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# Spheroid

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## Spheroid Meaning

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In-plane geometry, a spheroid shape, or ellipsoid of revolution, refers to a quadric surface obtained by rotating an ellipse about one of its principal axes. This is to say, a spheroid is an ellipsoid with 2 equal semi-diameters with a circular symmetry.

If the ellipse is revolved about its major axis, the outcome is a prolate (elongated) spheroid, shaped like a rugby ball. An oblate or flattened spheroid is an outcome of a rotating ellipse around its minor axis. If the producing ellipse is a circle, the outcome is a sphere.

### Applications of Spheroid

The neutrons and protons of an atomic nucleus are mostly found in the spherical, oblate, or prolate spherical shapes along with having a spinning axis. Deformed nuclear shapes typically form as an outcome of the competition between electromagnetic repulsion between protons, quantum shell effects, and surface tension.

### Oblate Spheroids Meaning

A ''squashed'' Spheroid of which the equatorial radius ‘a’ is larger than the polar radius ‘c’, such that a > c. To a first approximation, the shape assumed by a rotating fluid (inclusive of the Earth, that is fluid'' over astronomical time scales) is known as an oblate spheroid. The oblate spheroid can be identified parametrically by the general Spheroid equations (for a Spheroid having z-Axis as the symmetry axis).

### Oblate Spheroid Shape

The oblate spheroid shape can be defined as an assumed shape for various celestial bodies and planets that are rotating rapidly at their own axis. For example, the Earth, Saturn, and Jupiter. The English mathematician, Enlightenment scientist, and astronomer –Isaac Newton reasoned that Earth and Jupiter are oblate spheroids owing to their centrifugal force. Earth's diverse geodetic and cartographic systems are formed on reference ellipsoids, all of which are oblate.

### Example of Oblate Spheroids

An example of an oblate spheroid is the planet Jupiter with a flattening spheroid of 0.06487. Another science-fiction of an extremely oblate spheroid earth is Mesklin from Hal Clement's novel Mission of Gravity.

### Prolate Spheroids

The prolate spheroid is an estimated shape of the ball in various sports, such as rugby football. The word is also used to depict the shape of some nebulae like the Crab Nebula.

Several moons of the Solar System estimate prolate spheroids in shape, although they are really triaxial ellipsoids.

On contrary to being distorted into oblate spheroids through quick rotation, celestial objects distort little into prolate spheroids through tidal forces when they orbit a massive body in a close orbit. An utmost example is Jupiter's moon Io, which becomes slightly more or less prolate in its orbit because of little eccentricity, inducing intense volcanism. However, the major axis of a prolate spheroid does not run across the satellite's poles, but through the two points on its equator straightaway facing toward and away from the primary.

### Example of a Prolate Spheroids

• An Australian rules football is an example of a prolate spheroid.

• Many submarines have a shape that can be depicted as a prolate spheroid.

• Another example includes the atomic nucleus of the element belonging to the lanthanide and actinide groups.

• In anatomy, near-spheroid organs such as testis.

• Fresnel zones used to evaluate wave propagation and interference in space.

Other Examples of prolates include Saturn's satellites Enceladus, Mimas, and Uranus' and Tethys satellite Miranda.

### Geoid and Spheroid

The geoid is essentially described as the surface of the earth's gravity field that approximates mean sea level. The geoid is perpendicular to the direction of the force of gravity. Because the mass of the Earth is not uniform in nature at all points, the magnitude of gravity thus differs, and the shape of the geoid is irregular.

### Fun Facts

• Saturn is considered to be the most oblate planet in the Solar System. It has a flattening of 0.09796.

Q1. Why Actually is a Spheroid?

Answer: The term spheroid originally meant "an estimated spherical body", disclosing irregularities even beyond the bi- or tri-axial ellipsoidal shape, and that is how the word is frequently being used in some older publishing on geodesy (for example, referring to truncated spherical harmonic diversifications of the Earth.

Q2. Why is Planet Earth Considered an Oblate Sphere?

Answer: owing to the combined effects of rotation and gravity, the figure of the Earth (and matter of fact of all planets) is not quite a sphere, but instead is bit flattened in the direction of its axis of rotation. For that reason, in geodesy and cartography the Earth is often estimated by an oblate spheroid shape, referred to as the reference ellipsoid, instead of a sphere. The current World Geodetic System model makes use of a spheroid of which the radius is 3,963.191 mi (6,378.137 km) at the Equator and 3,949.903 mi (6,356.752 km) at the poles.

Q3. What is an Ellipsoid?

Answer: Ellipsoid is a closed surface whose all plane cross-sections are either circles or ellipses. An ellipsoid is symmetrical in shape about three mutually perpendicular axes that bisect at the centre.

If m, n, and o are the principal semiaxes, a basic equation of such an ellipsoid is x2/m2 + y2/n2 + z2/o2 = 1.  A unique case occurs when m = n= o: then the surface is a sphere, and the bisection with any plane crossing through it is a circle. If two axes are equivalent, say m = n, and different from the 3rd, o, then the ellipsoid is an ellipsoid of revolution, or spheroid (a shape formed by revolving an ellipse about one of its axes). If n is smaller than both m and o, then the spheroid is said to be an oblate; but it is said to be a prolate spheroid if m and n are lesser than o.