Apsis

The apsides indicate the nearest and farthest points of an orbiting body around its host.

(1) farthest	(3) focus	(2) nearest
apocenter	primary	pericenter
aphelion	Sun	perihelion
apastron	star	periastron
apogee	Earth	perigee

Example of periapsis and apoapsis, with two large bodies in elliptic orbits around their center of mass

An apsis (Greek: ἁψίς; plural apsides /ˈæpsɪdiːz/, Greek: ἁψῖδες) is an extreme point in the orbit of an object. The word comes via Latin from Greek and is cognate with apse.^[1] For elliptic orbits about a larger body, there are two apsides, named with the prefixes peri- (from περί (peri), meaning 'near') and ap-/apo- (from ἀπ(ό) (ap(ó)), meaning 'away from') added to a reference to the body being orbited.

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.
For objects in lunar orbit, the point of least distance is the pericynthion (/ˌpɛrɪˈsɪnθiən/) and the greatest distance the apocynthion (/ˌæpəˈsɪnθiən/). Perilune and apolune are also used.^[3]
For an orbit around any barycenter, the terms periapsis and apoapsis (or apapsis) are used. Pericenter and apocenter are equivalent alternatives.

A straight line connecting the periapsis and apoapsis is the line of apsides. This is the major axis of the ellipse, its greatest diameter. The center of mass, or barycenter, of a two-body system lies on this line at one of the two foci of the ellipse. When one body is sufficiently larger than the other, this focus may be located within the larger body. However, whether this is the case, both bodies are in similar elliptical orbits. Both orbits share a common focus at the system's barycenter, with their respective lines of apsides being of length inversely proportional to their masses.

Historically, in geocentric systems, apsides were measured from the center of the Earth. However, in the case of the Moon, the barycenter of the Earth–Moon system (or the Earth–Moon barycenter) as the common focus of both bodies' orbits about each other, is about 75% of the way from Earth's center to its surface.

In orbital mechanics, the apsis technically refers to the distance measured between the barycenters of the central body and orbiting body. However, in the case of spacecraft, the family of terms are commonly used to refer to the orbital altitude of the spacecraft from the surface of the central body (assuming a constant, standard reference radius).

Mathematical formulae

Keplerian orbital elements: point F is at the pericenter, point H is at the apocenter, and the red line between them is the line of apsides.

These formulae characterize the pericenter and apocenter of an orbit:

Pericenter: Maximum speed, ${\textstyle v_{\text{per}}={\sqrt {\frac {(1+e)\mu }{(1-e)a}}}\,}$ , at minimum (pericenter) distance, ${\textstyle r_{\text{per}}=(1-e)a}$ .
Apocenter: Minimum speed, ${\textstyle v_{\text{ap}}={\sqrt {\frac {(1-e)\mu }{(1+e)a}}}\,}$ , at maximum (apocenter) distance, ${\textstyle r_{\text{ap}}=(1+e)a}$ .

While, in accordance with Kepler's laws of planetary motion (based on the conservation of angular momentum) and the conservation of energy, these two quantities are constant for a given orbit:

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

where:

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

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

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

which is the speed of a body in a circular orbit whose radius is $a$ .

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 Geoffrey A. Landis in 1998, before peri/aponigricon (from Latin) appeared in the scientific literature in 2002,^[5] as well as peri/apobothron (from Greek bothros, meaning hole or pit).^[6]

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.

Solar System objects
Astronomical object	Sun	Mercury	Venus	Earth	Moon	Mars	Jupiter	Saturn	Uranus	Neptune	Pluto
Suffix	-⁠helion	-⁠hermion	-⁠cytherion	-⁠gee	-⁠lune^[3] -⁠cynthion -⁠selene^[3]	-⁠areion	-⁠zene -jove	-⁠chron^[3] -⁠krone -⁠saturnium	-⁠uranion	-⁠poseidon	-⁠hadion
Origin of the name	Helios	Hermes	Cytherea	Gaia	Luna Cynthia Selene	Ares	Zeus Jupiter	Cronos Saturn	Uranus	Poseidon	Hades

Other objects
Astronomical object	Star	Galaxy	Barycenter	Black hole
Suffix	-⁠astron	-⁠galacticon	-⁠center -⁠focus -⁠apsis	-⁠melasma -⁠bothron -⁠nigricon

Perihelion and aphelion of the Earth

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.)

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.

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).

In the short term, the dates of perihelion and aphelion can vary up to 2 days from one year to another.^[7] 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).^[8]

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°.^[9]

The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:^[10]

Year	Perihelion		Aphelion
Year	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

Planetary perihelion and aphelion

The following table shows the distances of the planets and dwarf planets from the Sun at their perihelion and aphelion.^[11]

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

References

1 2 "the definition of apsis". Dictionary.com.
↑ 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 /əˈfiːliən/ 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
1 2 3 4 "Basics of Space Flight". NASA. Retrieved 30 May 2017.
↑ "Apollo 15 Mission Report". Glossary. Retrieved October 16, 2009.
↑ 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.
↑ Koberlein, Brian (2015-03-29). "Peribothron – Star makes closest approach to a black hole". briankoberlein.com. Retrieved 2018-01-10.
↑ "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.
↑ "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

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[:0-1] 1 2 "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 /əˈfiːliən/ 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

[nasaglossary-3] 1 2 3 4 "Basics of Space Flight". NASA. Retrieved 30 May 2017.

[4] "Apollo 15 Mission Report". Glossary. Retrieved October 16, 2009.

[5] 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.

[6] Koberlein, Brian (2015-03-29). "Peribothron – Star makes closest approach to a black hole". briankoberlein.com. Retrieved 2018-01-10.

[7] "Perihelion, Aphelion and the Solstices". timeanddate.com. Retrieved 2018-01-10.

[8] "Variation in Times of Perihelion and Aphelion". Astronomical Applications Department of the U.S. Naval Observatory. 2011-08-11. Retrieved 2018-01-10.

[9] "Data.GISS: Earth's Orbital Parameters". data.giss.nasa.gov.

[solex-10] "Solex by Aldo Vitagliano". Retrieved 2018-01-10. (calculated by Solex 11)

[11] NASA planetary comparison chart