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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°.
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]
A sphere of influence (SOI) in astrodynamics and astronomy is the oblate spheroid-shaped region where a particular celestial body exerts the main gravitational influence on an orbiting object. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects such as moons , despite the ...
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.
In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of a flattened ("oblate") ellipsoid of revolution, generated by an ellipse rotated around its minor diameter; a shape which he termed an oblate spheroid. [2] [3]
which, as follows from basic trigonometric identities, are equivalent expressions (i.e. the formula for S oblate can be used to calculate the surface area of a prolate ellipsoid and vice versa). In both cases e may again be identified as the eccentricity of the ellipse formed by the cross section through the symmetry axis.
Still, Trump's nomination of Scott Bessent to the top Treasury post raised hopes that tariffs will be more measured. And with only 21 trading days left in the year, analysts, investors, and market ...
The WGS 84 datum surface is an oblate spheroid with equatorial radius a = 6 378 137 m at the equator and flattening f = 1 ⁄ 298.257 223 563. The refined value of the WGS 84 gravitational constant (mass of Earth's atmosphere included) is GM = 3.986 004 418 × 10 14 m 3 /s 2. The angular velocity of the Earth is defined to be ω = 72.921 15 × ...