Apsis
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![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Apogee_%28PSF%29_mul.svg/langzxx-345px-Apogee_%28PSF%29_mul.svg.png)
Anapsis(fromAncient Greekἁψίς(hapsís)'arch, vault';pl.apsides/ˈæpsɪˌdiːz/AP-sih-deez)[1][2]is the farthest or nearest point in theorbitof aplanetary bodyabout itsprimary body.Theline of apsidesis the line connecting the twoextreme values.
Apsides pertaining to orbits around theSunhave distinct names to differentiate themselves from other apsides; these names areaphelionfor the farthest andperihelionfor the nearest point in the solar orbit.[3]TheMoon's two apsides are the farthest point,apogee,and the nearest point,perigee,of its orbit around the hostEarth.Earth's two apsides are the farthest point,aphelion,and the nearest point,perihelion,of its orbit around the host Sun. The termsaphelionandperihelionapply in the same way to the orbits ofJupiterand the otherplanets,thecomets,and theasteroidsof theSolar System.
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General description[edit]
![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/a0/Periapsis_apoapsis.png/250px-Periapsis_apoapsis.png)
∗Periapsis and apoapsis as distances: the smallest and largest distances between the orbiter and its host body.
There are two apsides in anyelliptic orbit.The name for each apsis is created from the prefixesap-,apo-(fromἀπ(ό),(ap(o)-)'away from') for the farthest orperi-(fromπερί(peri-)'near') for the closest point to theprimary body,with a suffix that describes the primary body. The suffix for Earth is-gee,so the apsides' names areapogeeandperigee.For the Sun, the suffix is-helion,so the names areaphelionandperihelion.
According toNewton'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.[4]If, compared to the larger mass, the smaller mass is negligible (e.g., for satellites), then theorbital parametersare 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 theperiapsispoint, or 2) at theapoapsispoint (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).
Inorbital mechanics,the apsides technically refer to the distance measured between thecenter of massof thecentral bodyand the center of mass of the orbiting body. However, in the case of aspacecraft,the terms are commonly used to refer to the orbitalaltitudeof the spacecraft above the surface of the central body (assuming a constant, standard reference radius).
![](https://upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Angular_Parameters_of_Elliptical_Orbit.png/250px-Angular_Parameters_of_Elliptical_Orbit.png)
Terminology[edit]
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 termspericenterandapocenterare used for naming the extreme points of orbits (see table, top figure);periapsisandapoapsis(orapapsis) 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 theSun,the point of least distance is theperihelion(/ˌpɛrɪˈhiːliən/), and the point of greatest distance is theaphelion(/æpˈhiːliən/);[5]when discussing orbits around other stars the terms becomeperiastronandapastron.
- When discussing a satellite ofEarth,including theMoon,the point of least distance is theperigee(/ˈpɛrɪdʒiː/), and of greatest distance, theapogee(fromAncient Greek:Γῆ (Gē), "land" or "earth" ).[6]
- For objects inlunar orbit,the point of least distance are called thepericynthion(/ˌpɛrɪˈsɪnθiən/) and the greatest distance theapocynthion(/ˌæpəˈsɪnθiən/). The termsperiluneandapolune,as well asperiseleneandaposeleneare also used.[7]Since the Moon has no natural satellites this only applies to man-made objects.
Etymology[edit]
The wordsperihelionandaphelionwere coined byJohannes Kepler[8]to describe the orbital motions of the planets around the Sun. The words are formed from the prefixesperi-(Greek:περί,near) andapo-(Greek:ἀπό,away from), affixed to the Greek word for the Sun, (ἥλιος,orhēlíos).[5]
Various related terms are used for othercelestial objects.The suffixes-gee,-helion,-astronand-galacticonare frequently used in the astronomical literature when referring to the Earth, Sun, stars, and theGalactic Centerrespectively. The suffix-joveis occasionally used for Jupiter, but-saturniumhas very rarely been used in the last 50 years for Saturn. The-geeform is also used as a generic closest-approach-to "any planet" term—instead of applying it only to Earth.
During theApollo program,the termspericynthionandapocynthionwere used when referring toorbiting the Moon;they reference Cynthia, an alternative name for the Greek Moon goddessArtemis.[9]More recently, during theArtemis program,the termsperiluneandapolunehave been used.[10]
Regarding black holes, the term peribothron was first used in a 1976 paper by J. Frank and M. J. Rees,[11]who credit W. R. Stoeger for suggesting creating a term using the greek word for pit: "bothron".
The termsperimelasmaandapomelasma(from a Greek root) were used by physicist and science-fiction authorGeoffrey A. Landisin a story published in 1998,[12]thus appearing beforeperinigriconandaponigricon(from Latin) in the scientific literature in 2002.[13]
Terminology summary[edit]
The suffixes shown below may be added to prefixesperi-orapo-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.Exoplanetstudies commonly use-astron,but typically, for other host systems the generic suffix,-apsis,is used instead.[14][failed verification]
Astronomical host object |
Suffix | Origin of the name |
---|---|---|
Sun | -helion | Helios |
Mercury | -hermion | Hermes |
Venus | -cythe | Cytherean |
Earth | -gee | Gaia |
Moon | -lune[7] -cynthion -selene[7] |
Luna Cynthia Selene |
Mars | -areion | Ares |
Ceres | -demeter[15] | Demeter |
Jupiter | -jove | Zeus Jupiter |
Saturn | -chron[7] -kronos -saturnium -krone[16] |
Cronos Saturn |
Uranus | -uranion | Uranus |
Neptune | -poseideum[17] -poseidion |
Poseidon |
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:niger;black |
Perihelion and aphelion[edit]
![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/94/Perihelion-Aphelion.svg/220px-Perihelion-Aphelion.svg.png)
The perihelion (q) and aphelion (Q) are the nearest and farthest points respectively of a body's directorbitaround theSun.
Comparingosculating elementsat a specificepochto effectively 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 generictwo-body model) of the actual minimum distance to the Sun using thefull dynamical model.Precise predictions of perihelion passage requirenumerical integration.
Inner planets and outer planets[edit]
The two images below show the orbits,orbital nodes,and positions of perihelion (q) and aphelion (Q) for the planets of the Solar System[18]as seen from above the northern pole ofEarth's ecliptic plane,which iscoplanarwithEarth'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 theinnerplanets, situated outward from the Sun as Mercury, Venus, Earth, and Mars. ThereferenceEarth-orbit is colored yellow and represents theorbital plane of reference.At the time of vernal equinox, the Earth is at the bottom of the figure. The second image (below-right) shows theouterplanets, 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;[19]here they may be 'seen' as the points where the blue section of an orbit meets the pink.
-
The perihelion (green) and aphelion (orange) points of theinner planetsof the Solar System
-
The perihelion (green) and aphelion (orange) points of theouter planetsof the Solar System
Lines of apsides[edit]
The chart shows the extreme range—from the closest approach (perihelion) to farthest point (aphelion)—of several orbitingcelestial bodiesof theSolar System:the planets, the known dwarf planets, includingCeres,andHalley'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) arethe lines of apsidesof the orbits of various objects around a host body.
Earth perihelion and aphelion[edit]
Currently, the Earth reaches perihelion in early January, approximately 14 days after theDecember solstice.At perihelion, the Earth's center is about0.98329astronomical 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 theJune solstice.The aphelion distance between the Earth's and Sun's centers is currently about1.01671AUor 152,097,700 km (94,509,100 mi).
The dates of perihelion and aphelion change over time due to precession and other orbital factors, which follow cyclical patterns known asMilankovitch cycles.In the short term, such dates can vary up to 2 days from one year to another.[20]This significant variation is due to the presence of the Moon: while the Earth–Moonbarycenteris 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).[21]
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 theseasons,which result instead from thetilt of Earth's axisof 23.4° away from perpendicular to the plane of Earth's orbit.[22]Indeed, at both perihelion and aphelion it issummerin one hemisphere while it iswinterin 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 2.3 °C (4 °F) warmer than in the southern hemisphere, because the northern hemisphere contains larger land masses, which are easier to heat than the seas.[23]
Perihelion and aphelion do however have an indirect effect on the seasons: because Earth'sorbital speedis 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).[24]
Astronomers commonly express the timing of perihelion relative to theFirst Point of Ariesnot in terms of days and hours, but rather as an angle of orbital displacement, the so-calledlongitude of the periapsis(also called longitude of the pericenter). For the orbit of the Earth, this is called thelongitude 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°,[25]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 theplane of the ecliptic.The Earth'seccentricityand 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 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, called theapsidal precession.(This is closely related to theprecession of the axes.) The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:[26]
Year | Perihelion | Aphelion | ||
---|---|---|---|---|
Date | Time (UT) | Date | 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 |
2025 | January 4 | 13:28 | July 3 | 19:55 |
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 |
Other planets[edit]
The following table shows the distances of theplanetsanddwarf planetsfrom the Sun at their perihelion and aphelion.[27]
Type of body | Body | Distance from Sun at perihelion | Distance from Sun at aphelion | difference (%) | insolation difference (%) |
---|---|---|---|---|---|
Planet | Mercury | 46,001,009 km (28,583,702 mi) | 69,817,445 km (43,382,549 mi) | 34% | 57% |
Venus | 107,476,170 km (66,782,600 mi) | 108,942,780 km (67,693,910 mi) | 1.3% | 2.8% | |
Earth | 147,098,291 km (91,402,640 mi) | 152,098,233 km (94,509,460 mi) | 3.3% | 6.5% | |
Mars | 206,655,215 km (128,409,597 mi) | 249,232,432 km (154,865,853 mi) | 17% | 31% | |
Jupiter | 740,679,835 km (460,237,112 mi) | 816,001,807 km (507,040,016 mi) | 9.2% | 18% | |
Saturn | 1,349,823,615 km (838,741,509 mi) | 1,503,509,229 km (934,237,322 mi) | 10% | 19% | |
Uranus | 2,734,998,229 km (1.699449110×109mi) | 3,006,318,143 km (1.868039489×109mi) | 9.0% | 17% | |
Neptune | 4,459,753,056 km (2.771162073×109mi) | 4,537,039,826 km (2.819185846×109mi) | 1.7% | 3.4% | |
Dwarf planet | Ceres | 380,951,528 km (236,712,305 mi) | 446,428,973 km (277,398,103 mi) | 15% | 27% |
Pluto | 4,436,756,954 km (2.756872958×109mi) | 7,376,124,302 km (4.583311152×109mi) | 40% | 64% | |
Haumea | 5,157,623,774 km (3.204798834×109mi) | 7,706,399,149 km (4.788534427×109mi) | 33% | 55% | |
Makemake | 5,671,928,586 km (3.524373028×109mi) | 7,894,762,625 km (4.905578065×109mi) | 28% | 48% | |
Eris | 5,765,732,799 km (3.582660263×109mi) | 14,594,512,904 km (9.068609883×109mi) | 60% | 84% |
Mathematical formulae[edit]
Theseformulaecharacterize the pericenter and apocenter of an orbit:
- Pericenter
- Maximum speed,,at minimum (pericenter) distance,.
- Apocenter
- Minimum speed,,at maximum (apocenter) distance,.
While, in accordance withKepler's laws of planetary motion(based on the conservation ofangular momentum) and the conservation of energy, these two quantities are constant for a given orbit:
where:
- is the distance from the apocenter to the primary focus
- is the distance from the pericenter to the primary focus
- ais thesemi-major axis:
- μis thestandard gravitational parameter
- eis theeccentricity,defined as
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.
Thearithmetic meanof the two limiting distances is the length of the semi-major axisa.Thegeometric meanof the two distances is the length of thesemi-minor axisb.
The geometric mean of the two limiting speeds is
which is the speed of a body in a circular orbit whose radius is.
Time of perihelion[edit]
Orbital elementssuch as thetime of perihelion passageare defined at theepochchosen using an unperturbedtwo-body solutionthat does not account for then-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–Boppshows perihelion on 1 April 1997.[28]Using an epoch of 2008 shows a less accurate perihelion date of 30 March 1997.[29]Short-period cometscan be even more sensitive to the epoch selected. Using an epoch of 2005 shows101P/Chernykhcoming to perihelion on 25 December 2005,[30]but using an epoch of 2012 produces a less accurate unperturbed perihelion date of 20 January 2006.[31]
Epoch | Date of perihelion (tp) |
---|---|
2010 | 2024-Apr-19.892 |
n-body[32] | 2024-Apr-21.139 |
2018 | 2024-Apr-23.069 |
Numerical integrationshowsdwarf planetEriswill come to perihelion around December 2257.[33]Using an epoch of 2021, which is 236 years early, less accurately shows Eris coming to perihelion in 2260.[34]
4 Vestacame to perihelion on 26 December 2021,[35]but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.[36]
Short arcs[edit]
Trans-Neptunian objectsdiscovered when 80+ AU from the Sun need dozens of observations over multiple years to well constrain their orbits because they move very slowly against the background stars. Due to statistics of small numbers, trans-Neptunian objects such as2015 TH367when it had only 8 observations over anobservation arcof 1 year that have not or will not come to perihelion for roughly 100 years can have a1-sigmauncertainty of 77.3 years (28,220 days) in the perihelion date.[37]
See also[edit]
- Distance of closest approach
- Eccentric anomaly
- Flyby (spaceflight)
- Hyperbolic trajectory § Closest approach
- Mean anomaly
- Perifocal coordinate system
- True anomaly
References[edit]
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- ^JPL SBDB: 101P/Chernykh (Epoch 2012)
- ^"Horizons Batch for 12P/Pons-Brooks (90000223) at 2024-Apr-21 03:20"(Perihelion occurs when rdot flips from negative to positive).JPL Horizons.Archivedfrom the original on February 12, 2023.RetrievedFebruary 11,2023.(JPL#K242/3 Soln.date: 2022-Oct-24)
- ^"Horizons Batch for Eris at perihelion around 7 December 2257 ±2 weeks".JPL Horizons(Perihelion occurs when rdot flips from negative to positive. The JPL SBDB generically (incorrectly) lists an unperturbed two-body perihelion date in 2260). Jet Propulsion Laboratory.Archivedfrom the original on September 13, 2021.RetrievedSeptember 13,2021.
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- ^"JPL SBDB: 2015 TH367".Archived from the original on March 14, 2018.RetrievedSeptember 23,2021.
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External links[edit]
![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png)
- Apogee – PerigeePhotographic Size Comparison, perseus.gr
- Aphelion – PerihelionPhotographic Size Comparison, perseus.gr
- Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000–2020ArchivedOctober 13, 2007, at theWayback Machine,usno.navy.mil
- Dates and times of Earth's perihelion and aphelion, 2000–2025ArchivedOctober 13, 2007, at theWayback Machinefrom theUnited States Naval Observatory
- List of asteroids currently closer to the Sun than Mercury(These objects will be close to perihelion)
- JPL SBDBlist of Main-Belt Asteroids (H<8) sorted by perihelion date