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An apsis ( (third declension); ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides pertaining to orbits around different bodies have distinct names to differentiate themselves from other apsides. Apsides pertaining to , orbits around the Earth, are at the farthest point called the apogee, and at the nearest point the perigee, as with orbits of satellites and the Moon around Earth. Apsides pertaining to orbits around the Sun are named aphelion for the farthest and perihelion for the nearest point in a heliocentric orbit. 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 , the , and the of the Solar System.
According to Newton's laws of motion, all periodic orbits are ellipses. The barycenter of the two bodies may lie well within the bigger body—e.g., the Earth–Moon barycenter is about 75% of the way from Earth's center to its surface. If, compared to the larger mass, the smaller mass is negligible (e.g., for satellites), then the orbital elements are independent of the smaller mass.
When used as a suffix—that is, -apsis—the term can refer to the two distances from the primary body to the orbiting body when the latter is located: 1) at the periapsis point, or 2) at the apoapsis point (compare both graphics, second figure). The line of apsides denotes the distance of the line that joins the nearest and farthest points across an orbit; it also refers simply to the extreme range of an object orbiting a host body (see top figure; see third figure).
In orbital mechanics, the apsides technically refer to the distance measured between the barycenter of the 2-body system and the center of mass of the orbiting body. However, in the case of a spacecraft, the terms are commonly used to refer to the orbital altitude of the spacecraft above the surface of the central body (assuming a constant, standard reference radius).
Various related terms are used for other Celestial body. The suffixes -gee, -helion, -astron and -galacticon are frequently used in the astronomical literature when referring to the Earth, Sun, stars, and the Galactic Center respectively. The suffix -jove is occasionally used for Jupiter, but -saturnium has very rarely been used in the last 50 years for Saturn. The -gee form is also used as a generic closest-approach-to "any planet" term—instead of applying it only to Earth.
During the Apollo program, the terms pericynthion and apocynthion were used when referring to lunar orbit; they reference Cynthia, an alternative name for the Greek Moon goddess Artemis. More recently, during the Artemis program, the terms perilune and apolune have been used.
Regarding black holes, the term peribothron was first used in a 1976 paper by J. Frank and M. J. Rees, who credit W. R. Stoeger for suggesting creating a term using the greek word for pit: "bothron".
The terms perimelasma and apomelasma (from a Greek root) were used by physicist and science-fiction author Geoffrey A. Landis in a story published in 1998, Perimelasma , by Geoffrey Landis, first published in Asimov's Science Fiction, January 1998, republished at Infinity Plus thus appearing before perinigricon and aponigricon (from Latin) in the scientific literature in 2002.
| + Host objects in the Solar System with named/nameable apsides | ||
| Sun | Helios | |
| Mercury | Hermes | |
| Venus | Cytherean | |
| Earth | Gaia | |
| Moon | Luna Artemis Selene | |
| Mars | Ares | |
| Ceres | Demeter | |
| Jupiter | Zeus Jupiter | |
| Saturn | Cronus Saturn | |
| Uranus | Uranus | |
| Neptune | Example of use: | Poseidon |
| +Other host objects with named/nameable apsides | ||
| Star | -astron | ; stars |
| Galaxy | -galacticon | Gr: galaxy |
| Barycenter | -center -focus -apsis | |
| Black hole | -melasma -bothron -nigricon | Gr: melos; black Gr: bothros; hole Lat: niger; black |
Comparing osculating elements at a specific epoch to those at a different epoch will generate differences. The time-of-perihelion-passage as one of six osculating elements is not an exact prediction (other than for a generic Two-body problem) of the actual minimum distance to the Sun using the n-body problem. Precise predictions of perihelion passage require numerical integration.
The first image (below-left) features the inner planets, situated outward from the Sun as Mercury, Venus, Earth, and Mars. The reference Earth-orbit is colored yellow and represents the orbital plane of reference. At the time of vernal equinox, the Earth is at the bottom of the figure. The second image (below-right) shows the outer planets, being Jupiter, Saturn, Uranus, and Neptune.
The orbital nodes are the two end points of the "line of nodes" where a planet's tilted orbit intersects the plane of reference; here they may be 'seen' as the points where the blue section of an orbit meets the pink.
The dates of perihelion and aphelion change over a century due to precession and other orbital factors, which follow cyclical patterns known as Milankovitch cycles. In the short-term, such dates can vary up to 3 days from one year to another as with aphelion on 3 July 2025 and 6 July 2026. This short-term variation is due to the presence of the Moon: while the Earth–Moon barycenter is moving on a stable orbit around the Sun, the position of the Earth's center which is on average about from the barycenter, could be shifted in any direction from it—and this affects the timing of the actual closest approach between the Sun's and the Earth's centers (which in turn defines the timing of perihelion in a given year). On a longer time scale, the last July 3 aphelion is in 2060, and the last January 2 perihelion is in 2089. The first July 7 aphelion is in 2067.
Because of the increased distance at aphelion, only 93.55% of the radiation from the Sun falls on a given area of Earth's surface as does at perihelion, but this does not account for the , which result instead from the Axial tilt of 23.4° away from perpendicular to the plane of Earth's orbit. Indeed, at both perihelion and aphelion it is summer in one hemisphere while it is winter in the other one. Winter falls on the hemisphere where sunlight strikes least directly, and summer falls where sunlight strikes most directly, regardless of the Earth's distance from the Sun.
In the northern hemisphere, summer occurs at the same time as aphelion, when solar radiation is lowest. Despite this, summers in the northern hemisphere are on average warmer than in the southern hemisphere, because the northern hemisphere contains larger land masses, which are easier to heat than the seas.
Perihelion and aphelion do however have an indirect effect on the seasons: because Earth's orbital speed is minimum at aphelion and maximum at perihelion, the planet takes longer to orbit from June solstice to September equinox than it does from December solstice to March equinox. Therefore, summer in the northern hemisphere lasts slightly longer (93 days) than summer in the southern hemisphere (89 days).
Astronomers commonly express the timing of perihelion relative to the First Point of Aries not in terms of days and hours, but rather as an angle of orbital displacement, the so-called longitude of the periapsis (also called longitude of the pericenter). For the orbit of the Earth, this is called the longitude of perihelion, and in 2000 it was about 282.895°; by 2010, this had advanced by a small fraction of a degree to about 283.067°, i.e. a mean increase of 62" per year.
For the orbit of the Earth around the Sun, the time of apsis is often expressed in terms of a time relative to seasons, since this determines the contribution of the elliptical orbit to seasonal variations. The variation of the seasons is primarily controlled by the annual cycle of the elevation angle of the Sun, which is a result of the tilt of the axis of the Earth measured from the plane of the ecliptic. The Earth's eccentricity and other orbital elements are not constant, but vary slowly due to the perturbing effects of the planets and other objects in the solar system (Milankovitch cycles).
On a very long time scale, the dates of perihelion and of aphelion progress through the seasons, and they make one complete cycle in 22,000 to 26,000 years. By the year 3800, perihelion will regularly occur in February. There is a corresponding movement of the position of the stars as seen from Earth, called the apsidal precession. (This is closely related to the precession of the axes.) The dates and times of perihelion and aphelion for several past and future years are listed in the following table:
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 .
Numerical integration shows dwarf planet Eris will come to perihelion around December 2257. Using an epoch of 2021, which is 236 years early, less accurately shows Eris coming to perihelion in 2260.
4 Vesta came to perihelion on 26 December 2021, (Epoch 2021-Jul-01/Soln.date: 2021-Apr-13) but using a two-body solution at an epoch of July 2021 less accurately shows Vesta came to perihelion on 25 December 2021.
Other planets
The following table shows the distances of the and from the Sun at their perihelion and aphelion.
Planet 56.6% 2.7% 6.5% 31.2% 17.6% 19.4% 17.2% 3.4% Dwarf planet 27.2% 63.8% 55.2% 48.4% 84.4%
Mathematical formulae
These characterize the pericenter and apocenter of an orbit:
Time of perihelion
Orbital elements such as the time of perihelion passage are defined at the epoch chosen using an unperturbed Two-body problem that does not account for the n-body problem. To get an accurate time of perihelion passage you need to use an epoch close to the perihelion passage. For example, using an epoch of 1996, Comet Hale–Bopp shows perihelion on 1 April 1997. Using an epoch of 2008 shows a less accurate perihelion date of 30 March 1997. Short-period comets can be even more sensitive to the epoch selected. Using an epoch of 2005 shows 101P/Chernykh coming to perihelion on 25 December 2005, but using an epoch of 2012 produces a less accurate unperturbed perihelion date of 20 January 2006.
target="_blank" rel="nofollow"> JPL SBDB: 101P/Chernykh (Epoch 2012)
+Two-body problem solution vs n-body problem solution for 12P/Pons–Brooks time of perihelion passage
! Epoch
! Date of perihelion (tp)
target="_blank" rel="nofollow"> 20102024-Apr-19.892 2024-Apr-21.139
target="_blank" rel="nofollow"> 20182024-Apr-23.069
target="_blank" rel="nofollow"> JPL SBDB: 4 Vesta (Epoch 2021)
Short arcs
Trans-Neptunian objects discovered when 80+ AU from the Sun need dozens of observations over multiple years to well constrain their orbits because they move very slowly against the background stars. Due to statistics of small numbers, trans-Neptunian objects such as when it had only 8 observations over an observation arc of 1 year that have not or will not come to perihelion for roughly 100 years can have a 1-sigma uncertainty of in the perihelion date.
See also
External links
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