# 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
apogeeEarthperigee
aphelionSunperihelion
apastronstarperiastron
apocentergenericpericenter
apoapsisprimaryperiapsis
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 z/, 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 (n/), and the point of greatest distance is the aphelion (n/).[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 (/) and greatest distance the apogee, from Ancient Greek Γῆ (), "land" or "earth".
• For objects in lunar orbit, the point of least distance is sometimes called the pericynthion (n/) and the greatest distance the apocynthion (n/). 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).

## 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
${\displaystyle h={\sqrt {\left(1-e^{2}\right)\mu a}}}$
Specific orbital energy
${\displaystyle \varepsilon =-{\frac {\mu }{2a}}}$

where:

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

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

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

which is the speed of a body in a circular orbit whose radius is ${\displaystyle a}$.

Other Languages
Afrikaans: Apside
Alemannisch: Apsis (Astronomie)
العربية: قبا
asturianu: Ápside
беларуская (тарашкевіца)‎: Пэрыцэнтар і апацэнтар
भोजपुरी: एप्सिस
català: Àpside
español: Ápside
Esperanto: Apsido
euskara: Apside
فارسی: اوج و حضیض
français: Apside
galego: Apse
한국어: 장축단
हिन्दी: मन्द
Bahasa Indonesia: Apsis
italiano: Apside
עברית: אפסיד
Latina: Apsis
latviešu: Apsīda
magyar: Apszispont
മലയാളം: അപസൗരം
Bahasa Melayu: Apsis

norsk nynorsk: Apsis i astronomi
Plattdüütsch: Apsis (Astronomie)
português: Apside
română: Apsidă
Scots: Apsis
Simple English: Apsis
slovenščina: Apsidna točka
српски / srpski: Apsida (astronomija)
srpskohrvatski / српскохрватски: Apsida (astronomija)
svenska: Apsis
Türkçe: Apsis
тыва дыл: Апогей
українська: Апсиди