in a circular orbit whose radius is $$a$$.

Terminology
The words "pericenter" and "apocenter" are often seen, although periapsis/apoapsis are preferred in technical usage.

Various related terms are used for other celestial objects. The '-gee', '-helion' and '-astron' and '-galacticon' forms are frequently used in the astronomical literature when referring to the Earth, Sun, stars and the Galactic Center respectively. -jove is occasionally used, while '-saturnium' has very rarely been used in the last 50 years. The '-gee' form is commonly used as a generic 'closest approach to planet' term instead of specifically applying to the Earth. During the Apollo program, the terms pericynthion and apocynthion (referencing Cynthia, an alternative name for the Greek Moon goddess Artemis) were used when referring to the Moon. Regarding black holes, the term peri/apomelasma (from a Greek root) was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon (from a Latin) appeared in the scientific literature in 2002.

Terminology graph
The following suffixes are added to peri- and apo- to form the terms for the nearest and farthest orbital distances from these objects.

Perihelion and aphelion of the Earth
For the orbit of the Earth around the Sun, the time of apsis is often expressed in terms of a time relative to seasons, since this determines the contribution of the elliptical orbit to seasonal variations. The variation of the seasons is primarily controlled by the annual cycle of the elevation angle of the Sun, which is a result of the tilt of the axis of the Earth measured from the plane of the ecliptic. The Earth's eccentricity and other orbital elements are not constant, but vary slowly due to the perturbing effects of the planets and other objects in the solar system. See Milankovitch cycles.

Currently, the Earth reaches perihelion in early January, approximately 14 days after the December Solstice. At perihelion, the Earth's center is about $0.983$ astronomical units (AU) or 147,098,070 km from the Sun's center.

The Earth reaches aphelion currently in early July, approximately 14 days after the June Solstice. The aphelion distance between the Earth's and Sun's centers is currently about $1.017 AU$ or 152,097,700 km.

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 apsidal precession. (This is closely related to the precession of the axis.)

Astronomers commonly 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 pericenter. For the orbit of the Earth, this is called the longitude of perihelion, and in 2000 was about 282.895°. By the year 2010, this had advanced by a small fraction of a degree to about 283.067°.

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 table shows the distances of the planets and dwarf planets from the Sun at their 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 (green dot) and aphelion (red dot) points of the inner and outer planets.