![Apogee (PSF)](https://upload.wikimedia.org/wikipedia/commons/a/a4/Apogee_%28PSF%29.png)
An apsis (; ) is the farthest or nearest point in the
orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
of a
planetary body
A planetary-mass object (PMO), planemo, or planetary body is by geophysical definition of planet, geophysical definition of celestial objects any celestial object massive enough to achieve hydrostatic equilibrium (to be rounded under its own gra ...
about its
primary body
A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the syst ...
. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any
elliptic orbit
In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it ...
. The name for each apsis is created from the prefixes ''ap-'', ''apo-'' (), or ''peri-'' (), each referring to the farthest and closest point to the
primary body
A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the syst ...
the affixing necessary suffix that describes the primary body in the orbit. In this case, the suffix for Earth is ''-gee'', so the apsides' names are ''apogee'' and ''perigee''. For the Sun, its suffix is ''-helion'', so the names are ''aphelion'' and ''perihelion''.
According to
Newton's laws of motion
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in moti ...
, 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 parameters
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same ...
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
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
, the apsides technically refer to the distance measured between the barycenters of the
central body
A primary (also called a gravitational primary, primary body, or central body) is the main physical body of a gravitationally bound, multi-object system. This object constitutes most of that system's mass and will generally be located near the syst ...
and orbiting body. However, in the case of a
spacecraft
A spacecraft is a vehicle or machine designed to fly in outer space. A type of artificial satellite, spacecraft are used for a variety of purposes, including communications, Earth observation, meteorology, navigation, space colonization, p ...
, the terms are commonly used to refer to the orbital
altitude
Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
of the spacecraft above the surface of the central body (assuming a constant, standard reference radius).
Terminology
The words "pericenter" and "apocenter" are often seen, although periapsis/apoapsis are preferred in technical usage.
* 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
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
, the point of least distance is the ''perihelion'' (), and the point of greatest distance is the ''aphelion'' ();
[Since the Sun, Ἥλιος in Greek, begins with a vowel (H is the long ē vowel in Greek), the final o in "apo" is omitted from the prefix. =The pronunciation "Ap-helion" is given in many dictionarie]
, pronouncing the "p" and "h" in separate syllables. However, the pronunciation
is also common (''e.g.,'' ''McGraw Hill Dictionary of Scientific and Technical Terms,'' 5th edition, 1994, p. 114), since in late Greek, 'p' from ἀπό followed by the 'h' from ἥλιος becomes phi; thus, the Greek word is αφήλιον. (see, for example, Walker, John, ''A Key to the Classical Pronunciation of Greek, Latin, and Scripture Proper Names'', Townsend Young 185
, page 26.) Man
dictionaries give both pronunciations when discussing orbits around other stars the terms become ''periastron'' and ''apastron''.
* When discussing a satellite of
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
, including the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
, the point of least distance is the ''perigee'' (), and of greatest distance, the ''apogee'' (from
Ancient Greek
Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...
: Γῆ (''Gē''), "land" or "earth").
* For objects in
lunar orbit
In astronomy, lunar orbit (also known as a selenocentric orbit) is the orbit of an object around the Moon.
As used in the space program, this refers not to the orbit of the Moon about the Earth, but to orbits by spacecraft around the Moon. The ...
, the point of least distance are called the ''pericynthion'' () and the greatest distance the ''apocynthion'' (). The terms ''perilune'' and ''apolune'', as well as ''periselene'' and ''apselene'' are also used.
Since the Moon has no natural satellites this only applies to man-made objects.
Etymology
The words ''perihelion'' and ''aphelion'' were coined by
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
to describe the orbital motions of the planets around the Sun.
The words are formed from the prefixes ''peri-'' (Greek: ''περί'', near) and ''apo-'' (Greek: ''ἀπό'', away from), affixed to the Greek word for the sun, (''ἥλιος'', or ''hēlíos'').
[
Various related terms are used for other ]celestial objects
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
. 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 orbiting the Moon; they reference Cynthia, an alternative name for the Greek Moon goddess Artemis
In ancient Greek mythology and religion, Artemis (; grc-gre, Ἄρτεμις) is the goddess of the hunt, the wilderness, wild animals, nature, vegetation, childbirth, care of children, and chastity. She was heavily identified wit ...
. More recently, during the Artemis program
The Artemis program is a robotic and human Moon exploration program led by the United States' National Aeronautics and Space Administration (NASA) along with three partner agencies: European Space Agency (ESA), Japan Aerospace Exploration ...
, the terms ''perilune'' and ''apolune'' have been used. Regarding black holes, 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
''Asimov's Science Fiction'' is an American science fiction magazine which publishes science fiction and fantasy named after science fiction author Isaac Asimov. It is currently published by Penny Publications. From January 2017, the publication ...
'', January 1998, republished at ''Infinity Plus
''Infinity Plus'' (sometimes stylized as ''infinity plus'' and ''infinityplus'') was a science fiction webzine active from 1997 to 2007, '' thus appearing before ''perinigricon'' and ''aponigricon'' (from Latin) in the scientific literature in 2002, and before ''peribothron'' (from Greek ''bothros Bothros (Greek βόθρος, plural ''bothroi'') is the Ancient Greek word for "hole", "pit" or "trench". In contemporary use it can refer to a variety of holes or depressions found at ancient sites and referred to in literature, and has also been u ...
'', meaning "hole" or "pit") in 2015.
Terminology summary
The suffixes shown below may be added to prefixes ''peri-'' or ''apo-'' to form unique names of apsides for the orbiting bodies of the indicated host/ (primary) system. However, only for the Earth, Moon and Sun systems are the unique suffixes commonly used. Exoplanet
An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
studies commonly use ''-astron'', but typically, for other host systems the generic suffix, ''-apsis'', is used instead.
Perihelion and aphelion
The perihelion (q) and aphelion (Q) are the nearest and farthest points respectively of a body's direct orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a p ...
around the Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
.
Comparing osculating elements
In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturba ...
at a specific epoch
In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured.
The moment of epoch is usually decided by ...
to effectively 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 model) of the actual minimum distance to the Sun using the full dynamical model. Precise predictions of perihelion passage require numerical integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...
.
Inner planets and outer planets
The two images below show the orbits, orbital node
An orbital node is either of the two points where an orbit intersection (Euclidean geometry), intersects a plane of reference to which it is inclined. A non-inclined orbit, which is coplanarity, contained in the reference plane, has no nodes.
P ...
s, and positions of perihelion (q) and aphelion (Q) for the planets of the Solar System as seen from above the northern pole of Earth's ecliptic plane, which is coplanar
In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. Howe ...
with Earth's orbital plane. The planets travel counterclockwise around the Sun and for each planet, the blue part of their orbit travels north of the ecliptic plane, the pink part travels south, and dots mark perihelion (green) and aphelion (orange).
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.
Image:Inner Planet Orbits 02.svg, The perihelion (green) and aphelion (orange) points of the inner planets
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
of the Solar System
Image:Outer Planet Orbits 02.svg, The perihelion (green) and aphelion (orange) points of the outer planets
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
of the Solar System
Lines of apsides
The chart shows the extreme range—from the closest approach (perihelion) to farthest point (aphelion)—of several orbiting celestial bodies
An astronomical object, celestial object, stellar object or heavenly body is a naturally occurring physical entity, association, or structure that exists in the observable universe. In astronomy, the terms ''object'' and ''body'' are often us ...
of the Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
: the planets, the known dwarf planets, including Ceres
Ceres most commonly refers to:
* Ceres (dwarf planet), the largest asteroid
* Ceres (mythology), the Roman goddess of agriculture
Ceres may also refer to:
Places
Brazil
* Ceres, Goiás, Brazil
* Ceres Microregion, in north-central Goiás ...
, and Halley's Comet
Halley's Comet or Comet Halley, officially designated 1P/Halley, is a short-period comet visible from Earth every 75–79 years. Halley is the only known short-period comet that is regularly visible to the naked eye from Earth, and thus the o ...
. The length of the horizontal bars correspond to the extreme range of the orbit of the indicated body around the Sun. These extreme distances (between perihelion and aphelion) are ''the lines of apsides'' of the orbits of various objects around a host body.
Earth perihelion and aphelion
Currently, the Earth reaches perihelion in early January, approximately 14 days after the December solstice
The December solstice, also known as the southern solstice, is the solstice that occurs each December – typically on 21 December, but may vary by one day in either direction according to the Gregorian calendar. In the Northern Hemisphere, the ...
. At perihelion, the Earth's center is about astronomical unit
The astronomical unit (symbol: au, or or AU) is a unit of length, roughly the distance from Earth to the Sun and approximately equal to or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits t ...
s (AU) or from the Sun's center. In contrast, the Earth reaches aphelion currently in early July, approximately 14 days after the June solstice
The June solstice is the solstice on Earth that occurs annually between 20 and 22 June according to the Gregorian calendar. In the Northern Hemisphere, the June solstice is the summer solstice (the day with the longest period of daylight), whil ...
. The aphelion distance between the Earth's and Sun's centers is currently about or .
The dates of perihelion and aphelion change over time due to precession and other orbital factors, which follow cyclical patterns known as Milankovitch cycles
Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term was coined and named after Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypot ...
. In the short term, such dates can vary up to 2 days from one year to another. This significant variation is due to the presence of the Moon: while the Earth–Moon barycenter
In astronomy, the barycenter (or barycentre; ) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. A barycenter is a dynamical point, not a physical object. It is an important conc ...
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).
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 season
A season is a division of the year based on changes in weather, ecology, and the number of daylight hours in a given region. On Earth, seasons are the result of the axial parallelism of Earth's tilted orbit around the Sun. In temperate and pol ...
s, which result instead from the tilt of Earth's axis of 23.4° away from perpendicular to the plane of Earth's orbit. Indeed, at both perihelion and aphelion it is summer
Summer is the hottest of the four temperate seasons, occurring after spring and before autumn. At or centred on the summer solstice, the earliest sunrise and latest sunset occurs, daylight hours are longest and dark hours are shortest, wit ...
in one hemisphere while it is winter
Winter is the coldest season of the year in polar and temperate climates. It occurs after autumn and before spring. The tilt of Earth's axis causes seasons; winter occurs when a hemisphere is oriented away from the Sun. Different cultures ...
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
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter or, if one body is much more massi ...
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
In celestial mechanics, the longitude of the periapsis, also called longitude of the pericenter, of an orbiting body is the longitude (measured from the point of the vernal equinox) at which the periapsis (closest approach to the central body) woul ...
(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°.
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 ecliptic or ecliptic plane is the orbital plane of the Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic agains ...
. The Earth's eccentricity
Eccentricity or eccentric may refer to:
* Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal"
Mathematics, science and technology Mathematics
* Off-center, in geometry
* Eccentricity (graph theory) of a v ...
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 the perihelion and of the aphelion progress through the seasons, and they make one complete cycle in 22,000 to 26,000 years. There is a corresponding movement of the position of the stars as seen from Earth, called the apsidal precession
In celestial mechanics, apsidal precession (or apsidal advance) is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical body's orbit. The apsides are the orbital points closest (periapsi ...
. (This is closely related to the precession of the axes.) The dates and times of the perihelions and aphelions for several past and future years are listed in the following table:
Other planets
The following table shows the distances of the planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s and dwarf planet
A dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to p ...
s from the Sun at their perihelion and aphelion.
Mathematical formulae
These formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship betwee ...
e characterize the pericenter and apocenter of an orbit:
; Pericenter: Maximum speed, , at minimum (pericenter) distance, .
; Apocenter: Minimum speed, , at maximum (apocenter) distance, .
While, in accordance with Kepler's laws of planetary motion
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...
(based on the conservation of angular momentum
In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
) and the conservation of energy, these two quantities are constant for a given orbit:
; Specific relative angular momentum
In celestial mechanics, the specific relative angular momentum (often denoted \vec or \mathbf) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative positi ...
:
; Specific orbital energy
In the gravitational two-body problem, the specific orbital energy \varepsilon (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy (\varepsilon_p) and their total kinetic energy (\varepsilon_k), divided ...
:
where:
* ''a'' is the semi-major axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...
:
*:
* ''μ'' is the standard gravitational parameter
In celestial mechanics, the standard gravitational parameter ''μ'' of a celestial body is the product of the gravitational constant ''G'' and the mass ''M'' of the bodies. For two bodies the parameter may be expressed as G(m1+m2), or as GM when ...
* ''e'' is the eccentricity
Eccentricity or eccentric may refer to:
* Eccentricity (behavior), odd behavior on the part of a person, as opposed to being "normal"
Mathematics, science and technology Mathematics
* Off-center, in geometry
* Eccentricity (graph theory) of a v ...
, defined as
*:
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
In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...
of the two limiting distances is the length of the semi-major axis ''a''. The geometric mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...
of the two distances is the length of the semi-minor axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both focus (geometry), foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major wikt: ...
''b''.
The geometric mean of the two limiting speeds is
:
which is the speed of a body in a circular orbit whose radius is .
Time of perihelion
Orbital elements
Orbital elements are the parameters required to uniquely identify a specific orbit. In celestial mechanics these elements are considered in two-body systems using a Kepler orbit. There are many different ways to mathematically describe the same ...
such as the ''time of perihelion passage'' are defined at the epoch
In chronology and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured.
The moment of epoch is usually decided by ...
chosen using an unperturbed two-body solution that does not account for the n-body problem
In physics, the -body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally.Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some histor ...
. 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
Comet Hale–Bopp (formally designated C/1995 O1) is a comet that was one of the most widely observed of the 20th century and one of the brightest seen for many decades.
Alan Hale and Thomas Bopp discovered Comet Hale–Bopp separately ...
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.
Numerical integration
In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations ...
shows dwarf planet
A dwarf planet is a small planetary-mass object that is in direct orbit of the Sun, smaller than any of the eight classical planets but still a world in its own right. The prototypical dwarf planet is Pluto. The interest of dwarf planets to p ...
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
Vesta (minor-planet designation: 4 Vesta) is one of the largest objects in the asteroid belt, with a mean diameter of . It was discovered by the German astronomer Heinrich Wilhelm Matthias Olbers on 29 March 1807 and is named after Vesta, the ...
comes 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 coming to perihelion on 25 December 2021.
Short arcs
Trans-Neptunian object
A trans-Neptunian object (TNO), also written transneptunian object, is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune, which has a semi-major axis of 30.1 astronomical units (au).
Typically, ...
s 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 with only 8 observations over an observation arc
In observational astronomy, the observation arc (or arc length) of a Solar System body is the time period between its earliest and latest observations, used for tracing the body's path. It is usually given in days or years. The term is mostly use ...
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
* Distance of closest approach
The distance of closest approach of two objects is the distance between their centers when they are externally tangent. The objects may be geometric shapes or physical particles with well-defined boundaries. The distance of closest approach is ...
* Eccentric anomaly In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit. The eccentric anomaly is one of three angular parameters ("anomalies") that define a position alo ...
* Flyby (spaceflight)
A flyby () is a spaceflight operation in which a spacecraft passes in proximity to another body, usually a target of its space exploration mission and/or a source of a gravity assist to impel it towards another target. Spacecraft which are specif ...
*
* Mean anomaly
In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body in the classical ...
* Perifocal coordinate system
The perifocal coordinate (PQW) system is a frame of reference for an orbit. The frame is centered at the focus of the orbit, i.e. the celestial body about which the orbit is centered. The unit vectors \mathbf and \mathbf lie in the plane of the or ...
* True anomaly
In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit. It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus ...
References
External links
Apogee – Perigee
Photographic Size Comparison, perseus.gr
Photographic Size Comparison, perseus.gr
Earth's Seasons: Equinoxes, Solstices, Perihelion, and Aphelion, 2000–2020
, usno.navy.mil
Dates and times of Earth's perihelion and aphelion, 2000–2025
from the United States Naval Observatory
United States Naval Observatory (USNO) is a scientific and military facility that produces geopositioning, navigation and timekeeping data for the United States Navy and the United States Department of Defense. Established in 1830 as the Depo ...
List of asteroids currently closer to the Sun than Mercury
(These objects will be close to perihelion)
* JPL SBD
list of Main-Belt Asteroids (H<8) sorted by perihelion date
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Orbits