Apsis

This article is about the astronomical term. In architecture, apsis is a synonym for apse.

Apogee is also the name of a major video game publisher.

elements of an orbit

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 centre of attraction (the centre 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.

We have:

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

where one easily verifies

<math>h = \sqrt{(1-e^2)\mu a}<math>

<math>\epsilon=-\frac{\mu}{2a}<math>

(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:

• <math>a<math> is the semi-major axis
• <math>e<math> is the eccentricity
• <math>h<math> is the specific relative angular momentum
• <math>\epsilon<math> is the specific orbital energy

Properties:

<math>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<math>

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 <math>a<math>. The geometric mean of the two distances is the semi-minor axis <math>b<math>.

The geometric mean of the two speeds is <math>\sqrt{-2\epsilon}<math>, 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

Related and increasingly specific terms are often used to identify the body being orbited. For example, the terms apogee and perigee refer to an orbit around the earth, aphelion and perihelion refer to an orbit around the sun, and apastron and periastron refer to an orbit around a star. Other terms are less commonly or rarely used:

The terms are formed from the Greek roots for the planet names rather than the Latin ones, since "peri" and "apo" are Greek and it is considered bad form to mix Greek and Latin roots.
(1) Pronounced "Ap-helion", not "Aff-elion".
(2) Pronounced "Ap-hermion", not "Aff-ermion".
(3) Perilune/Apolune are to be avoided. Pericynthion/Apocynthion are sometimes used for artificial bodies.
(4) In theory, Perijove/Apojove are to be avoided as they mix Greek and Latin roots. In practice, however, perijove and apojove are widely used and are more recognizable than perizene/apozene.
(5) Pronounced "Ap-hadion", not "Aff-adion".

See also

• Eccentric anomaly

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