# Apsis

The apsides refer to the farthest (1) and nearest (2) points reached by an orbiting planetary body (1 and 2) with respect to a primary, or host, body (3). For the given primary (or host), the table names the (two) apsides of an orbiting body:
(1) farthest (3) host (2) nearest
apogee Earth perigee
aphelion Sun perihelion
apastron star periastron
apocenter generic pericenter
apoapsis primary periapsis
Periapsis and apoapsis as distances: the smaller, satellite body (blue) orbits the primary body (yellow); both are in elliptic orbits around their common center of mass (red +).

The term apsis (Greek: ἁψίς; plural apsides /ˈæpsɪdz/, Greek: ἁψῖδες; "orbit") refers to an extreme point in the orbit of an object. It denotes either the points on the orbit, or the respective distance of the bodies. The word comes via Latin from Greek, there denoting a whole orbit, and is cognate with apse.[1] Except for a theoretical possibility, there are two apsides in any elliptic orbit, (see discussion below, in article body); they are named with the prefixes peri- (from περί (peri), meaning 'near') and ap-, apo- (from ἀπ(ό) (ap(o)), meaning 'away from'), added in reference to the body being orbited. According to Newton's laws of motion all periodic orbits are ellipses: either the two individual ellipses of both bodies (see the two graphs in the second figure), with the center of mass (or barycenter) of this two-body system at the one common focus of the ellipses, or the orbital ellipses, with one body taken as fixed at one focus, and the other body orbiting this focus (see top figure). All these ellipses share a straight line, the line of apsides, that contains their major axes (the greatest diameter), the foci, and the vertices, and thus also the periapsis and the apoapsis (see both figures). The major axis of the orbital ellipse (top figure) is the distance of the apsides, when taken as points on the orbit, or their sum, when taken as distances.

The major axes of the individual ellipses around the barycenter, respectively the contributions to the major axis of the orbital ellipses are inverse proportional to the masses of the bodies, i.e., a bigger mass implies a smaller axis/contribution. Only when one mass is sufficiently larger than the other, the individual ellipse of the smaller body around the barycenter comprises the individual ellipse of the larger body as shown in the second figure. For remarkable asymmetry, the barycenter of the two bodies may lie well within the bigger body, e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If the smaller mass is negligible compared to the larger, then the orbital parameters are independent of the smaller mass (e.g. for satellites).

• For general orbits, the terms periapsis and apoapsis (or apapsis) are used. Pericenter and apocenter are equivalent alternatives, referring explicitly to the respective points on the orbits, whereas periapsis and apoapsis may also refer to the smallest and largest distances between the orbiter and its host, (see second figure).
• For a body orbiting the Sun, the point of least distance is the perihelion (/ˌpɛrɪˈhliən/), and the point of greatest distance is the aphelion (/æpˈhliən/).[2]
• 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 (/ˈpɛrɪ/) and greatest distance the apogee, from Ancient Greek Γῆ (), "land" or "earth".
• For objects in lunar orbit, the point of least distance is sometimes called the pericynthion (/ˌpɛrɪˈsɪnθiən/) and the greatest distance the apocynthion (/ˌæpəˈsɪnθiən/). Perilune and apolune are also used.[3]

In orbital mechanics, the apsides technically refer to the distance measured between the barycenters of the central body and orbiting body. However, in the case of a spacecraft, the terms are commonly used to refer to the orbital altitude of the spacecraft above 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, ${\textstyle v_{\text{per}}={\sqrt {\frac {(1+e)\mu }{(1-e)a}}}\,}$, at minimum (pericenter) distance, ${\textstyle r_{\text{per}}=(1-e)a}$.
Apocenter
Minimum speed, ${\textstyle v_{\text{ap}}={\sqrt {\frac {(1-e)\mu }{(1+e)a}}}\,}$, at maximum (apocenter) distance, ${\textstyle r_{\text{ap}}=(1+e)a}$.

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
${\displaystyle h={\sqrt {\left(1-e^{2}\right)\mu a}}}$
Specific orbital energy
${\displaystyle \varepsilon =-{\frac {\mu }{2a}}}$

where:

• a is the semi-major axis:
${\displaystyle a={\frac {r_{\text{per}}+r_{\text{ap}}}{2}}}$
• μ is the standard gravitational parameter
• e is the eccentricity, defined as
${\displaystyle e={\frac {r_{\text{ap}}-r_{\text{per}}}{r_{\text{ap}}+r_{\text{per}}}}=1-{\frac {2}{{\frac {r_{\text{ap}}}{r_{\text{per}}}}+1}}}$

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

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

which is the speed of a body in a circular orbit whose radius is ${\displaystyle a}$.

## 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', '-astron' and '-galacticon' forms are frequently used in the astronomical literature when referring to the Earth, Sun, stars and the Galactic Center respectively. The suffix '-jove' is occasionally used for Jupiter, while '-saturnium' has very rarely been used in the last 50 years for Saturn. 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.[4] Regarding black holes, the term peri/apomelasma (from a Greek root) was used by physicist and science-fiction author Geoffrey A. Landis in a 1998 story,[5] before peri/aponigricon (from Latin) appeared in the scientific literature in 2002,[6] as well as peri/apobothron (from Greek bothros, meaning hole or pit).[7]

### Terminology summary

The following suffixes are added to peri- and apo- to form the terms for the nearest and farthest orbital distances from these objects. For the Solar System objects, only the suffixes for the Earth and Sun are commonly used – the other suffixes are rarely used. Instead, the generic suffix of -apsis is used[8][not in citation given].

 Suffix Originof the name Astronomical object Sun Mercury Earth Moon Mars Ceres Jupiter Saturn -⁠helion -⁠hermion -⁠gee -⁠lune[3] -⁠cynthion-⁠selene[3] -⁠areion -⁠demeter[9] -⁠jove -⁠chron[3] -⁠krone -⁠saturnium Helios Hermes Gaia LunaCynthiaSelene Ares Demeter ZeusJupiter CronosSaturn
 Astronomical object Suffix Originof the name Star Galaxy Barycenter Black hole -⁠astron -⁠galacticon -⁠center-⁠focus-⁠apsis -⁠melasma-⁠bothron-⁠nigricon lat. astra: stars galaxy gr. melos: blackgr. bothros: holelat. niger: black

## Perihelion and aphelion

### Etymology

The words "perihelion" and "aphelion" were coined by Johannes Kepler[10] to describe the orbital motions of the planets around the Sun. The words are formed from the prefixes "peri-" (Greek: περί, near) and "apo-" (Greek: ἀπό, away from), affixed to the Greek word for the sun, (ἥλιος, or hēlíou).[11]

### Earth

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 km (91,402,500 mi) from the Sun's center. In contrast, 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 km (94,509,100 mi). Dates change over time due to precession and other orbital factors, which follow cyclical patterns known as Milankovitch cycles. In the short term, the dates of perihelion and aphelion can vary up to 2 days from one year to another.[12] This significant variation is due to the presence of the Moon: while the Earth–Moon barycenter is moving on a stable orbit around the Sun, the position of the Earth's center which is on average about 4,700 kilometres (2,900 mi) from the barycenter, could be shifted in any direction from it – and this affects the timing of the actual closest approach between the Sun's and the Earth's centers (which in turn defines the timing of perihelion in a given year).[13]

Because of the increased distance at aphelion, only 93.55% of the solar radiation from the Sun falls on a given area of land as does at perihelion. However, this fluctuation does not account for the seasons,[14] as it is summer in the northern hemisphere when it is winter in the southern hemisphere and vice versa. Instead, seasons result from the tilt of Earth's axis, which is 23.4 degrees away from perpendicular to the plane of Earth's orbit around the sun. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, regardless of the Earth's distance from the Sun. In the northern hemisphere, summer occurs at the same time as aphelion. Despite this, there are larger land masses in the northern hemisphere, which are easier to heat than the seas. Consequently, summers are 2.3 °C (4 °F) warmer in the northern hemisphere than in the southern hemisphere under similar conditions.[15] 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 periapsis (also called longitude of the pericenter). For the orbit of the Earth, this is called the longitude of perihelion, and in 2000 it was about 282.895°; by the year 2010, this had advanced by a small fraction of a degree to about 283.067°.[16]

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. 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.) The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:[17]

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
 PERIHELION UT TIMEZONE APHELION UT TIMEZONE P - A YEARS A - P YEARS P - P YEARS A - A YEARS 3-Jan-2007 19:43 6-Jul-2007 23:53 0.504 2-Jan-2008 23:51 4-Jul-2008 7:41 0.493 0.502 0.997 0.995 4-Jan-2009 15:30 4-Jul-2009 1:40 0.505 0.494 1.007 0.999 3-Jan-2010 0:09 6-Jul-2010 11:30 0.501 0.505 0.995 1.006 3-Jan-2011 18:32 4-Jul-2011 14:54 0.496 0.498 1.001 0.994 5-Jan-2012 0:32 5-Jul-2012 3:32 0.505 0.499 1.003 1.004 2-Jan-2013 4:38 5-Jul-2013 14:44 0.496 0.505 0.994 1.001 4-Jan-2014 11:59 4-Jul-2014 0:13 0.501 0.494 1.006 0.995 4-Jan-2015 6:36 6-Jul-2015 19:40 0.505 0.503 0.999 1.007 2-Jan-2016 22:49 4-Jul-2016 16:24 0.493 0.503 0.996 0.996 4-Jan-2017 14:18 3-Jul-2017 20:11 0.504 0.493 1.007 0.997 3-Jan-2018 5:35 6-Jul-2018 16:47 0.502 0.505 0.996 1.007 3-Jan-2019 5:20 4-Jul-2019 22:11 0.494 0.500 0.999 0.994 5-Jan-2020 7:48 4-Jul-2020 11:35 0.505 0.496 1.005 1.001

### Other planets

The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.[18]

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)
Haumea 5,157,623,774 km (3.204798834×109 mi) 7,706,399,149 km (4.788534427×109 mi)
Makemake 5,671,928,586 km (3.524373028×109 mi) 7,894,762,625 km (4.905578065×109 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, hence 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.[1]

## References

1. ^ a b "the definition of apsis". Dictionary.com.
2. ^ Since the Sun, Ἥλιος in Greek, begins with a vowel (H is considered a vowel in Greek), the final o in "apo" is omitted from the prefix. The pronunciation "Ap-helion" is given in many dictionaries [1], pronouncing the "p" and "h" in separate syllables. However, the pronunciation /əˈfliən/ [2] is also common (e.g., McGraw Hill Dictionary of Scientific and Technical Terms, 5th edition, 1994, p. 114), since in late Greek, 'p' from ἀπό followed by the 'h' from ἥλιος becomes phi; thus, the Greek word is αφήλιον. (see, for example, Walker, John, A Key to the Classical Pronunciation of Greek, Latin, and Scripture Proper Names, Townsend Young 1859 [3], page 26.) Many [4] dictionaries give both pronunciations
3. ^ a b c d "Basics of Space Flight". NASA. Retrieved 30 May 2017.
4. ^ "Apollo 15 Mission Report". Glossary. Retrieved October 16, 2009.
5. ^ Perimelasma, by Geoffrey Landis, first published in Asimov's Science Fiction, January 1998, republished at Infinity Plus
6. ^ R. Schödel, T. Ott, R. Genzel, R. Hofmann, M. Lehnert, A. Eckart, N. Mouawad, T. Alexander, M. J. Reid, R. Lenzen, M. Hartung, F. Lacombe, D. Rouan, E. Gendron, G. Rousset, A.-M. Lagrange, W. Brandner, N. Ageorges, C. Lidman, A. F. M. Moorwood, J. Spyromilio, N. Hubin, K. M. Menten (17 October 2002). "A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way". Nature. 419: 694–696. arXiv:astro-ph/0210426. Bibcode:2002Natur.419..694S. doi:10.1038/nature01121.CS1 maint: Uses authors parameter (link)
7. ^ Koberlein, Brian (2015-03-29). "Peribothron – Star makes closest approach to a black hole". briankoberlein.com. Retrieved 2018-01-10.