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Definition
Merriam-Webster's online dictionary states the definition of ellipticity as a "deviation of an ellipse or a spheroid from the form of a circle or a sphere."
Significance
There are two types of spheroid with ellipticity: an oblate spheroid and a prolate spheroid.
An oblate spheroid is a sphere that has been slightly flattened at the top and the bottom, tending to bulge out at the middle. It can be formed by rotating an ellipse about its minor axis (the shorter axis).
A prolate spheroid is a sphere whose middle has been slightly compressed. It can be formed by rotating an ellipse around its major axis (the longer one).
The measured deviation in both of these objects from a perfect sphere is the ellipticity of the objects and can be measured by two formulas.
Formulas for Ellipticity
From Wolfram MathWorld: "given a spheroid with equatorial radius a and polar radius c, the ellipticity is defined by:
e = Sqrt((a^2-c^2)/a^2) where in this case c < a and is an oblate spheroid. In words, the ellipticity is the square root of the equation--the equatorial radius squared minus the polar radius squared, all divided by the equatorial radius squared.
e = Sqrt((c^2-a^2)/c^2) where in this case c > a and is a prolate spheroid. In words, the ellipticity is the square root of the equation--the polar radius squared minus the equatorial radius squared, all divided by the polar radius squared
Cause
The ellipticity of an object is typically due to the relationship between the rotation of the object and the object's centrifugal force and gravity. The higher the ellipticity, the faster the object is moving.
Examples
Oblate spheroids are the approximate representations of many celestial bodies, the one most familiar to us being Earth. Earth's ellipticity can be calculated by the above formula for an oblate spheroid with 6378.1 km as the equatorial radius of the Earth (a) and 6356.8 km as the polar radius. The ellipticity of the Earth is then calculated to be 0.00335, as calculated on NASA's Earth Fact Sheet.