Apsis

(Redirected from Perilune)

This article is about several astronomical terms (apogee & perigee, aphelion & perihelion, generic equivalents based on apsis, and related but rarer terms). In architecture, apsis is a synonym for apse; Apogee is also the name of a video game publisher.

In astronomy, an apsis (plural apsides "ap-si-deez") is the point of greatest or least distance of the elliptical orbit of a celestial body from its center of attraction (the center of mass of the system).

The point of closest approach is called the periapsis and the point of farthest approach is the apoapsis. A straight line drawn through the periapsis and apoapsis is the line of apsides. This is the major axis of the ellipse, the line through the longest part of the ellipse.

Related terms are used to identify the body being orbited. The most common are perigee and apogee, referring to earth orbits, and perihelion and aphelion, referring to orbits around the sun.
We have:

Periapsis: maximum speed $v_\mathrm{per} = \sqrt{ \frac{(1+e)\mu}{(1-e)a} } \,$ at minimum distance $r_\mathrm{per}=(1-e)a\!\,$ (periapsis distance)
Apoapsis: minimum speed $v_\mathrm{ap} = \sqrt{ \frac{(1-e)\mu}{(1+e)a} } \,$ at maximum distance $r_\mathrm{ap}=(1+e)a\!\,$ (apoapsis distance)

where one easily verifies

$h = \sqrt{(1-e^2)\mu a}$

$\epsilon=-\frac{\mu}{2a}$

(each the same for both points, like they are for the whole orbit, in accordance with Kepler's laws of planetary motion (conservation of angular momentum) and the conservation of energy)

where:

$a\!\,$ is the semi-major axis
$e\!\,$ is the eccentricity
$h\!\,$ is the specific relative angular momentum
$\epsilon\!\,$ is the specific orbital energy
$\mu\!\,$ is the standard gravitational parameter

Properties:

$e=\frac{r_\mathrm{ap}-r_\mathrm{per}}{r_\mathrm{ap}+r_\mathrm{per}}=1-\frac{2}{\frac{r_\mathrm{ap}}{r_\mathrm{per}}+1}=\frac{2}{\frac{r_\mathrm{per}}{r_\mathrm{ab}}+1}-1$

Note that for conversion from heights above the surface to distances, the radius of the central body has to be added, and conversely.

The arithmetic mean of the two distances is the semi-major axis $a\!\,$ . The geometric mean of the two distances is the semi-minor axis $b\!\,$ .

The geometric mean of the two speeds is $\sqrt{-2\epsilon}$ , the speed corresponding to a kinetic energy which, at any position of the orbit, added to the existing kinetic energy, would allow the orbiting body to escape (the square root of the sum of the squares of the two speeds is the local escape velocity).

Terminology

Various related terms are used for other celestial objects. 'Perigee', 'perihelion' and 'periastron' and corresponding 'apo-' forms are very frequently used in the astronomical literature, while '-lune', '-selene', '-cytherion', '-areion' and '-jove' are very occasionally used; other terms are never used in practice, with 'perigee' being quite commonly used as a generic 'closest approach to planet' term instead of specifically applying to the Earth.

Body	Closest approach	Farthest approach
Star	Periastron	Apastron
Black hole	Perimelasma	Apomelasma
Sun	Perihelion	Aphelion ⁽¹⁾
Mercury	Perihermion	Aphermion ⁽¹⁾
Venus	Pericytherion	Apocytherion
Earth	Perigee	Apogee
Moon	Periselene/Pericynthion/Perilune	Aposelene/Apocynthion/Apolune
Mars	Periareion	Apoareion
Jupiter	Perizene/Perijove	Apozene/Apojove
Saturn	Perikrone/Perisaturnium	Apokrone/Aposaturnium
Uranus	Periuranion	Apuranion
Neptune	Periposeidion	Apoposeidion
Pluto	Perihadion	Aphadion ⁽¹⁾

⁽¹⁾ These terms are properly pronounced 'affelion', 'affermion' and 'affadion', but in practice, 'ap-helion' is commonly heard, while the latter two terms are not used.

Since "peri" and "apo" are Greek, it is considered more correct to use the Greek form for the body. In practice, the '-selene' and '-lune' forms are both used, albeit very infrequently, like the '-cynthion' form, which is reserved for artificial bodies. For Jupiter, the '-jove' form is occasionally seen whilst the '-zene' form is essentially never used, like '-hermion', '-krone', '-uranion', '-poseidion' and '-hadion'. The '-saturnium' form was occasionally used in the late 19th century and early 20th century (see these two examples: 2 and 3).

Apsis

Terminology

See also