Apsis

An apsis (from Ancient Greek ἁψίς (hapsís) 'arch, vault'; pl. apsides /ˈæpsɪˌdiːz/ AP-sih-deez)^[1]^[2] is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides is the line connecting the two extreme values.

Several terms redirect here. For other uses, see Apogee (disambiguation), Perigee (disambiguation), and Apse (disambiguation).

Apsides pertaining to orbits around the Sun have distinct names to differentiate themselves from other apsides; these names are aphelion for the farthest and perihelion for the nearest point in the solar orbit.^[3] The Moon's two apsides are the farthest point, apogee, and the nearest point, perigee, of its orbit around the host Earth. Earth's two apsides are the farthest point, aphelion, and the nearest point, perihelion, of its orbit around the host Sun. The terms aphelion and perihelion apply in the same way to the orbits of Jupiter and the other planets, the comets, and the asteroids of the Solar System.

For generic situations where the primary is not specified, the terms pericenter and apocenter are used for naming the extreme points of orbits (see table, top figure); periapsis and apoapsis (or apapsis) are equivalent alternatives, but these terms also frequently refer to distances—that is, the smallest and largest distances between the orbiter and its host body (see second figure).

For a body orbiting the , the point of least distance is the perihelion (/ˌpɛrɪˈhiːliən/), and the point of greatest distance is the aphelion (/æpˈhiːliən/);^[5] when discussing orbits around other stars the terms become periastron and apastron.

Sun

When discussing a satellite of , including the Moon, the point of least distance is the perigee (/ˈpɛrɪdʒiː/), and of greatest distance, the apogee (from Ancient Greek: Γῆ (Gē), "land" or "earth").^[6]

Earth

For objects in , the point of least distance are called the pericynthion (/ˌpɛrɪˈsɪnθiən/) and the greatest distance the apocynthion (/ˌæpəˈsɪnθiən/). The terms perilune and apolune, as well as periselene and aposelene are also used.^[7] Since the Moon has no natural satellites this only applies to man-made objects.

lunar orbit

The perihelion (green) and aphelion (orange) points of the inner planets of the Solar System

The perihelion (green) and aphelion (orange) points of the outer planets of the Solar System

${\textstyle r_{\text{ap}}}$ is the distance from the apocenter to the primary focus

${\textstyle r_{\text{per}}}$ is the distance from the pericenter to the primary focus

a is the :
$a={\frac {r_{\text{per}}+r_{\text{ap}}}{2}}$

semi-major axis

μ is the

standard gravitational parameter

e is the , defined as
$e={\frac {r_{\text{ap}}-r_{\text{per}}}{r_{\text{ap}}+r_{\text{per}}}}=1-{\frac {2}{{\frac {r_{\text{ap}}}{r_{\text{per}}}}+1}}$

eccentricity

These formulae characterize the pericenter and apocenter of an orbit:

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:

where:

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

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

Distance of closest approach

Eccentric anomaly

Flyby (spaceflight)

Hyperbolic trajectory § Closest approach

Mean anomaly

Perifocal coordinate system

True anomaly

Photographic Size Comparison, perseus.gr

Apogee – Perigee