Mass distribution

For other uses, see Weight distribution.

In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous.

Astronomy

In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation.

Mathematical modelling

A mass distribution can be modeled as a measure. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution. For example, a point mass is represented by a delta function defined in 3-dimensional space. A surface mass on a surface given by the equation f (x, y, z) = 0 may be represented by a density distribution g(x, y, z) δ(f (x, y, z)), where ${\textstyle g/\left|\nabla f\right|}$ is the mass per unit area.

The mathematical modelling can be done by potential theory, by numerical methods (e.g. a great number of mass points), or by theoretical equilibrium figures.

Geology

In geology the aspects of rock density are involved.

Rotating solids

Rotating solids are affected considerably by the mass distribution, either if they are homogeneous or inhomogeneous - see Torque, moment of inertia, wobble, imbalance and stability.

See also

• Bouguer plate
• Gravity
• Mass function
• Mass concentration (astronomy)

External links

• Mass distribution of the Earth