In physics, the center of mass
[technically, the “center of gravity in non-uniform fields”] of a
distribution of mass in space is the unique point where the weighted relative
position of the distributed mass sums to zero. The distribution of mass is
balanced around the center of mass and the average of the weighted position
coordinates of the distributed mass defines its coordinates. Calculations in mechanics
are often simplified when formulated with respect to the center of mass.
In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The centerof mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system.
Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish. Near the surface of the earth, where the gravity acts downward as a parallel force field, the center of gravity and the center of mass of an arbitrary body are the same.
The study of the dynamics of aircraft, vehicles and vessels assumes that the system moves in near-earth gravity, and therefore the terms center of gravity and center of mass are used interchangeably.
In physics the benefits of using the center of mass to model a mass distribution can be seen by considering the resultant of the gravity forces on a continuous body.
In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass. The centerof mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system.
Definition
The center of
mass is the unique point at the center of a distribution of mass in space that
has the property that the weighted position vectors relative to this point sum
to zero. In analogy to statistics, the center of mass is the mean location of a
distribution of mass in space.
Center of Gravity
Center of gravity is the point in a body around which the resultant torque due to gravity forces vanish. Near the surface of the earth, where the gravity acts downward as a parallel force field, the center of gravity and the center of mass of an arbitrary body are the same.
The study of the dynamics of aircraft, vehicles and vessels assumes that the system moves in near-earth gravity, and therefore the terms center of gravity and center of mass are used interchangeably.
In physics the benefits of using the center of mass to model a mass distribution can be seen by considering the resultant of the gravity forces on a continuous body.
Astronomy
The center of
mass plays an important role in astronomy and astrophysics, where it is
commonly referred to as the barycenter. The barycenter is the point
between two objects where they balance each other; it is the center of mass
where two or more celestial bodies orbit each other. When a moon orbits a
planet, or a planet orbits a star, both bodies are actually orbiting around a
point that lies away from the center of the primary (larger) body. For example, the Moon does not orbit the exact
center of the, but a point on a line between the center of the Earth and the
Moon, approximately 1,710km (1062 miles) below the surface of the Earth, where
their respective masses balance. This is the point about which the Earth and
Moon orbit as they travel around the Sun. If the masses are more similar, e.g.,
Pluto and Charon, the barycenter will fall outside both bodies.
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