Apsis
The apsides refer to the farthest(1) and nearest(2) points of an orbiting body(1, 2) around its host(3).
| (1) farthest | (3) host | (2) nearest |
|---|---|---|
| apogee | Earth | perigee |
| aphelion | Sun | perihelion |
| apastron | star | periastron |
| apocenter | generic | pericenter |
| apoapsis | primary | periapsis |
Example of periapsis and apoapsis, with a smaller body (blue) around a larger body (yellow) in elliptic orbits around their center of mass (red +)
The term apsis (Greek: ἁψίς; plural apsides /ˈæpsɪdiːz/, 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 the theoretical possibility of one common circular orbit for two bodies of equal mass at diametral positions (symmetric binary star), there are two apsides for any elliptic orbit, named with the prefixes peri- (from περί (peri), meaning 'near') and ap-/apo- (from ἀπ(ό) (ap(ó)), meaning 'away from'), added in reference to the body being orbited. All periodic orbits are, according to Newton's Laws of motion, 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 of the orbiter and its host.
- For a body orbiting the Sun, the point of least distance is the perihelion (/ˌpɛrɪˈhiːliən/), and the point of greatest distance is the aphelion (/æpˈhiːliən/).[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 (/ˈpɛrɪdʒiː/) and greatest distance the apogee, from Ancient Greek Γῆ (Gē), "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).
Contents
1 Mathematical formulae
2 Terminology
2.1 Terminology summary
3 Perihelion and aphelion
3.1 Etymology
3.2 Earth
3.3 Other planets
4 See also
5 References
6 External links
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, vper=(1+e)μ(1−e)a{textstyle v_{text{per}}={sqrt {frac {(1+e)mu }{(1-e)a}}},}
, at minimum (pericenter) distance, rper=(1−e)a{textstyle r_{text{per}}=(1-e)a}
.
- Apocenter
- Minimum speed, vap=(1−e)μ(1+e)a{textstyle v_{text{ap}}={sqrt {frac {(1-e)mu }{(1+e)a}}},}
, at maximum (apocenter) distance, rap=(1+e)a{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
- h=(1−e2)μa{displaystyle h={sqrt {left(1-e^{2}right)mu a}}}
- Specific orbital energy
- ε=−μ2a{displaystyle varepsilon =-{frac {mu }{2a}}}
where:
a is the semi-major axis:
- a=rper+rap2{displaystyle a={frac {r_{text{per}}+r_{text{ap}}}{2}}}
- a=rper+rap2{displaystyle a={frac {r_{text{per}}+r_{text{ap}}}{2}}}
μ is the standard gravitational parameter
e is the eccentricity, defined as
- e=rap−rperrap+rper=1−2raprper+1{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}}}
- e=rap−rperrap+rper=1−2raprper+1{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
- −2ε=μa{displaystyle {sqrt {-2varepsilon }}={sqrt {frac {mu }{a}}}}
which is the speed of a body in a circular orbit whose radius is a{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].
Astronomical object | Sun | Mercury | Earth | Moon | Mars | Ceres | Jupiter | Saturn |
|---|---|---|---|---|---|---|---|---|
| Suffix | -helion | -hermion | -gee | -lune[3] -cynthion -selene[3] | -areion | -demeter[9] | -jove | -chron[3] -krone -saturnium |
| Origin of the name | Helios | Hermes | Gaia | Luna Cynthia Selene | Ares | Demeter | Zeus Jupiter | Cronos Saturn |
| Astronomical object | Star | Galaxy | Barycenter | Black hole |
|---|---|---|---|---|
| Suffix | -astron | -galacticon | -center -focus -apsis | -melasma -bothron -nigricon |
| Origin of the name | lat. astra: stars | galaxy | gr. melos: black gr. bothros: hole lat. 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 6999983290000000000♠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 7011152097651119397♠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.
The images below show the perihelion (green dot) and aphelion (red dot) points of the inner and outer planets.[1]
- Perihelion and aphelion points
The perihelion and aphelion points of the inner planets of the Solar System
The perihelion and aphelion points of the outer planets of the Solar System
See also
- Eccentric anomaly
- Flyby (spaceflight)
- Mean anomaly
- Perifocal coordinate system
- Solstice
- True anomaly
References
^ ab "the definition of apsis". Dictionary.com..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
^ 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 /əˈfiːliən/ [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
^ abcd "Basics of Space Flight". NASA. Retrieved 30 May 2017.
^ "Apollo 15 Mission Report". Glossary. Retrieved October 16, 2009.
^ Perimelasma, by Geoffrey Landis, first published in Asimov's Science Fiction, January 1998, republished at Infinity Plus
^ 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)
^ Koberlein, Brian (2015-03-29). "Peribothron – Star makes closest approach to a black hole". briankoberlein.com. Retrieved 2018-01-10.
^ http://lasp.colorado.edu/home/maven/science/science-orbit/
^ http://www.planetary.org/blogs/guest-blogs/marc-rayman/20181019-dawn-journal-11-years-in-space.html
^ Klein, Ernest, A Comprehensive Etymological Dictionary of the English Language, Elsevier, Amsterdam, 1965. (Archived version)
^ 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 [5], pronouncing the "p" and "h" in separate syllables. However, the pronunciation /əˈfiːliən/ [6] 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 [7], page 26.) Many [8] dictionaries give both pronunciations
^ "Perihelion, Aphelion and the Solstices". timeanddate.com. Retrieved 2018-01-10.
^ "Variation in Times of Perihelion and Aphelion". Astronomical Applications Department of the U.S. Naval Observatory. 2011-08-11. Retrieved 2018-01-10.
^ "Solar System Exploration: Science & Technology: Science Features: Weather, Weather, Everywhere?". NASA. Retrieved 2015-09-19.
^ "Earth at Aphelion". Space Weather. July 2008. Retrieved 7 July 2015.
^ "Data.GISS: Earth's Orbital Parameters". data.giss.nasa.gov.
^ "Solex by Aldo Vitagliano". Retrieved 2018-01-10. (calculated by Solex 11)
^ NASA planetary comparison chart
External links
 | Look up apsis in Wiktionary, the free dictionary. |
Apogee – Perigee Photographic Size Comparison, perseus.gr
Aphelion – Perihelion Photographic Size Comparison, perseus.gr
Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000–2020, usno.navy.mil
Dates and times of Earth's perihelion and aphelion, 2000–2025 from the United States Naval Observatory
List of asteroids currently closer to the Sun than Mercury (These objects will be close to perihelion)
