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For a spheroid having uniform density, the moment of inertia is that of an ellipsoid with an additional axis of symmetry. Given a description of a spheroid as having a major axis c, and minor axes a = b, the moments of inertia along these principal axes are C, A, and B. However, in a spheroid the minor axes are symmetrical.
A Maclaurin spheroid is an oblate spheroid which arises when a self-gravitating fluid body of uniform density rotates with a constant angular velocity. This spheroid is named after the Scottish mathematician Colin Maclaurin, who formulated it for the shape of Earth in 1742. [1]
Rotation causes a distortion from this spherical shape; a common measure of the distortion is the flattening (sometimes called ellipticity or oblateness), which can depend on a variety of factors including the size, angular velocity, density, and elasticity.
The surface area of an ellipsoid of revolution (or spheroid) ... Thus the density function is a scalar-to-scalar transformation of a quadric expression.
The dip in the charge density near the Y-axis indicates the lower nuclear core density of some light nuclides. [26] Electron scattering techniques have yielded clues as to the internal structure of light nuclides. Proton-neutron pairs experience a strongly repulsive component of the nuclear force within ≈ 0.5 fm (see "Space between nucleons ...
The gravity anomaly at a location on the Earth's surface is the difference between the observed value of gravity and the value predicted by a theoretical model. If the Earth were an ideal oblate spheroid of uniform density, then the gravity measured at every point on its surface would be given precisely by a simple algebraic expression.
The red oblate spheroid (flattened sphere) corresponds to μ = 1, whereas the blue half-hyperboloid corresponds to ν = 45°. The azimuth φ = −60° measures the dihedral angle between the green xz half-plane and the yellow half-plane that includes the point P. The Cartesian coordinates of P are roughly (1.09, −1.89, 1.66).
This work was subsequently pursued by Laplace, who assumed surfaces of equal density which were nearly spherical. [12] [14] The English mathematician George Stokes showed in 1849 [12] that the theorem applied to any law of density so long as the external surface is a spheroid of equilibrium.