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In
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
, the barycenter (or barycentre; ) is the
center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the d ...
of two or more bodies that
orbit In celestial mechanics, an orbit (also known as orbital revolution) 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 ...
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 concept in fields such as astronomy and
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
. The distance from a body's center of mass to the barycenter can be calculated as a
two-body problem In classical mechanics, the two-body problem is to calculate and predict the motion of two massive bodies that are orbiting each other in space. The problem assumes that the two bodies are point particles that interact only with one another; th ...
. If one of the two orbiting bodies is much more massive than the other and the bodies are relatively close to one another, the barycenter will typically be located within the more massive object. In this case, rather than the two bodies appearing to orbit a point between them, the less massive body will appear to orbit about the more massive body, while the more massive body might be observed to wobble slightly. This is the case for the Earth–Moon system, whose barycenter is located on average from Earth's center, which is 74% of Earth's radius of . When the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will orbit around it. This is the case for
Pluto Pluto (minor-planet designation: 134340 Pluto) is a dwarf planet in the Kuiper belt, a ring of Trans-Neptunian object, bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Su ...
and
Charon In Greek mythology, Charon or Kharon ( ; ) is a psychopomp, the ferryman of the Greek underworld. He carries the souls of those who have been given funeral rites across the rivers Acheron and Styx, which separate the worlds of the living and ...
, one of Pluto's
natural satellite A natural satellite is, in the most common usage, an astronomical body that orbits a planet, dwarf planet, or small Solar System body (or sometimes another natural satellite). Natural satellites are colloquially referred to as moons, a deriv ...
s, as well as for many
binary asteroid A binary asteroid is a system of two asteroids orbiting their common barycenter. The binary nature of 243 Ida was discovered when the Galileo spacecraft flew by the asteroid in 1993. Since then numerous binary asteroids and several triple a ...
s and
binary star A binary star or binary star system is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved as separate stars us ...
s. When the less massive object is far away, the barycenter can be located outside the more massive object. This is the case for
Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined a ...
and the
Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...
; despite the Sun being a thousandfold more massive than Jupiter, their barycenter is slightly outside the Sun due to the relatively large distance between them. In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the barycenter of two or more bodies. The International Celestial Reference System (ICRS) is a barycentric coordinate system centered on 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 "Sola ...
's barycenter.


Two-body problem

The barycenter is one of the foci of the
elliptical orbit In astrodynamics or celestial mechanics, an elliptical orbit or eccentric orbit is an orbit with an orbital eccentricity, eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. Some or ...
of each body. This is an important concept in the fields of
astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
and
astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline, James Keeler, said, astrophysics "seeks to ascertain the ...
. In a simple two-body case, the distance from the center of the primary to the barycenter, ''r''1, is given by: :r_1 = a \cdot \frac = \frac where : *''r''1 is the
distance Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...
from body 1's center to the barycenter *''a'' is the distance between the centers of the two bodies *''m''1 and ''m''2 are the
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
es of the two bodies. 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 longe ...
of the secondary's orbit, ''r''2, is given by . When the barycenter is located ''within'' the more massive body, that body will appear to "wobble" rather than to follow a discernible orbit.


Primary–secondary examples

The following table sets out some examples from 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 "Sola ...
. Figures are given rounded to three
significant figures Significant figures, also referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcom ...
. The terms "primary" and "secondary" are used to distinguish between involved participants, with the larger being the primary and the smaller being the secondary.


Example with the Sun

If —which is true for the Sun and any planet—then the ratio approximates to: :\frac \cdot \frac. Hence, the barycenter of the Sun–planet system will lie outside the Sun only if: : \cdot > 1 \; \Rightarrow \; > \approx 2.3 \times 10^ \; m_\oplus \; \mbox \approx 1530 \; m_\oplus \; \mbox —that is, where the planet is massive ''and'' far from the Sun. If Jupiter had Mercury's orbit (), the Sun–Jupiter barycenter would be approximately 55,000 km from the center of the Sun (). But even if the Earth had Eris's orbit (), the Sun–Earth barycenter would still be within the Sun (just over 30,000 km from the center). To calculate the actual motion of the Sun, only the motions of the four giant planets (Jupiter, Saturn, Uranus, Neptune) need to be considered. The contributions of all other planets, dwarf planets, etc. are negligible. If the four giant planets were on a straight line on the same side of the Sun, the combined center of mass would lie at about 1.17 solar radii, or just over 810,000 km, above the Sun's surface. The calculations above are based on the mean distance between the bodies and yield the mean value ''r''1. But all celestial orbits are elliptical, and the distance between the bodies varies between the apses, depending on 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-Centre (geometry), center, in geometry * Eccentricity (g ...
, ''e''. Hence, the position of the barycenter varies too, and it is possible in some systems for the barycenter to be ''sometimes inside and sometimes outside'' the more massive body. This occurs where: :\frac > \frac > \frac The Sun–Jupiter system, with ''e''Jupiter = 0.0484, just fails to qualify: .


Relativistic corrections

In
classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
(Newtonian gravitation), this definition simplifies calculations and introduces no known problems. In
general relativity General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
(Einsteinian gravitation), complications arise because, while it is possible, within reasonable approximations, to define the barycenter, we find that the associated coordinate system does not fully reflect the inequality of clock rates at different locations. Brumberg explains how to set up barycentric coordinates in general relativity. The coordinate systems involve a world-time, i.e. a global time coordinate that could be set up by
telemetry Telemetry is the in situ collection of measurements or other data at remote points and their automatic transmission to receiving equipment (telecommunication) for monitoring. The word is derived from the Greek roots ''tele'', 'far off', an ...
. Individual clocks of similar construction will not agree with this standard, because they are subject to differing
gravitational potential In classical mechanics, the gravitational potential is a scalar potential associating with each point in space the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point in the ...
s or move at various velocities, so the world-time must be synchronized with some ideal clock that is assumed to be very far from the whole self-gravitating system. This time standard is called Barycentric Coordinate Time (TCB).


Selected barycentric orbital elements

Barycentric osculating orbital elements for some objects in the Solar System are as follows: For objects at such high eccentricity, barycentric coordinates are more stable than heliocentric coordinates for a given epoch because the barycentric
osculating orbit 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 pertur ...
is not as greatly affected by where Jupiter is on its 11.8 year orbit.


See also

* Barycentric Dynamical Time * Centers of gravity in non-uniform fields *
Center of mass In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the d ...
*
Lagrange point In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. Mathematically, this involves t ...
* Mass point geometry *
Roll center The roll center of a vehicle is the notional point at which the cornering forces in the suspension are reacted to the vehicle body. There are two definitions of roll center. The most commonly used is the geometric (or kinematic) roll center, whe ...
*
Weight distribution Weight distribution is the apportioning of weight within a vehicle, especially cars, airplanes, and trains. Typically, it is written in the form ''x''/''y'', where ''x'' is the percentage of weight in the front, and ''y'' is the percentage in t ...


References

{{Portal bar, Physics, Astronomy, Stars, Spaceflight, Outer space, Solar System, Science Astronomical coordinate systems Celestial mechanics Mass Geometric centers