Apsis

{{Short description|Either of two extreme points in a celestial object's orbit}} {{Redirect-several|Apogee|Perigee|Apse}} {{Distinguish|Apse|Aspis}} {{More citations needed|date=December 2020}} {{Use mdy dates|date=July 2020}}

[[File:Apogee (PSF) mul.svg|lang=zxx|thumb|345px|The apsides refer to the farthest (2) and nearest (3) points reached by an orbiting planetary body (2 and 3) with respect to a primary, or host, body (1)]] An '''apsis''' ({{etymology|grc|''{{Wikt-lang|grc|ἁψίς}}'' ({{grc-transl|ἁψίς}})|arch, vault}} (third declension); {{plural form|'''apsides'''}} {{IPAc-en|ˈ|æ|p|s|ɪ|ˌ|d|iː|z}} {{respell|AP|sih|deez}})<ref>{{cite Dictionary.com|apsis}}</ref><ref>{{cite American Heritage Dictionary|apsis}}</ref> is the farthest or nearest point in the orbit of a planetary body about its primary body. The '''line of apsides''' (also called '''apse line,''' or '''major axis of the orbit''') is the line connecting the two extreme values.

Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to geocentric orbits, orbits around the Earth, are at the farthest point called the '''''apogee''''', and at the nearest point the '''''perigee''''', as with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named '''''aphelion''''' for the farthest and '''''perihelion''''' for the nearest point in a heliocentric orbit.<ref>{{Cite web |author1=Joe Rao |date=2023-07-06 |title=Happy Aphelion Day! Earth is at its farthest from the sun for 2023 today |url=https://www.space.com/earth-farthest-from-sun-aphelion-july-2023 |access-date=2024-04-22 |website=Space.com |language=en}}</ref> Earth's two apsides are the farthest point, ''aphelion'', and the nearest point, ''perihelion'', of its orbit around the host Sun. The terms ''aphelion'' and ''perihelion'' apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of the Solar System.

==General description== [[File:Periapsis_apoapsis.svg|thumb|upright=1.15|The two-body system of interacting elliptic orbits: The smaller, satellite body (blue) orbits the primary body (yellow); both are in elliptic orbits around their common center of mass (or barycenter), (red +). ∗Periapsis and apoapsis as distances: the smallest and largest distances between the orbiter and its host body.]]

There are two apsides in any elliptic orbit. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' ({{ety||''ἀπ(ό)'', (ap(o)-)|away from}}) for the farthest or ''peri-'' ({{ety||''περί'' (peri-)|near}}) for the closest point to the primary body, with a suffix that describes the primary body. The suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, the suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''.

According to Newton's laws of motion, all periodic orbits are ellipses. 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.<ref>{{Cite web |title=Earth-Moon Barycenter - SkyMarvels.com |url=https://www.skymarvels.com/gallery/Vid%20-%20Earth-Moon%20Barycenter.htm |access-date=2024-04-23 |website=www.skymarvels.com}}</ref> 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 barycenter of the 2-body system and the center of mass of the 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).

[[Image:Angular Parameters of Elliptical Orbit.png|thumb|upright=1.15|Keplerian orbital elements: point ''G'', the nearest point of approach of an orbiting body, is the pericenter (also periapsis) of an orbit; point ''H'', the farthest point of the orbiting body, is the apocenter (also apoapsis) of the orbit; and the red line between them is the line of apsides.]]

==Terminology== The words "pericenter" and "apocenter" are often seen, although periapsis and 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 also frequently 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'' ({{IPAc-en|ˌ|p|ɛr|ᵻ|ˈ|h|i:|l|i|ə|n}}), and the point of greatest distance is the ''aphelion'' ({{IPAc-en|æ|p|ˈ|h|i:|l|i|ə|n}});<ref name="Sun">Since the Sun, Ἥλιος in Greek, begins with a vowel (H is the long ē vowel in Greek), the final o in "apo" is omitted from the prefix. The pronunciation "Ap-helion" is given in many dictionaries [https://www.oxforddictionaries.com/definition/english/aphelion] {{Webarchive|url=https://web.archive.org/web/20151222075218/https://www.oxforddictionaries.com/definition/english/aphelion|date=December 22, 2015}}, pronouncing the "p" and "h" in separate syllables. However, the pronunciation {{IPAc-en|ə|ˈ|f|iː|l|i|ə|n}} [http://www.dictionary.com/browse/aphelion] {{Webarchive|url=https://web.archive.org/web/20170729001850/http://www.dictionary.com/browse/aphelion|date=July 29, 2017}} 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 [https://play.google.com/store/books/details?id=LuF-9HKGbl4C&rdid=book-LuF-9HKGbl4C&rdot=1] {{Webarchive|url=https://web.archive.org/web/20190921013331/https://play.google.com/store/books/details?id=LuF-9HKGbl4C&rdid=book-LuF-9HKGbl4C&rdot=1|date=September 21, 2019}}, page 26.) Many [https://www.merriam-webster.com/dictionary/aphelion] dictionaries give both pronunciations</ref> 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'' ({{IPAc-en|ˈ|p|ɛr|ᵻ|dʒ|i:}}), and of greatest distance, the ''apogee'' (from Ancient Greek: Γῆ (''Gē''), "land" or "earth").<ref>{{cite EB1911 |wstitle=Perigee |volume=21 |page=149}}</ref><ref name=Spencer_Conte_2023>{{cite book | title=Interplanetary Astrodynamics | first1=David B. | last1=Spencer | first2=Davide | last2=Conte | publisher=CRC Press | year=2023 | page=362 | isbn=9781000859744 | url=https://books.google.com/books?id=6J63EAAAQBAJ&pg=PA362 }}</ref> * For objects in lunar orbit, the point of least distance are called the ''pericynthion'' ({{IPAc-en|ˌ|p|ɛr|ɪ|ˈ|s|ɪ|n|θ|i|ə|n}}) and the greatest distance the ''apocynthion'' ({{IPAc-en|ˌ|æ|p|ə|ˈ|s|ɪ|n|θ|i|ə|n}}). The terms ''perilune'' and ''apolune'', as well as ''periselene'' and ''aposelene'' are also used.<ref name="nasaglossary">{{cite web|url=https://solarsystem.nasa.gov/basics/glossary|title=Basics of Space Flight|publisher=NASA|access-date=May 30, 2017|archive-date=September 30, 2019|archive-url=https://web.archive.org/web/20190930063643/https://solarsystem.nasa.gov/basics/glossary/|url-status=live}}</ref><ref name=Spencer_Conte_2023/> Since the Moon has no natural satellites this only applies to man-made objects.

===Etymology=== The words ''perihelion'' and ''aphelion'' were coined by Johannes Kepler<ref>Klein, Ernest, ''A Comprehensive Etymological Dictionary of the English Language'', Elsevier, Amsterdam, 1965. ([https://archive.org/stream/AComprehensiveEtymologicalDictionaryOfTheEnglishLanguageByErnestKlein/A%20Comprehensive%20Etymological%20Dictionary%20of%20the%20English%20Language%20by%20Ernest%20Klein_djvu.txt Archived version])</ref> 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 ''hēlíos'').<ref name=Sun/>

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.<ref>{{cite web | title = Apollo 15 Mission Report | work = Glossary | url = https://history.nasa.gov/alsj/a15/a15mr-f.htm | access-date = October 16, 2009 | archive-date = March 19, 2010 | archive-url = https://web.archive.org/web/20100319081116/http://history.nasa.gov/alsj/a15/a15mr-f.htm | url-status = live }}</ref> More recently, during the Artemis program, the terms ''perilune'' and ''apolune'' have been used.<ref>{{cite conference |author=R. Dendy |author2=D. Zeleznikar |author3=M. Zemba | title = NASA Lunar Exploration – Gateway's Power and Propulsion Element Communications Links | conference = 38th International Communications Satellite Systems Conference (ICSSC) | date = September 27, 2021 | location = Arlington, VA | url = https://ntrs.nasa.gov/citations/20210019019 | access-date = July 18, 2022 | archive-date = Mar 29, 2022 | archive-url=https://web.archive.org/web/20220329140256/https://ntrs.nasa.gov/citations/20210019019 | url-status = live }}</ref>

Regarding black holes, the term peribothron was first used in a 1976 paper by J. Frank and M. J. Rees,<ref>{{cite journal |author1=Frank, J. |author2=Rees, M.J. |title=Effects of massive black holes on dense stellar systems. |journal=MNRAS |volume=176 |pages=633–646 |date=September 1, 1976 |issue=6908 |doi=10.1093/mnras/176.3.633|bibcode=1976MNRAS.176..633F|doi-access=free }}</ref> who credit W. R. Stoeger for suggesting creating a term using the greek word for pit: "bothron". The terms ''perimelasma'' and ''apomelasma'' (from a Greek root) were used by physicist and science-fiction author Geoffrey A. Landis in a story published in 1998,<ref name="Asimov's">[http://www.infinityplus.co.uk/stories/perimelasma.htm ''Perimelasma''] {{Webarchive|url=https://web.archive.org/web/20190225210759/http://www.infinityplus.co.uk/stories/perimelasma.htm |date=February 25, 2019 }}, by Geoffrey Landis, first published in ''Asimov's Science Fiction'', January 1998, republished at ''Infinity Plus''</ref> thus appearing before ''perinigricon'' and ''aponigricon'' (from Latin) in the scientific literature in 2002.<ref>{{cite journal |author=R. Schödel |author2=T. Ott |author3=R. Genzel |author4=R. Hofmann |author5=M. Lehnert |author6=A. Eckart |author7=N. Mouawad |author8=T. Alexander |author9=M. J. Reid |author10=R. Lenzen |author11=M. Hartung |author12=F. Lacombe |author13=D. Rouan |author14=E. Gendron |author15=G. Rousset |author16=A.-M. Lagrange |author17=W. Brandner |author18=N. Ageorges |author19=C. Lidman |author20=A. F. M. Moorwood |author21=J. Spyromilio |author22=N. Hubin |author23=K. M. Menten |title=A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way |journal=Nature |volume=419 |pages=694–696 |date=October 17, 2002 |issue=6908 |doi=10.1038/nature01121|arxiv=astro-ph/0210426 |bibcode=2002Natur.419..694S |pmid=12384690|s2cid=4302128 }}</ref>

===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, Moon and Sun systems are the unique suffixes commonly used. Exoplanet studies commonly use ''-astron'', but typically, for other host systems the generic suffix, ''-apsis'', is used instead.<ref>{{cite web |url=http://lasp.colorado.edu/home/maven/science/science-orbit/|title=MAVEN » Science Orbit|access-date=November 7, 2018|archive-date=November 8, 2018|archive-url=https://web.archive.org/web/20181108025706/http://lasp.colorado.edu/home/maven/science/science-orbit/|url-status=live}}</ref>{{Failed verification|date=January 2019| reason=Reference is simply one example of the use of -apsis for an orbit around Mars}}  {|class="wikitable" |+ Host objects in the Solar System with named/nameable apsides |- ! Astronomical host object ! Suffix ! Origin of the name |- | Sun | {{nobr|-helion}} | Helios |- | Mercury | {{nobr|-hermion}} | Hermes |- | Venus | {{nobr|-cythe}} {{nobr|-cytherion}} | Cytherean |- | Earth | {{nobr|-gee}} | Gaia |- | Moon | {{nobr|-lune}}<ref name="nasaglossary"/> {{nobr|-cynthion}} {{nobr|-selene}}<ref name="nasaglossary"/> | Luna Cynthia Selene |- | Mars | {{nobr|-areion}} | Ares |- | Ceres | {{nobr|-demeter}}<ref>{{cite web|url=http://www.planetary.org/blogs/guest-blogs/marc-rayman/20181019-dawn-journal-11-years-in-space.html|title=Dawn Journal: 11 Years in Space|website=www.planetary.org|access-date=October 24, 2018|archive-date=October 24, 2018|archive-url=https://web.archive.org/web/20181024152511/http://www.planetary.org/blogs/guest-blogs/marc-rayman/20181019-dawn-journal-11-years-in-space.html|url-status=live}}</ref> | Demeter |- | Jupiter | {{nobr|-jove}} | Zeus Jupiter |- | Saturn | {{nobr|-chron}}<ref name="nasaglossary"/> {{nobr|-kronos}} {{nobr|-saturnium}} {{nobr|-krone}}<ref>{{Cite journal|url=https://ui.adsabs.harvard.edu/abs/2009JGRA..114.3215C/abstract|title=Goniopolarimetric study of the revolution 29 perikrone using the Cassini Radio and Plasma Wave Science instrument high-frequency radio receiver| first1=B.|last1=Cecconi| first2=L.|last2=Lamy| first3=P.|last3=Zarka| first4=R.|last4=Prangé| first5=W. S.|last5=Kurth| first6=P.|last6=Louarn|date=March 4, 2009|journal= Journal of Geophysical Research: Space Physics| volume=114| issue=A3| pages=A03215| via=ui.adsabs.harvard.edu| doi=10.1029/2008JA013830| bibcode=2009JGRA..114.3215C| access-date=December 9, 2019|archive-date=December 9, 2019|archive-url=https://web.archive.org/web/20191209095159/https://ui.adsabs.harvard.edu/abs/2009JGRA..114.3215C/abstract|url-status=live}}</ref> | Cronos Saturn |- | Uranus |{{nobr|-uranion}} | Uranus |- | Neptune |{{nobr|-poseideum}}<ref name="McKevitt Bulla Dixon Criscola 2021">Example of use: {{cite journal | last1=McKevitt | first1=James | last2=Bulla | first2=Sophie | last3=Dixon | first3=Tom | last4=Criscola | first4=Franco | last5=Parkinson-Swift | first5=Jonathan | last6=Bornberg | first6=Christina | last7=Singh | first7=Jaspreet | last8=Patel | first8=Kuren | last9=Laad | first9=Aryan | last10=Forder | first10=Ethan | last11=Ayin-Walsh | first11=Louis | last12=Beegadhur | first12=Shayne | last13=Wedde | first13=Paul | last14=Pappula | first14=Bharath Simha Reddy | last15=McDougall | first15=Thomas | last16=Foghis | first16=Madalin | last17=Kent | first17=Jack | last18=Morgan | first18=James | last19=Raj | first19=Utkarsh | last20=Heinreichsberger | first20=Carina | title=An L-class Multirole Observatory and Science Platform for Neptune|journal=2021 Global Space Exploration Conference Proceedings| date=18 June 2021 | arxiv=2106.09409 }}</ref> {{nobr|-poseidion}} | Poseidon |}

{|class="wikitable" |+Other host objects with named/nameable apsides |- ! Astronomical host object ! Suffix ! Origin of the name |- | Star | -astron | Lat: astra; ''stars'' |- | Galaxy | -galacticon | Gr: galaxias; ''galaxy'' |- | Barycenter | -center -focus -apsis | |- | Black hole | -melasma -bothron -nigricon | Gr: melos; ''black'' Gr: bothros; ''hole'' Lat: {{lang|la|niger}}; ''black'' |}

==Perihelion and aphelion== {{Redirect|Perihelion}} {{Redirect|Aphelion}} [[File:Perihelion-Aphelion.svg|thumb|Diagram of a body's direct orbit around the Sun with its nearest (perihelion) and farthest (aphelion) points]]

The perihelion (q) and aphelion (Q) are the nearest and farthest points, respectively, of a body's direct orbit around the Sun.

Comparing osculating elements at a specific epoch to those at a different epoch will generate differences. The time-of-perihelion-passage as one of six osculating elements is not an exact prediction (other than for a generic two-body model) of the actual minimum distance to the Sun using the full dynamical model. Precise predictions of perihelion passage require numerical integration.

===Inner planets and outer planets=== The two images below show the orbits, orbital nodes, and positions of perihelion (q) and aphelion (Q) for the planets of the Solar System<ref name=":0">{{cite web|title=the definition of apsis|url=http://dictionary.reference.com/browse/apsis|website=Dictionary.com|access-date=November 29, 2015|archive-date=December 8, 2015|archive-url=https://web.archive.org/web/20151208101127/http://dictionary.reference.com/browse/apsis|url-status=live}}</ref> as seen from above the northern pole of Earth's ecliptic plane, which is coplanar with Earth's orbital plane. The planets travel counterclockwise around the Sun and for each planet, the blue part of their orbit travels north of the ecliptic plane, the pink part travels south, and dots mark perihelion (green) and aphelion (orange).

The first image (below-left) features the ''inner'' planets, situated outward from the Sun as Mercury, Venus, Earth, and Mars. The ''reference'' Earth-orbit is colored yellow and represents the orbital plane of reference. At the time of vernal equinox, the Earth is at the bottom of the figure. The second image (below-right) shows the ''outer'' planets, being Jupiter, Saturn, Uranus, and Neptune.

The orbital nodes are the two end points of the "line of nodes" where a planet's tilted orbit intersects the plane of reference;<ref name="darlinglon">{{cite encyclopedia |url=http://www.daviddarling.info/encyclopedia/L/line_of_nodes.html |title=line of nodes |encyclopedia=The Encyclopedia of Astrobiology, Astronomy, and Spaceflight |first=David |last=Darling |access-date=May 17, 2007 |archive-date=August 23, 2019 |archive-url=https://web.archive.org/web/20190823203510/http://www.daviddarling.info/encyclopedia/L/line_of_nodes.html |url-status=live }}</ref> here they may be 'seen' as the points where the blue section of an orbit meets the pink.

<gallery caption="" widths="300px" heights="300px" class="skin-invert-image"> Image:Inner Planet Orbits 02.svg|The perihelion (green) and aphelion (orange) points of the inner planets of the Solar System Image:Outer Planet Orbits 02.svg|The perihelion (green) and aphelion (orange) points of the outer planets of the Solar System </gallery>

===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 length of the horizontal bars 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.

===Earth perihelion and aphelion=== In the 21st century, the Earth reaches perihelion in early January, approximately 14 days after the December solstice. At perihelion, the Earth's center is about {{Convert|0.9833|AU|km mi|abbr=unit|lk=on}}<ref name=Tanner/> 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 {{Convert|1.01664|AU|km mi|abbr=unit|lk=on}}.<ref name="Tanner">{{cite web |title=Earth Perihelion and Aphelion Calculator |url=https://www.phpsciencelabs.com/nasa-jpl-horizons-perigees-and-apogees-calculators/NASA-JPL-Horizons-Earth-Perihelion-Aphelion-Calculator.php |first=Jay |last=Tanner |work=Science Labs |date=2023-10-04 |access-date=2025-07-01|archive-url=https://web.archive.org/web/20250131063120/https://www.phpsciencelabs.com/nasa-jpl-horizons-perigees-and-apogees-calculators/NASA-JPL-Horizons-Earth-Perihelion-Aphelion-Calculator.php|archive-date=2025-01-31}}</ref>

The dates of perihelion and aphelion change over a century due to precession and other orbital factors, which follow cyclical patterns known as Milankovitch cycles. In the short-term, such dates can vary up to 3 days from one year to another as with aphelion on 3 July 2025 and 6 July 2026. This short-term 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 {{convert|4700|km|mi|-2}} 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).<ref>{{cite web |url=http://aa.usno.navy.mil/faq/docs/apsides.php |title=Variation in Times of Perihelion and Aphelion |publisher=Astronomical Applications Department of the U.S. Naval Observatory |date=August 11, 2011 |access-date=January 10, 2018 |archive-date=January 11, 2018 |archive-url=https://web.archive.org/web/20180111165154/http://aa.usno.navy.mil/faq/docs/apsides.php |url-status=dead }}</ref> On a longer time scale, the last July 3 aphelion is in 2060, and the last January 2 perihelion is in 2089.<ref name=Espenak1998/> The first July 7 aphelion is in 2067.<ref name=Espenak1998/>

Because of the increased distance at aphelion, only 93.55% of the radiation from the Sun falls on a given area of Earth's surface as does at perihelion, but this does not account for the seasons, which result instead from the tilt of Earth's axis of 23.4° away from perpendicular to the plane of Earth's orbit.<ref>{{cite web|title=Solar System Exploration: Science & Technology: Science Features: Weather, Weather, Everywhere?|url=http://www.nasa.gov/audience/foreducators/postsecondary/features/F_Planet_Seasons.html|publisher=NASA|access-date=September 19, 2015|archive-date=September 29, 2015|archive-url=https://web.archive.org/web/20150929033150/http://www.nasa.gov/audience/foreducators/postsecondary/features/F_Planet_Seasons.html|url-status=live}}</ref> Indeed, at both perihelion and aphelion it is summer in one hemisphere while it is winter in the other one. 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, when solar radiation is lowest. Despite this, summers in the northern hemisphere are on average {{convert|2.3|C-change|F-change|0}} warmer than in the southern hemisphere, because the northern hemisphere contains larger land masses, which are easier to heat than the seas.<ref name="Earth at Aphelion">{{cite web |url=http://spaceweather.com/glossary/aphelion.html |title=Earth at Aphelion |publisher=Space Weather |date=July 2008 |access-date=July 7, 2015 |archive-date=July 17, 2015 |archive-url=https://web.archive.org/web/20150717184242/http://spaceweather.com/glossary/aphelion.html |url-status=live }}</ref>

Perihelion and aphelion do however have an indirect effect on the seasons: because Earth's orbital speed is minimum at aphelion and maximum at perihelion, the planet takes longer to orbit from June solstice to September equinox than it does from December solstice to March equinox. Therefore, summer in the northern hemisphere lasts slightly longer (93 days) than summer in the southern hemisphere (89 days).<ref>{{cite web |last1=Rockport |first1=Steve C. |title=How much does aphelion affect our weather? We're at aphelion in the summer. Would our summers be warmer if we were at perihelion, instead? |url=https://usm.maine.edu/planet/how-much-does-aphelion-affect-our-weather-were-aphelion-summer-would-our-summers-be-warmer-if |website=Planetarium |publisher=University of Southern Maine |access-date=4 July 2020 |archive-date=July 6, 2020 |archive-url=https://web.archive.org/web/20200706154815/https://usm.maine.edu/planet/how-much-does-aphelion-affect-our-weather-were-aphelion-summer-would-our-summers-be-warmer-if |url-status=live }}</ref>

Astronomers commonly express the timing of perihelion relative to the First Point of Aries 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 2010, this had advanced by a small fraction of a degree to about 283.067°,<ref>{{cite web|url=http://data.giss.nasa.gov/ar5/srorbpar.html|archive-url=https://web.archive.org/web/20151002065753/http://data.giss.nasa.gov/ar5/srorbpar.html|archive-date=2015-10-02|title=Data.GISS: Earth's Orbital Parameters|website=data.giss.nasa.gov}}</ref> i.e. a mean increase of 62" per year.

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 (Milankovitch cycles).

On a very long time scale, the dates of perihelion and of aphelion progress through the seasons, and they make one complete cycle in 22,000 to 26,000 years. By the year 3800, perihelion will regularly occur in February.<ref name=Tanner/> There is a corresponding movement of the position of the stars as seen from Earth, called the apsidal precession. (This is closely related to the precession of the axes.) The dates and times of perihelion and aphelion for several past and future years are listed in the following table:<ref name=Espenak1998>{{Cite web|url=http://astropixels.com/ephemeris/perap2001.html|title=Earth at Perihelion and Aphelion: 2001 to 2100|last=Espenak|first=Fred|website=astropixels|type=based on DE405 released in 1998|access-date=June 24, 2021|archive-date=July 13, 2021|archive-url=https://web.archive.org/web/20210713131143/http://astropixels.com/ephemeris/perap2001.html|url-status=live}}</ref>

{| class="wikitable" style="margin-left:auto; margin-right:auto;" ! rowspan=2 width=50 | Year ! colspan=2 | Perihelion ! colspan=2 | Aphelion |- ! width=95| Date !! width=80 | Time (UT) ! width=95| Date !! width=80 | Time (UT) |- ! 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 |- !2021 |January 2 |13:51 |July 5 |22:27 |- !2022 |January 4 |06:55 |July 4 |07:11 |- !2023 |January 4 |16:17 |July 6 |20:07 |- !2024 |January 3 |00:39 |July 5 |05:06 |-id=2025 !2025 |January 4 |13:28 |July 3 |19:55<ref name=Tanner/> |-id=2026 !2026 |January 3 |17:16 |July 6 |17:31 |- !2027 |January 3 |02:33 |July 5 |05:06 |- !2028 |January 5 |12:28 |July 3 |22:18 |- !2029 |January 2 |18:13 |July 6 |05:12 |- !2030 |January 3 |10:12 |July 4 |12:58 |- !2031 |January 4 |20:48 |July 6 |07:10 |- !2032 |January 3 |05:11 |July 5 |11:54 |- !2033 |January 4 |11:51 |July 3 |20:52 |- !2034 |January 4 |04:47 |July 6 |18:49 |- !2035 |January 3 |00:54 |July 5 |18:22 |-id=3800 ! 3800 |February 2<ref name=Tanner/> || |August 4 || |}

===Other planets=== The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.<ref>{{Cite web |url=http://solarsystem.nasa.gov/planets/compare |title=NASA planetary comparison chart |access-date=August 4, 2016 |archive-url=https://web.archive.org/web/20160804162808/http://solarsystem.nasa.gov/planets/compare |archive-date=August 4, 2016 }}</ref>  {{table alignment}} <div class="noresize"> {| class="wikitable sortable col7right col8right col6right" style="margin-left:auto; margin-right:auto;" !class="unsortable" rowspan=2|Type of body !rowspan=2|Body !colspan=2|Distance from Sun at perihelion !colspan=2|Distance from Sun at aphelion !rowspan=2|Difference (%){{efn|Difference is defined as <math display="inline">1-\frac{\text{perihelion distance}}{\text{aphelion distance}}</math>}} !rowspan=2|Insolation difference (%){{efn|Insolation difference is defined as <math display="inline">1-\left(\frac{\text{perihelion distance}}{\text{aphelion distance}}\right)^2</math>}} |- !(km)!!(miles)!!(km)!!(miles) |- |rowspan=8|Planet |{{sort|1|Mercury}}||{{convert|46001009|km|mi|abbr=on|disp=table}}||{{convert|69817445|km|mi|abbr=on|disp=table}} || 34.1% || 56.6% |- |{{sort|2|Venus}}||{{convert|107476170|km|mi|abbr=on|disp=table}}||{{convert|108942780|km|mi|abbr=on|disp=table}} || 1.3% || 2.7% |- |{{sort|3|Earth}} || {{convert|147098291|km|mi|abbr=on|disp=table}}||{{convert|152098233|km|mi|abbr=on|disp=table}} || 3.3% || 6.5% |- |{{sort|4|Mars}} || {{convert|206655215|km|mi|abbr=on|disp=table}}||{{convert|249232432|km|mi|abbr=on|disp=table}} || 17.1% || 31.2% |- |{{sort|5|Jupiter}}||{{convert|740679835|km|mi|abbr=on|disp=table}}||{{convert|816001807|km|mi|abbr=on|disp=table}} || 9.2% || 17.6% |- |{{sort|6|Saturn}}||{{convert|1349823615|km|mi|abbr=on|disp=table}}||{{convert|1503509229|km|mi|abbr=on|disp=table}} || 10.2% || 19.4% |- |{{sort|7|Uranus}}||{{convert|2734998229|km|mi|abbr=on|disp=table}}||{{convert|3006318143|km|mi|abbr=on|disp=table}} || 9.0% || 17.2% |- |{{sort|8|Neptune}}||{{convert|4459753056|km|mi|abbr=on|disp=table}}||{{convert|4537039826|km|mi|abbr=on|disp=table}} || 1.7% || 3.4% |- |rowspan=5|Dwarf planet |{{sort|9|Ceres}}||{{convert|380951528|km|mi|abbr=on|disp=table}}||{{convert|446428973|km|mi|abbr=on|disp=table}} || 14.7% || 27.2% |- |{{sort|10|Pluto}}||{{convert|4436756954|km|mi|abbr=on|disp=table}}||{{convert|7376124302|km|mi|abbr=on|disp=table}} || 39.8% || 63.8% |- |{{sort|11|Haumea}}||{{convert|5157623774|km|mi|abbr=on|disp=table}}||{{convert|7706399149|km|mi|abbr=on|disp=table}} || 33.1% || 55.2% |- |{{sort|12|Makemake}}||{{convert|5671928586|km|mi|abbr=on|disp=table}}||{{convert|7894762625|km|mi|abbr=on|disp=table}} || 28.2% || 48.4% |- |{{sort|13|Eris}}||{{convert|5765732799|km|mi|abbr=on|disp=table}}||{{convert|14594512904|km|mi|abbr=on|disp=table}} || 60.5% || 84.4% |} </div> {{notelist}}

==Mathematical formulae==

These formulae characterize the pericenter and apocenter of an orbit: ; Pericenter: Maximum speed, <math display="inline">v_\text{per} = \sqrt{ \frac{(1 + e)\mu}{(1 - e)a} } \,</math>, at minimum (pericenter) distance, <math display="inline">r_\text{per} = (1 - e)a</math>. ; Apocenter: Minimum speed, <math display="inline"> v_\text{ap} = \sqrt{\frac{(1 - e)\mu}{(1 + e)a} } \,</math>, at maximum (apocenter) distance, <math display="inline">r_\text{ap} = (1 + e)a</math>.

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: <math>h = \sqrt{\left(1 - e^2\right)\mu a}</math> ; Specific orbital energy: <math>\varepsilon = -\frac{\mu}{2a}</math>

where: * <math display="inline">r_\text{ap}</math> is the distance from the apocenter to the primary focus * <math display="inline">r_\text{per}</math> is the distance from the pericenter to the primary focus * ''a'' is the semi-major axis: *: <math>a = \frac{r_\text{per} + r_\text{ap}}{2}</math> * ''μ'' is the standard gravitational parameter * ''e'' is the eccentricity, defined as *: <math>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}</math>

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 :<math>\sqrt{-2\varepsilon} = \sqrt{\frac{\mu}{a}}</math>

which is the speed of a body in a circular orbit whose radius is <math>a</math>.

== Time of perihelion == Orbital elements such as the ''time of perihelion passage'' are defined at the epoch chosen using an unperturbed two-body solution that does not account for the n-body problem. To get an accurate time of perihelion passage you need to use an epoch close to the perihelion passage. For example, using an epoch of 1996, Comet Hale–Bopp shows perihelion on 1 April 1997.<ref>[https://web.archive.org/web/20200716170854/https://ssd.jpl.nasa.gov/sbdb.cgi?soln=J971A%2F1&sstr=Hale-Bopp&cad=1 JPL SBDB: Hale-Bopp (Epoch 1996)]</ref> Using an epoch of 2022 shows a less accurate perihelion date of 29 March 1997.<ref>{{Cite web |url=https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1995O1 |title=JPL SBDB: Hale-Bopp }}</ref> Short-period comets can be even more sensitive to the epoch selected. Using an epoch of 2005 shows 101P/Chernykh coming to perihelion on 25 December 2005,<ref>{{Cite web |url=http://www.oaa.gr.jp/~oaacs/nk/nk1293.htm |title=101P/Chernykh – A (NK 1293) by Syuichi Nakano |access-date=July 17, 2020 |archive-date=October 3, 2020 |archive-url=https://web.archive.org/web/20201003194829/http://www.oaa.gr.jp/~oaacs/nk/nk1293.htm |url-status=live }}</ref> but using an epoch of 2012 produces a less accurate unperturbed perihelion date of 20 January 2006.<ref>[https://web.archive.org/web/20201128092431/https://ssd.jpl.nasa.gov/sbdb.cgi?ID=c00101_0 JPL SBDB: 101P/Chernykh (Epoch 2012)]</ref>

{{anchor|12P}} {| class="wikitable sortable" style="text-align: center; font-size: 0.9em;" |+Two body solution vs n-body solution for 12P/Pons–Brooks time of perihelion passage ! Epoch ! Date of perihelion (tp) |- | [https://archive.today/20220623124113/https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html%23/?sstr=12P&view=OPC 2010] || 2024-Apr-19.892 |- | n-body<ref name="Horizons2024">{{cite web |title=Horizons Batch for 12P/Pons-Brooks (90000223) at 2024-Apr-21 |publisher=JPL Horizons |type=Perihelion occurs when rdot flips from negative to positive |url=https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%2790000223%27&START_TIME=%272024-Apr-21%27&STOP_TIME=%272024-Apr-21%2004:00%27&STEP_SIZE=%2720%20min%27&QUANTITIES=%2719%27 |archive-url=https://web.archive.org/web/20230212102447/https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%2790000223%27&START_TIME=%272024-Apr-21%2003:00%27&STOP_TIME=%272024-Apr-21%2003:40%27&STEP_SIZE=%27120%27&QUANTITIES=%2719%27 |archive-date=2023-02-12 |url-status=live |access-date=2023-02-11}} (JPL#K242/3 Soln.date: 2022-Oct-24)</ref> || 2024-Apr-21.139 |- | [https://archive.today/20230211111847/https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html%23/?sstr=12P&view=OPC 2018] || 2024-Apr-23.069 |}

Numerical integration shows dwarf planet Eris will come to perihelion around December 2257.<ref name="Eris">{{cite web |title = Horizons Batch for Eris at perihelion around 7 December 2257 ±2 weeks |type = Perihelion occurs when rdot flips from negative to positive. The JPL SBDB generically lists an unperturbed two-body perihelion date in August 2257 |url = https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27136199%27&START_TIME=%272257-11-28%27&STOP_TIME=%272257-12-17%27&STEP_SIZE=%273%20hours%27&QUANTITIES=%2719%27 |work = JPL Horizons |publisher = Jet Propulsion Laboratory |access-date = 13 September 2021 |archive-date = September 13, 2021 |archive-url = https://web.archive.org/web/20210913110143/https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Eris%27&START_TIME=%272257-11-28%27&STOP_TIME=%272257-12-17%27&STEP_SIZE=%273%20hours%27&QUANTITIES=%2719%27 |url-status = live }}</ref> Using an epoch of 2025 less accurately shows Eris coming to perihelion in August 2257.<ref>{{Cite web |url=https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Eris |title=JPL SBDB: Eris (Epoch 2021) |access-date=January 5, 2021 |archive-date=September 13, 2021 |archive-url=https://web.archive.org/web/20210913043027/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Eris |url-status=live }}</ref>

4 Vesta came to perihelion on 26 December 2021,<ref name="Horizons2021">{{cite web |title=Horizons Batch for 4 Vesta on 2021-Dec-26 |publisher=JPL Horizons |type=Perihelion occurs when rdot flips from negative to positive |url=https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Vesta%27&START_TIME=%272021-Dec-25%2023:00%27&STOP_TIME=%272021-Dec-26%2004:00%27&STEP_SIZE=%2715%20minutes%27&QUANTITIES=%2719%27 |access-date=2021-09-26 |archive-date=September 26, 2021 |archive-url=https://web.archive.org/web/20210926095954/https://ssd.jpl.nasa.gov/horizons_batch.cgi?batch=1&COMMAND=%27Vesta%27&START_TIME=%272021-Dec-25%2023%3A00%27&STOP_TIME=%272021-Dec-26%2004%3A00%27&STEP_SIZE=%2715%20minutes%27&QUANTITIES=%2719%27 |url-status=live }} (Epoch 2021-Jul-01/Soln.date: 2021-Apr-13)</ref> but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.<ref>[https://web.archive.org/web/20210926095422/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=4 JPL SBDB: 4 Vesta (Epoch 2021)]</ref>

===Short observation periods=== Trans-Neptunian objects that are discovered when they are more than 80 AU from the Sun present a major challenge for astronomers. Because these objects move extremely slowly across the sky, scientists need many observations taken over several years to accurately determine their orbital paths.

When astronomers have only limited data—like when there were only 8 observations of object {{mpl|2015 TH|367}} collected over just one year—the uncertainty becomes enormous. For objects that won’t reach their closest point to the Sun (perihelion) for roughly 100 years, this limited data can lead to massive uncertainties. In the case of {{mpl|2015 TH|367}}, scientists originally estimated the perihelion date could be off by plus or minus {{Convert|28220|day|year|order=flip|abbr=off}} (a 1-sigma uncertainty) —that’s nearly an entire human lifetime of uncertainty.<ref>[https://web.archive.org/web/20180314133928/https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2015TH367 Archive of JPL #1 for 2015 TH367]</ref>

This demonstrates why tracking these distant objects requires patience and long-term observation campaigns to pin down their true orbital characteristics.<ref>{{Cite web |title=JPL SBDB: 2015 TH367 |url=https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2015TH367 }}</ref>

==See also== * Distance of closest approach * Eccentric anomaly * Flyby (spaceflight) * {{slink|Hyperbolic trajectory#Closest approach}} * Mean anomaly * Perifocal coordinate system * True anomaly

==References== {{reflist}}

==External links== {{Wiktionary|apsis}} * [http://www.perseus.gr/Astro-Lunar-Scenes-Apo-Perigee.htm Apogee – Perigee] Photographic Size Comparison, perseus.gr * [http://www.perseus.gr/Astro-Solar-Scenes-Aph-Perihelion.htm Aphelion – Perihelion] Photographic Size Comparison, perseus.gr * [https://newton.spacedys.com/astdys/index.php?pc=3.2.1&pc0=3.2&udfs=0.3 List of asteroids currently closer to the Sun than Mercury] (These objects will be close to perihelion)

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Category:Orbits