# Apsis

Apsis (Greek: ἁψίς; plural apsides /ˈæpsɪdz/, Greek: ἁψῖδες; "orbit") denotes either of the two extreme points (i.e., the farthest or nearest point) in the orbit of a planetary body about its primary body (or simply, "the primary"). The plural term, "apsides," usually implies both apsis points (i.e., farthest and nearest); apsides can also refer to the distance of the extreme range of an object orbiting a host body. For example, the apsides of Earth's orbit of the Sun are two: the apsis for Earth's farthest point from the Sun, dubbed the aphelion; and the apsis for Earth's nearest point, the perihelion (see top figure). (The term "apsis", a cognate with apse, comes via Latin from Greek).[1]

There are two apsides in any elliptic orbit. Each is named by selecting the appropriate prefix: ap-, apo- (from ἀπ(ό), (ap(o)-), meaning 'away from'), or peri- (from περί (peri-), meaning 'near') — then joining it to the reference suffix of the "host" body being orbited. (For example, the reference suffix for Earth is -gee, hence apogee and perigee are the names of the apsides for the Moon, and any other (man-made) satellites of the Earth. The suffix for the Sun is -helion, hence aphelion and perihelion are the names of the apsides for the Earth and for the Sun's other planets, comets, asteroids, etc., (see table, top figure).)

According to Newton's laws of motion all periodic orbits are ellipses, including: 1) the single orbital ellipse, where the primary body is fixed at one focus point and the planetary body orbits around that focus (see top figure); and 2) the two-body system of interacting elliptic orbits: both bodies orbit their joint center of mass (or barycenter), which is located at a focus point that is common to both ellipses, (see second figure). For such a two-body system, when one mass is sufficiently larger than the other, the smaller ellipse (of the larger body) around the barycenter comprises one of the orbital elements of the larger ellipse (of the smaller body).

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, compared to the larger mass, the smaller mass is negligible (e.g., for satellites), then the orbital parameters are independent of the smaller mass.

When used as a suffix—that is, -apsis—the term can refer to the two distances from the primary body to the orbiting body when the latter is located: 1) at the periapsis point, or 2) at the apoapsis point (compare both graphics, second figure). The line of apsides denotes the distance of the line that joins the nearest and farthest points across an orbit; it also refers simply to the extreme range of an object orbiting a host body (see top figure; see third figure).

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).

## Terminology

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

• For generic situations where the primary is not specified, the terms pericenter and apocenter are used for naming the extreme points of orbits (see table, top figure); periapsis and apoapsis (or apapsis) are equivalent alternatives, but these terms, frequently, also refer to distances—that is, the smallest and largest distances between the orbiter and its host body, (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] when discussing orbits around other stars the terms become periastron and apastron.
• When discussing a satellite of Earth, including the Moon, the point of least distance is the perigee (/ˈpɛrɪ/), and of greatest distance, the apogee, (from Ancient Greek: Γῆ (), "land" or "earth").
• There are no natural satellites of the Moon. For man-made objects in lunar orbit, the point of least distance may be called the pericynthion (/ˌpɛrɪˈsɪnθiən/) and the greatest distance the apocynthion (/ˌæpəˈsɪnθiən/); or perilune and apolune are sometimes used.[3]

### Etymology

The words perihelion and aphelion were coined by Johannes Kepler[4] 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).[5]

Various related terms are used for other celestial objects. The suffixes -gee, -helion, -astron and -galacticon 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, but -saturnium has very rarely been used in the last 50 years for Saturn. The -gee form is also used as a generic closest-approach-to "any planet" term—instead of applying it only to Earth.

During the Apollo program, the terms pericynthion and apocynthion were used when referring to orbiting the Moon; they reference Cynthia, an alternative name for the Greek Moon goddess Artemis.[6] Regarding black holes, the terms perimelasma and apomelasma (from a Greek root) were used by physicist and science-fiction author Geoffrey A. Landis in a 1998 story;[7] which occurred before perinigricon and aponigricon (from Latin) appeared in the scientific literature in 2002,[8] and before peribothron (from Greek bothros, meaning hole or pit) in 2015.[9]

### Terminology summary

The suffixes shown below may be added to prefixes peri- or apo- to form unique names of apsides for the orbiting bodies of the indicated host/(primary) system. However, only for the Earth and Sun systems are the unique suffixes commonly used. Typically, for other host systems the generic suffix, -apsis, is used instead.[10].

 Astronomical host object Suffix Originof the name Sun Mercury Venus Earth Moon Mars Ceres Jupiter Saturn -⁠helion -⁠hermion -⁠cythe -⁠gee -⁠lune[3] -⁠cynthion-⁠selene[3] -⁠areion -⁠demeter[11] -⁠jove -⁠chron[3] -⁠kronos -⁠saturnium-⁠krone[12] Helios Hermes Cytherean Gaia LunaCynthiaSelene Ares Demeter ZeusJupiter CronosSaturn
 Astronomical host object Suffix Originof the name Star Galaxy Barycenter Black hole -⁠astron -⁠galacticon -⁠center-⁠focus-⁠apsis -⁠melasma-⁠bothron-⁠nigricon Lat: astra; stars Gr: galaxias; galaxy Gr: melos; blackGr: bothros; holeLat: niger; black

## Perihelion and aphelion

The perihelion (q) and aphelion (Q) are the nearest and farthest points respectively of a body's direct orbit around the Sun. For a general introduction on the term apsides, the two extreme points of an astronomical object's orbit, see § top

### Inner planets and outer planets

The image below-left features the inner planets: their orbits, orbital nodes, and the points of perihelion (green dot) and aphelion (red dot), as seen from above Earth's northern pole and Earth's ecliptic plane, which is coplanar with Earth's orbital plane. From this orientation, the planets are situated outward from the Sun as Mercury, Venus, Earth, and Mars, with all planets travelling their orbits counterclockwise around the Sun. The reference Earth-orbit is colored yellow and represents the orbital plane of reference. For Mercury, Venus, and Mars, the section of orbit tilted above the plane of reference is here shaded blue; the section below the plane is shaded violet/pink.

The image below-right shows the outer planets: the orbits, orbital nodes, and the points of perihelion (green dot) and aphelion (red dot) of Jupiter, Saturn, Uranus, and Neptune—as seen from above the reference orbital plane, all travelling their orbits counterclockwise. For each planet the section of orbit tilted above the reference orbital plane is colored blue; the section below the plane is violet/pink.

The two orbital nodes are the two end points of the "line of nodes" where a tilted orbit intersects the plane of reference;[13] here they may be 'seen' where the blue section of an orbit becomes violet/pink.

The two images below show the positions of perihelion (q) and the aphelion (Q) in the orbits of the planets of the Solar System.[1]

The reference average distance from Sun to Earth is defined as one astronomical unit, AU. Per this reference, Mars averages slightly more than 1.5 AU from the Sun; Saturn averages almost 10 AU; and Neptune about 30 AU (see chart below)

### Lines of apsides

The chart shows the extreme range—from the closest approach (perihelion) to farthest point (aphelion)—of several orbiting celestial bodies of the Solar System: the planets, the known dwarf planets, including Ceres, and Halley's Comet. The thickness of a vertical line or bar, or the length of a horizontal bar: both correspond to the extreme range of the orbit of the indicated body around the Sun. These extreme distances (between perihelion and aphelion) are the lines of apsides of the orbits of various objects around a host body.

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.

Note, for the reference average distance (one AU) of the Earth from the Sun, Mars averages more than 1.5 AU from the Sun; Saturn almost 10 AU; and Neptune about 30 AU.

### Earth perihelion and aphelion

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.[14] 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).[15]

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,[16] 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.[17] 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°.[18]

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:[19]

Year Perihelion Aphelion
DateTime (UT) DateTime (UT)
2007 January 319:43 July 623:53
2008 January 223:51 July 407:41
2009 January 415:30 July 401:40
2010 January 300:09 July 611:30
2011 January 318:32 July 414:54
2012 January 500:32 July 503:32
2013 January 204:38 July 514:44
2014 January 411:59 July 400:13
2015 January 406:36 July 619:40
2016 January 222:49 July 416:24
2017 January 414:18 July 320:11
2018 January 305:35 July 616:47
2019 January 305:20 July 422:11
2020 January 507:48 July 411:35
 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.[20]

Type of bodyBodyDistance from Sun at perihelionDistance from Sun at aphelion
Planet Mercury46,001,009 km (28,583,702 mi)69,817,445 km (43,382,549 mi)
Venus107,476,170 km (66,782,600 mi)108,942,780 km (67,693,910 mi)
Earth147,098,291 km (91,402,640 mi)152,098,233 km (94,509,460 mi)
Mars206,655,215 km (128,409,597 mi)249,232,432 km (154,865,853 mi)
Jupiter740,679,835 km (460,237,112 mi)816,001,807 km (507,040,016 mi)
Saturn1,349,823,615 km (838,741,509 mi)1,503,509,229 km (934,237,322 mi)
Uranus2,734,998,229 km (1.699449110×109 mi)3,006,318,143 km (1.868039489×109 mi)
Neptune4,459,753,056 km (2.771162073×109 mi)4,537,039,826 km (2.819185846×109 mi)
Dwarf planet Ceres380,951,528 km (236,712,305 mi)446,428,973 km (277,398,103 mi)
Pluto4,436,756,954 km (2.756872958×109 mi)7,376,124,302 km (4.583311152×109 mi)
Haumea5,157,623,774 km (3.204798834×109 mi)7,706,399,149 km (4.788534427×109 mi)
Makemake5,671,928,586 km (3.524373028×109 mi)7,894,762,625 km (4.905578065×109 mi)
Eris5,765,732,799 km (3.582660263×109 mi)14,594,512,904 km (9.068609883×109 mi)

## Mathematical formulae

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 ${\displaystyle a}$.

## References

1. "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 , pronouncing the "p" and "h" in separate syllables. However, the pronunciation /əˈfliən/ 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 , page 26.) Many dictionaries give both pronunciations
3. "Basics of Space Flight". NASA. Retrieved 30 May 2017.
4. Klein, Ernest, A Comprehensive Etymological Dictionary of the English Language, Elsevier, Amsterdam, 1965. (Archived version)
5. Since the Sun, Ἥλιος in Greek, begins with a vowel, H is the long e vowel in Greek, the final o in "apo" is omitted from the prefix. The pronunciation "Ap-helion" is given in many dictionaries , pronouncing the "p" and "h" in separate syllables. However, the pronunciation /əˈfliən/ 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 , page 26.) Many dictionaries give both pronunciations
6. "Apollo 15 Mission Report". Glossary. Retrieved October 16, 2009.
7. Perimelasma, by Geoffrey Landis, first published in Asimov's Science Fiction, January 1998, republished at Infinity Plus
8. 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)
9. Koberlein, Brian (2015-03-29). "Peribothron – Star makes closest approach to a black hole". briankoberlein.com. Retrieved 2018-01-10.
10. "MAVEN » Science Orbit".
11. "Dawn Journal: 11 Years in Space". www.planetary.org.
12. https://ui.adsabs.harvard.edu/abs/2009JGRA..114.3215C/abstract
13. Darling, David. "line of nodes". The Encyclopedia of Astrobiology, Astronomy, and Spaceflight. Retrieved May 17, 2007.
14. "Perihelion, Aphelion and the Solstices". timeanddate.com. Retrieved 2018-01-10.
15. "Variation in Times of Perihelion and Aphelion". Astronomical Applications Department of the U.S. Naval Observatory. 2011-08-11. Retrieved 2018-01-10.
16. "Solar System Exploration: Science & Technology: Science Features: Weather, Weather, Everywhere?". NASA. Retrieved 2015-09-19.
17. "Earth at Aphelion". Space Weather. July 2008. Retrieved 7 July 2015.
18. "Data.GISS: Earth's Orbital Parameters". data.giss.nasa.gov.
19. "Solex by Aldo Vitagliano". Retrieved 2018-01-10. (calculated by Solex 11)
20. "NASA planetary comparison chart". Archived from the original on 2016-08-04. Retrieved 2016-08-04.
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