# Apsis

The apsides indicate the nearest and farthest points of an orbiting body around its host.
(1) farthest(3) focus(2) nearest
apocenterprimarypericenter
aphelionSunperihelion
apastronstarperiastron
apogeeEarthperigee
Example of periapsis and apoapsis, with two large bodies in elliptic orbits around their center of mass

An apsis (Greek: ἁψίς; plural apsides z/, 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 (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.
• 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]
• 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
${\displaystyle h={\sqrt {\left(1-e^{2}\right)\mu a}}}$
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
srpskohrvatski / српскохрватски: Apsida (astronomija)
svenska: Apsis
Türkçe: Apsis
тыва дыл: Апогей
українська: Апсиди