# Apsis

(Redirected from Apoapsis)
"Apogee" redirects here. For the literary journal, see Perigee: Publication for the Arts. For other uses, see Apogee (disambiguation). For the architectural term, see Apse.
Not to be confused with Aspis.
Apsides:
Apocenter (1), Pericenter (2) and Focus (3).

An apsis (Greek ἁψίς, gen. ἁψίδος), plural apsides (; Greek: ἁψίδες), is a point of least or greatest distance of a body in an elliptic orbit about a larger body. 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. More generally, the prefixes peri- (from περί (peri), meaning "near") and ap-, or apo-, (from ἀπ(ό) (ap(ó)), meaning "away from") can be added to center (of mass) giving pericenter and apocenter. The words periapsis and apoapsis (or apapsis) are also used for these.

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

Keplerian orbital elements: point F is at the pericenter, point H is at the apocenter, and the red line between them is the line of apsides

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:

where:

• $a\!\,$ is the semi-major axis, equal to $\frac{r_\mathrm{per}+r_\mathrm{ap}}{2}$
• $\mu\!\,$ 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 $\sqrt{-2\epsilon}=\sqrt{\mu/a}$ 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 centre 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.[1] Regarding black holes, 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.[2]

### 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.

Object
All stars Other -apsis
The Sun Other stars Barycenter Galaxies
-helion Mercury Venus Earth Moon Mars Jupiter Saturn Uranus Neptune Pluto -astron -center
-focus
-galacticon
-hermion -cytherion -gee -lune
-cynthion
-selene
-areion -zene
-jove
-krone
-saturnium

## 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 0.98329 astronomical units (AU) or 147,098,070 kilometers (about 91,402,500 miles) 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 1.01671 AU or 152,097,700 kilometers (94,509,100 mi).

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 degrees. By the year 2010, this had advanced by a small fraction of a degree to about 283.067 degrees.[3]

The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:[4]

Year Perihelion Aphelion
Date Time (UT) Date Time (UT)
2007 January 3 19:43 July 6 23:53
2008 January 2 23:51 July 4 07:41
2009 January 4 15:30 July 4 01:40
2010 January 3 00:09 July 6 11:30
2011 January 3 18:32 July 4 14:54
2012 January 5 00:32 July 5 03:32
2013 January 2 04:38 July 5 14:44
2014 January 4 11:59 July 4 00:13
2015 January 4 06:36 July 6 19:40
2016 January 2 22:49 July 4 16:24
2017 January 4 14:18 July 3 20:11
2018 January 3 05:35 July 6 16:47
2019 January 3 05:20 July 4 22:11
2020 January 5 07:48 July 4 11:35

The dates and times of the perihelions and aphelions vary much more than those of the equinoxes and solstices due to the presence of the Moon. Because perihelion and aphelion are defined by the distance between the center of the Sun and the center of the Earth, the Earth's position in its monthly motion around the Earth-Moon barycenter greatly affects the time when the Earth is at its shortest or longest distance from the Sun.

## Planetary perihelion and aphelion

The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.[5]

Type of body Body Distance from Sun at perihelion Distance from Sun at aphelion
Planet Mercury 46,001,009 km (28,583,702 mi) 69,817,445 km (43,382,549 mi)
Venus 107,476,170 km (66,782,600 mi) 108,942,780 km (67,693,910 mi)
Earth 147,098,291 km (91,402,640 mi) 152,098,233 km (94,509,460 mi)
Mars 206,655,215 km (128,409,597 mi) 249,232,432 km (154,865,853 mi)
Jupiter 740,679,835 km (460,237,112 mi) 816,001,807 km (507,040,016 mi)
Saturn 1,349,823,615 km (838,741,509 mi) 1,503,509,229 km (934,237,322 mi)
Uranus 2,734,998,229 km (1.699449110×109 mi) 3,006,318,143 km (1.868039489×109 mi)
Neptune 4,459,753,056 km (2.771162073×109 mi) 4,537,039,826 km (2.819185846×109 mi)
Dwarf planet Ceres 380,951,528 km (236,712,305 mi) 446,428,973 km (277,398,103 mi)
Pluto 4,436,756,954 km (2.756872958×109 mi) 7,376,124,302 km (4.583311152×109 mi)
Makemake 5,671,928,586 km (3.524373028×109 mi) 7,894,762,625 km (4.905578065×109 mi)
Haumea 5,157,623,774 km (3.204798834×109 mi) 7,706,399,149 km (4.788534427×109 mi)
Eris 5,765,732,799 km (3.582660263×109 mi) 14,594,512,904 km (9.068609883×109 mi)

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

Distances of selected bodies of the Solar System from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively. Long bars denote high orbital eccentricity. The radius of the Sun is 0.7 million km, and the radius of Jupiter (the largest planet) is 0.07 million km, both too small to resolve on this image.

The images below show the perihelion (green dot) and aphelion (red dot) points of the inner and outer planets.