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Within a uniform spherical body of radius R, density ρ, and mass m, the gravitational force g inside the sphere varies linearly with distance r from the center, giving the gravitational potential inside the sphere, which is [7] [8] = [] = [],, which differentiably connects to the potential function for the outside of the sphere (see the figure ...
A corollary is that inside a solid sphere of constant density, the gravitational force within the object varies linearly with distance from the center, becoming zero by symmetry at the center of mass. This can be seen as follows: take a point within such a sphere, at a distance from the center of the sphere. Then you can ignore all of the ...
For example, a hollow sphere does not produce any net gravity inside. The gravitational field inside is the same as if the hollow sphere were not there (i.e. the resultant field is that of all masses not including the sphere, which can be inside and outside the sphere).
Siméon Denis Poisson. Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics.For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with the potential field known, one can then calculate the corresponding electrostatic or gravitational (force) field.
Examples of such potentials are the electric potential, the magnetic potential and the gravitational potential. For clarity, we illustrate the expansion for a point charge , [ 1 ] then generalize to an arbitrary charge density ρ ( r ′ ) . {\displaystyle \rho (\mathbf {r} ').}
The quadrupole moment tensor Q is a rank-two tensor—3×3 matrix. There are several definitions, but it is normally stated in the traceless form (i.e. + + =).The quadrupole moment tensor has thus nine components, but because of transposition symmetry and zero-trace property, in this form only five of these are independent.
The gravitational force experienced by a particle of light mass m, close to the surface of Earth is given by =, where g is Earth's gravity. [ 3 ] [ 4 ] An electric field E {\displaystyle \mathbf {E} } exerts a force on a point charge q , given by F = q E {\displaystyle \mathbf {F} =q\mathbf {E} } .
The electric potential arising from a point charge, Q, at a distance, r, from the location of Q is observed to be =, where ε 0 is the permittivity of vacuum [4], V E is known as the Coulomb potential.