Spheroid Formula

A spheroid is an ellipsoid shaped like a sphere. It has two axes and semi diameters of equal length . There are two types of spheroids namely, Oblate and Prolate. Oblate is represented when ellipse is rotated to its major axis and Prolate is represented when ellipse is rotated to its minor axis. World Geodetic System use spheroid with radius 6,378.137 km at the equator and 6,356.752 km at the poles. Use Spheroid formula to find area, volume and aspect ratio.

Oblate and Prolate Spheroid Formula

Area

Oblate


Soblate = 2πa2(1+((1-e2)/e)*(tanh-1*e))
Where
e2 = 1-c2/a2

Spheroid Formula

Prolate


Sprolate = 2πa2(1+(c/ae)*sin-1)*e)
Where
e2 = 1-a2/c2
Spheroid Formula

Volume(Common for both spheriod)

V = (4π/3)a2c ≈ 4.19a2c

Aspect ratio(Common for both spheriod)

Ratio f = (a-b)/a = 1-(b/a)

Where
c = Distance from centre to pole along the symmetry axis
a = Equatorial radius of the spheroid

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