A diagram of Keplerian orbital elements. Johannes Kepler (ˈkɛplɚ ( December 27 1571 &ndash November 15 1630) was a German Mathematician, Astronomer The elements of an orbit are the parameters needed to specify that Orbit uniquely given a model of two point-masses obeying the Newtonian laws of motion and the F Periaps, H Apoapsis and the red line between them is the line of apsides

In astronomy, an apsis, plural apsides (pronounced /ˈæpsɪdɪːz/) is the point of greatest or least distance of the elliptical orbit of an astronomical object from its center of attraction, which is generally the center of mass of the system. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study In Astrodynamics or Celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1 s are significant physical entities, associations or structures which current Science has confirmed to exist in Space. The point of closest approach is called the periapsis or pericentre and the point of farthest excursion is called the apoapsis (Greek από, from, which becomes απ before a vowel, and αφ before rough breathing), apocentre or apapsis (the latter term, although etymologically more correct, is much less used). 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. In Mathematics, an ellipse (from the Greek ἔλλειψις literally absence) is a Conic section, the locus of points in a

Related terms are used to identify the body being orbited. The most common are perigee and apogee, referring to orbits around the Earth, and perihelion and aphelion, referring to orbits around the Sun (Greek ‘ήλιος hēlios sun). During the Apollo program, the terms pericynthion and apocynthion were used when referring to the moon.

## Formula

These formulae characterize the periapsis and apoapsis of an orbit:

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

while, in accordance with Kepler's laws of planetary motion (conservation of angular momentum) and the conservation of energy, these quantities are constant for a given orbit:

where:

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

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. In Mathematics and in the Sciences a formula (plural formulae, formulæ or formulas) is a concise way of expressing information In Astronomy, Kepler's Laws of Planetary Motion are three mathematical laws that describe the motion of Planets in the Solar System. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Astrodynamics, the specific relative angular momentum of an Orbiting body with respect to a Central body is the Relative angular momentum In Astrodynamics the specific Orbital energy \epsilon\\! (or vis-viva energy) of an Orbiting body traveling through Space In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae Small body orbiting a central body Under Standard assumptions in astrodynamics we have m where m \ is the mass In Astrodynamics, under standard assumptions, any Orbit must be of Conic section shape

The arithmetic mean of the two limiting distances is the length of the semi-major axis $a\!\,$. In Mathematics and Statistics, the arithmetic Mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided In Geometry, the semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae The geometric mean of the two distances is the length of the semi-minor axis $b\!\,$. The geometric mean in Mathematics, is a type of Mean or Average, which indicates the central tendency or typical value of a set of numbers In Geometry, the semi-minor axis (also semiminor axis) is a Line segment associated with most Conic sections (that is with ellipses and

The geometric mean of the two limiting 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 product of the two speeds is the local escape velocity). In Physics, escape velocity is the speed where the Kinetic energy of an object is equal to the magnitude of its Gravitational potential energy

## Terminology

The words "pericentre" and "apocentre" are occasionally seen, although periapsis/apoapsis are preferred in technical usage.

Various related terms are used for other celestial objects. s are significant physical entities, associations or structures which current Science has confirmed to exist in Space. The '-gee', '-helion' and '-astron' and '-galacticon' forms are frequently used in the astronomical literature, while the other listed forms are occasionally used, although '-saturnium' has very rarely been used in the last 50 years. The '-gee' form is commonly (although incorrectly) used as a generic 'closest approach to planet' term instead of specifically applying to the Earth. The term peri/apomelasma (from the Greek root) was used by physicist Geoffrey A. Landis in 1998 before peri/aponigricon (from the Latin) appeared in the scientific literature in 2002. Geoffrey A Landis works as a scientist and writer of Science fiction.

BodyClosest approachFarthest approach
GalaxyPerigalacticonApogalacticon
StarPeriastronApastron
Black holePerimelasma/PerinigriconApomelasma/Aponigricon
SunPerihelionAphelion[1]
MercuryPerihermionApohermion
VenusPericytherion/Pericytherean/PerikritionApocytherion/Apocytherean/Apokrition
EarthPerigeeApogee
MoonPeriselene/Pericynthion/PeriluneAposelene/Apocynthion/Apolune
MarsPeriareionApoareion
JupiterPerizene/PerijoveApozene/Apojove
SaturnPerikrone/PerisaturniumApokrone/Aposaturnium
UranusPeriuranionApouranion
NeptunePeriposeidionApoposeidion

Since "peri" and "apo" are Greek, it is considered by some purists[2] more correct to use the Greek form for the body, giving forms such as '-zene' for Jupiter and '-krone' for Saturn. A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e The Sun (Sol is the Star at the center of the Solar System. The VENUS ( V ictoria E xperimental N etwork U nder the S ea project is a cabled sea floor observatory operated by the University EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 Neptune ( English|AmE] ] is the eighth and farthest Planet from the Sun in the Solar System. The daunting prospect of having to maintain a different word for every orbitable body in the solar system (and beyond) is the main reason why the generic '-apsis' has become the almost universal norm.

• In the Moon's case, in practice all three forms are used, albeit very infrequently. The '-cynthion' form is, according to some, reserved for artificial bodies, whilst others reserve '-lune' for an object launched from the Moon and '-cynthion' for an object launched from elsewhere. The '-cynthion' form was the version used in the Apollo Project, following a NASA decision in 1964.
• For Venus, the form '-cytherion' is derived from the commonly used adjective 'cytherean'; the alternate form '-krition' (from Kritias, an older name for Aphrodite) has also been suggested.
• For Jupiter, the '-jove' form is occasionally used by astronomers whilst the '-zene' form is never used, like the other pure Greek forms ('-areion' (Mars), '-hermion' (Mercury), '-krone' (Saturn), '-uranion' (Uranus), '-poseidion' (Neptune) and '-hadion' (Pluto)).

## Earth's perihelion and aphelion

The Earth is closest to the Sun in early January and farthest in early July. The relation between perihelion, aphelion and the Earth's seasons changes over a 21,000 year cycle. This anomalistic precession contributes to periodic climate change (see Milankovitch cycles). In Astronomy, Precession refers to the movement of the rotational axis of a body such as a planet with respect to Inertial space. Climate change is any long-term significant change in the “average weather” that a given region experiences Milankovitch cycles are the collective effect of changes in the Earth 's movements upon its climate named after Serbian civil engineer and Mathematician

The day and hour of these events for the next few years are:[3]

YearPerihelionAphelion
2007Jan 3 20ZJuly 7 00Z
2008Jan 3 00ZJuly 4 08Z
2009Jan 4 15ZJuly 4 02Z
2010Jan 3 00ZJuly 6 11Z
2011Jan 3 19ZJuly 4 15Z
2012Jan 5 00ZJuly 5 03Z
2013Jan 2 05ZJuly 5 15Z
2014Jan 4 12ZJuly 4 00Z
2015Jan 4 07ZJuly 6 19Z
2016Jan 2 23ZJuly 4 16Z