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====== Center of Mass ======

The **center of mass** (also called the **center of gravity** in uniform gravitational fields) of a physical system is the unique point at which the system's total mass may be considered to be concentrated for the purpose of analyzing its motion under external forces. For a rigid body or a collection of particles, the center of mass is the mass-weighted average position of all constituent matter. It is a fundamental concept in classical mechanics, celestial mechanics, and engineering, and applies to systems ranging from subatomic particles to galaxy clusters.

===== Definition and Properties =====

For a system of //n// discrete particles with masses //m,,i,,// at positions **r**,,i,,, the center of mass position **R** is defined as:

  R = (Σ mᵢrᵢ) / M

where //M// = Σ //m,,i,,// is the total mass of the system. For a continuous body, the sum becomes an integral over the mass distribution. The center of mass need not lie within the physical boundary of the object - a hollow sphere, a ring, or a crescent shape all have centers of mass located in empty space.

Key properties include:

  * **Newton's laws apply directly:** The net external force on a system equals the total mass times the acceleration of the center of mass, regardless of internal forces or the distribution of mass.
  * **Conservation:** In the absence of external forces, the center of mass moves at constant velocity (or remains at rest).
  * **Additivity:** The center of mass of a composite system can be computed from the centers of mass of its subsystems, weighted by their masses.

===== Role in Celestial Mechanics =====

In multi-body gravitational systems, bodies orbit their common center of mass rather than one another's geometric centers. In the Earth-Moon system, the center of mass (the **barycenter**) lies approximately 4,600 km from Earth's geometric center - well within Earth's radius of about 6,371 km. In the Sun-Jupiter system, the barycenter lies just outside the solar surface, at roughly 1.07 solar radii from the Sun's center. This has observational consequences: the Sun itself traces a small orbit around the solar system's barycenter, a fact exploited in exoplanet detection via the radial velocity method.

The concept of the barycenter is central to both Newtonian and Einsteinian models of orbital mechanics, though the two frameworks differ in their underlying descriptions. See [[heliocentrism|Heliocentrism]] for discussion of how the barycenter bears on questions about what, precisely, the planets orbit.

===== Consensus Status =====

The mathematical definition and physical predictions of center-of-mass mechanics are part of the [[center-of-mass-physics-consensus|consensus of classical and relativistic physics]]. The formalism is not scientifically contested. Debates involving center-of-mass concepts - such as those in heliocentric modeling - concern interpretation or terminology, not the underlying mechanics.

===== Viewpoints =====

Disagreements involving the center of mass tend to arise in adjacent interpretive contexts rather than about the concept itself:

  * **[[heliocentrism-barycentric-heliocentrism-viewpoint|Barycentric heliocentrism]]** - The view that the Sun is not literally the center of the solar system because the planets technically orbit the solar system's barycenter, which is sometimes outside the solar surface.
  * **[[heliocentrism-solar-heliocentrism-viewpoint|Solar heliocentrism]]** - The view that heliocentrism correctly places the Sun at or near enough to the center for the model to remain valid and useful, with the barycentric displacement being a refinement rather than a refutation.

===== Related Pages =====

  * [[center-of-mass-history|Center of Mass - History]]
  * [[heliocentrism|Heliocentrism]]
  * [[classical-mechanics|Classical Mechanics]]
  * [[barycenter|Barycenter]]
  * [[orbital-mechanics|Orbital Mechanics]]
  * [[center-of-mass-physics-consensus|Center of Mass - Physics Consensus]]

===== Footnotes =====

  - Halliday, David; Resnick, Robert; Krane, Kenneth S. //Physics//, 5th ed. (New York: Wiley, 2002), vol. 1, ch. 9.
  - Goldstein, Herbert; Poole, Charles; Safko, John. //Classical Mechanics//, 3rd ed. (San Francisco: Addison-Wesley, 2002), ch. 1.
  - Fitzpatrick, Richard. //An Introduction to Celestial Mechanics// (Cambridge: Cambridge University Press, 2012), ch. 5.
  - NASA Jet Propulsion Laboratory. "Solar System Dynamics." https://ssd.jpl.nasa.gov/ Accessed 2025.