Prove that the earth is oblate spheroid?

Answer 1

Short Answer:

Earth is an oblate spheroid, slightly bulged at the equator.

Centrifugal force and gravity together are responsible for the shape of the earth.

Explanation:

If the Earth were not rotating, it would only have gravity pulling all of its parts together and that tends to form a perfect sphere. It is not perfect, but the earth takes the shape of an oblate ellipsoid due to centrifugal forces perpendicular to the axis of rotation. The centrifugal force gets larger as the distance from the axis of rotation increases, so it is zero at the poles and increases to a maximum at the equator.

History:

In 1687 Isaac newton published in the Principia a proof that a rotating body with gravitation would develop a surface in the shape of an oblate ellipsoid. (The term oblate spheroid means the same thing.)

Half a century later, this became controversial in Europe and in 1736 the King of France sent the mathematician and physicist Pierre Louis Maupertuis on an expedition to Lapland to do the necessary grade measurements.

Data:

The Earth's equatorial radius (semi-major axis) is the distance from its center to the equator and equals 6,378.1370 kilometers (3,963.1906 mi).

The Earth's polar radius (semi-minor axis) is the distance from its center to the North and South Poles, and equals 6,356.7523 kilometers (3,949.9028 mi).

The surface of the Earth is obviously not smooth and mountains and trenches represent variations of several kilometers (or miles), about 0.02%. Other relatively minor variations in the shape of the earth are due to variations in the density of the crust and geomorphological processes.