From Wikipedia, the free encyclopedia
  (Redirected from Earth-Moon barycenter)
Jump to navigation Jump to search

The barycenter (or barycentre; from the Ancient Greek βαρύς heavy + κέντρον centre[1]) is the center of mass of two or more bodies that orbit each other and is the point about which the bodies orbit. It is an important concept in fields such as astronomy and astrophysics. The distance from a body's center of mass to the barycenter can be calculated as a two-body problem.

If one of 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, in which the barycenter is located on average 4,671 km (2,902 mi) from the Earth's center, well within Earth's radius of 6,378 km (3,963 mi). When the two bodies are of similar masses, the barycenter will generally be located between them and both bodies will follow an orbit around it. This is the case for Pluto and Charon, as well as for many binary asteroids and binary stars. When the less massive object is far away, the barycenter can be located outside the more massive object. This is the case for Jupiter and the Sun; despite the Sun being thousandfold more massive than Jupiter, their barycenter is outside the Sun due to the relatively large distance between them.[2]

In astronomy, barycentric coordinates are non-rotating coordinates with the origin at the barycenter of two or more bodies. The International Celestial Reference System is a barycentric coordinate system centered on the Solar System's barycenter.

In geometry, the term barycenter is synonymous with centroid, the geometric center of a geometric figure.

Two-body problem[edit]

Barycentric view of the PlutoCharon system as seen by New Horizons

The barycenter is one of the foci of the elliptical orbit of each body. This is an important concept in the fields of astronomy and astrophysics. If a is the distance between the centers of the two bodies (the semi-major axis of the system), r1 is the semi-major axis of the primary's orbit around the barycenter, and r2 = ar1 is the semi-major axis of the secondary's orbit. When the barycenter is located within the more massive body, that body will appear to "wobble" rather than to follow a discernible orbit. In a simple two-body case, r1, the distance from the center of the primary to the barycenter is given by:

where :

r1 is the distance from body 1 to the barycenter
a is the distance between the centers of the two bodies
m1 and m2 are the masses of the two bodies.

Primary–secondary examples[edit]

The following table sets out some examples from the Solar System. Figures are given rounded to three significant figures. The term primary–secondary is used to distinguish between involved participants; with the larger called "the primary", and the smaller called "the secondary".

  • R1 (km) is the radius of the primary
Primary–secondary examples
Primary m1
Secondary m2
Earth 1 Moon 0.0123 384,000 4,670 6,380 0.732[A]
Pluto 0.0021 Charon
(0.121 M)
  19,600 2,110 1,150 1.83[B]
Sun 333,000 Earth 1
(1 AU)
449 696,000 0.000646[C]
Sun 333,000 Jupiter
(0.000955 M)
(5.20 AU)
742,000 696,000 1.07[D]
C The Sun's wobble is barely perceptible.

Inside or outside the Sun?[edit]

Motion of the Solar System's barycenter relative to the Sun



That is, where the planet is massive and far from the Sun.


To calculate the actual motion of the Sun, you only need to consider the motions of the four giant planets (Jupiter, Saturn, Uranus, Neptune). 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 about 1.17 solar radii or just over 810,000 km above the Sun's surface.[5]


Note that the Sun–Jupiter system, with eJupiter = 0.0484, just fails to qualify: 1.05 < 1.07 > 0.954.


Images are representative (made by hand), not simulated.

Relativistic corrections[edit]



Selected barycentric orbital elements[edit]

Barycentric osculating orbital elements for some objects in the Solar System:[7]

Object Semi-major axis
(in AU)
(in AU)
Orbital period
(in years)
C/2006 P1 (McNaught) 2,050 4,100 92,600
C/1996 B2 (Hyakutake) 1,700 3,410 70,000
C/2006 M4 (SWAN) 1,300 2,600 47,000
(308933) 2006 SQ372 799 1,570 22,600
(87269) 2000 OO67 549 1,078 12,800
90377 Sedna 506 937 11,400
2007 TG422 501 967 11,200

For objects at such high eccentricity, the Sun's barycentric coordinates are more stable than heliocentric coordinates.[8]

See also[edit]


  1. ^ Oxford English Dictionary, Second Edition.
  2. ^ MacDougal, Douglas W. (December 2012). Newton's Gravity: An Introductory Guide to the Mechanics of the Universe. Berlin: Springer Science & Business Media. p. 199. ISBN 1-4614-5444-1. 
  4. ^ "What's a Barycenter?". Space Place @ NASA. 2005-09-08. Archived from the original on 23 December 2010. Retrieved 2011-01-20. 
  7. ^ Horizons output (2011-01-30). "Barycentric Osculating Orbital Elements for 2007 TG422". Archived from the original on 2014-03-28. Retrieved 2011-01-31.  (Select Ephemeris Type:Elements and Center:@0)