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The surface area of an ... (i.e. the formula for S oblate can be used to calculate the surface area of a ... The mass of an ellipsoid of uniform density ...
The planet Jupiter is a slight oblate spheroid with a flattening of 0.06487. The oblate spheroid is the approximate shape of rotating planets and other celestial bodies, including Earth, Saturn, Jupiter, and the quickly spinning star Altair. Saturn is the most oblate planet in the Solar System, with a flattening of 0.09796. [5]
Better approximations can be made by modeling the entire surface as an oblate spheroid, using spherical harmonics to approximate the geoid, or modeling a region with a best-fit reference ellipsoid. For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature.
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 ]
In geodesy, a reference ellipsoid is a mathematically defined surface that approximates the geoid, which is the truer, imperfect figure of the Earth, or other planetary body, as opposed to a perfect, smooth, and unaltered sphere, which factors in the undulations of the bodies' gravity due to variations in the composition and density of the ...
The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly or negative disturbing potential (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly or positive disturbing potential (mass deficit). [16]
Figure 1: Coordinate isosurfaces for a point P (shown as a black sphere) in oblate spheroidal coordinates (μ, ν, φ). The z-axis is vertical, and the foci are at ±2. The red oblate spheroid (flattened sphere) corresponds to μ = 1, whereas the blue half-hyperboloid corresponds to ν = 45°.
It is an oblate spheroid, with an equatorial diameter 8% larger than its polar diameter. [2] Measurements from the Dawn spacecraft found a mean diameter of 939.4 km (583.7 mi) [2] and a mass of 9.38 × 10 20 kg. [62] This gives Ceres a density of 2.16 g/cm 3, [2] suggesting that a quarter of its mass is water ice. [63]