What is the shape of the Earth?

To first approximation, out planet is a sphere. But how accurate is that approximation? What’s a better approximation? How good is that? This post will answer these questions and some related questions.

How well does a sphere describe the Earth’s shape? The Earth’s polar diameter is about 43 kilometers shorter than its equatorial diameter, a difference of about 0.3%.This is due to the equatorial bulge caused by the Earth’s rotation.

What’s a more accurate description of the Earth’s shape? An oblate spheroid.

What is an oblate spheroid? It’s the shape you get by spinning an ellipse around it’s minor axis. That says if you were to take a cross-section of the Earth containing the polar axis, the shape you get would be an ellipse. The polar axis would be the minor axis and the equatorial axis would be the major axis. But if you were to take a cross-section through the equator, or any plane parallel to the equator, you’d get a circle.

What is a prolate spheroid? A prolate spheroid is what you get by spinning an ellipse around its major axis.

What is an ellipsoid? An ellipsoid satisfies the following equation.

\left(\frac{x}{a}\right)^2 + \left(\frac{y}{b}\right)^2 + \left(\frac{z}{c}\right)^2 = 1

A sphere is an ellipsoid with a = b = c. An oblate spheroid is an ellipsoid with a = b > c. A prolate spheroid is an ellipsoid with a = b < c. A scalene ellipsoid is an ellipsoid for which a, b, and c are all distinct.

How good is the oblate spheroid model? The error in approximating the Earth’s shape as an oblate spheroid is less than 100 meters, two orders of magnitude better than the spherical model.

How are other planets shaped? The other planets in our solar system are also oblate spheroids with Saturn being the most oblate: the polar diameter of Saturn is about 10% shorter than its equatorial diameter.

Related post: Finding distances using longitude and latitude

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8 thoughts on “What is the shape of the Earth?

  1. The Earth does not conform to any true geometrical shape. Your suppositions are interesting but its known shape is what should be considered. They seem to imply that if the forces causing its known shape somehow ceased to be effective the Earth might contract to a sphere but it could as easily contract into an even more irregular shape.

  2. To first approximation, the radius is the same everywhere. But when more accuracy is needed, we have to consider that the radius changes. So we talk about equatorial radius or polar radius. But if we need even more accuracy, we have to consider that the earth is kinda lumpy.

  3. The rotation of the earth affects the winds and thereby the weather, but what about the non-spherity of the earth?

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