The Info List - Apoapsis

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An apsis (Greek: ἁψίς; plural apsides /ˈæpsɪdiːz/, Greek: ἁψῖδες) is an extreme point in an object's orbit. 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-, or apo- (from ἀπ(ό) (ap(ó)), meaning 'away from') added to a reference to the thing 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 any orbit around a center of mass, there are the terms periapsis and apoapsis (or apapsis). 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. For a two-body system the center of mass of the system lies on this line at one of the two foci of the ellipse. When one body is sufficiently larger than the other it may be taken to be at this focus. However whether or not this is the case, both bodies are in similar elliptical orbits each having one focus at the system's center of mass, 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 center of mass of the Earth–Moon system, or Earth– Moon
barycenter, as the common focus of both the Moon's and Earth's 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 centers of mass of the central 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).


1 Mathematical formulae 2 Terminology

2.1 Terminology summary

3 Perihelion and aphelion
Perihelion and aphelion
of the Earth 4 Planetary perihelion and aphelion 5 See also 6 References 7 External links

Mathematical formulae[edit]

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


p e r


( 1 + e ) μ

( 1 − e ) a

displaystyle v_ mathrm per = sqrt tfrac (1+e)mu (1-e)a ,

at minimum (pericenter) distance


p e r

= ( 1 − e ) a

displaystyle r_ mathrm per =(1-e)a!,

Apocenter: minimum speed


a p


( 1 − e ) μ

( 1 + e ) a

displaystyle v_ mathrm ap = sqrt tfrac (1-e)mu (1+e)a ,

at maximum (apocenter) distance


a p

= ( 1 + e ) a

displaystyle r_ mathrm ap =(1+e)a!,

while, in accordance with Kepler's laws of planetary motion
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 −




μ a

displaystyle h= sqrt left(1-e^ 2 right)mu a

specific orbital energy

ε = −


2 a

displaystyle varepsilon =- frac mu 2a


a is the semi-major axis, equal to


p e r



a p


displaystyle frac r_ mathrm per +r_ mathrm ap 2

μ is the standard gravitational parameter e is the eccentricity, defined as

e =


a p


p e r


a p



p e r

= 1 −



a p


p e r

+ 1

displaystyle e= frac r_ mathrm ap -r_ mathrm per r_ mathrm ap +r_ mathrm per =1- frac 2 frac r_ mathrm ap r_ mathrm 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

− 2 ε


μ a

displaystyle sqrt -2varepsilon = sqrt frac mu a

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


displaystyle a

. Terminology[edit] 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
Geoffrey A. Landis
in 1998,[citation needed] 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[edit] 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
Solar System

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 -bothron -nigricon

Perihelion and aphelion
Perihelion and aphelion
of the Earth[edit]

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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

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[edit] 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
Halley's Comet
from the Sun.

Distances of selected bodies of the Solar System
Solar System
from the Sun. The left and right edges of each bar correspond to the perihelion and aphelion of the body, respectively, hence long bars denote high orbital eccentricity. The radius of the Sun
is 0.7 million km, and the radius of Jupiter
(the largest planet) is 0.07 million km, both too small to resolve on this image.

The images below show the perihelion (green dot) and aphelion (red dot) points of the inner and outer planets.[1]

Perihelion and aphelion
Perihelion and aphelion

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[edit]

Eccentric anomaly Perifocal coordinate system Solstice


^ a b "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 [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 ^ a b c d "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. 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.  ^ "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[edit]

Look up apsis in Wiktionary, the free dictionary.

Apogee – Perigee Photographic Size Comparison, perseus.gr Aphelion
Photographic Size Comparison, perseus.gr Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000–2020, usno.navy.mil

v t e

Gravitational orbits



Box Capture Circular Elliptical / Highly elliptical Escape Graveyard Horseshoe Hyperbolic trajectory Inclined / Non-inclined Osculating Parabolic trajectory Parking Synchronous

semi sub

Transfer orbit


Geosynchronous Geostationary Sun-synchronous Low Earth Medium Earth High Earth Molniya Near-equatorial Orbit
of the Moon Polar Tundra

About other points

Areosynchronous Areostationary Halo Lissajous Lunar Heliocentric Heliosynchronous


Shape Size

e  Eccentricity a  Semi-major axis b  Semi-minor axis Q, q  Apsides


i  Inclination Ω  Longitude of the ascending node ω  Argument of periapsis ϖ  Longitude of the periapsis


M  Mean anomaly ν, θ, f  True anomaly E  Eccentric anomaly L  Mean longitude l  True longitude


T  Orbital period n  Mean motion v  Orbital speed t0  Epoch


Collision avoidance (spacecraft) Delta-v Delta-v
budget Bi-elliptic transfer Geostationary transfer Gravity assist Gravity turn Hohmann transfer Low energy transfer Oberth effect Inclination
change Phasing Rocket equation Rendezvous Transposition, docking, and extraction

Orbital mechanics

Celestial coordinate system Characteristic energy Escape velocity Ephemeris Equatorial coordinate system Ground track Hill sphere Interplanetary Transport Network Kepler's laws of planetary motion Lagrangian point n-body problem Orbit
equation Orbital state vectors Perturbation Retrograde motion Specific orbital energy Specific relative angular momentum Two-line elements