The Relativity of Wrong: Essays on the Solar System and Beyond (Oxford Paperbacks) by Isaac Asimov

Author:Isaac Asimov [Asimov, Isaac]
Language: eng
Format: epub, pdf
Tags: pol_guide
ISBN: 9780192826329
Amazon: 0192826328
Publisher: Clarendon Pr
Published: 1989-03-15T00:00:00+00:00

And yet is the Earth a sphere?

No, it is not a sphere; not in the strict mathematical sense. A sphere has certain mathematical properties—for instance, all diameters (that is, all straight lines that pass from one point on its surface, through the center, to another point on its surface) have the same length.

That, however, is not true of the Earth. Various diameters of the Earth differ in length.

What gave people the notion the Earth wasn't a true sphere? To begin with, the Sun and the Moon have outlines that are perfect circles within the limits of measurement in the early days of the telescope. This is consistent with the supposition that the Sun and Moon are perfectly spherical in shape.

However, when Jupiter and Saturn were observed by the first telescopic observers, it became quickly apparent that the outlines of those planets were not circles, but distinct ellipses. That meant that Jupiter and Saturn were not true spheres.

Isaac Newton, toward the end of the seventeenth century, showed that a massive body would form a sphere under the pull of gravitational forces (exactly as Aristotle had argued), but only if it were not rotating. If it were rotating, a centrifugal effect would be set up which would lift the body's substance against gravity, and the effect would be greater the closer to the equator you progressed. The effect would also be greater the more rapidly a spherical object rotated and Jupiter and Saturn rotated very rapidly indeed.

The Earth rotated much more slowly than Jupiter or Saturn so the effect should be smaller, but it should still be there. Actual measurements of the curvature of the Earth were carried out in the eighteenth century and Newton was proved correct.

The Earth has an equatorial bulge, in other words. It is flattened at the poles. It is an "oblate spheroid" rather than a sphere. This means that the various diameters of the earth differ in length. The longest diameters are any of those that stretch from one point on the equator to an opposite point on the equator. The "equatorial diameter" is 12,755 kilometers (7,927 miles). The shortest diameter is from the North Pole to the South Pole and this "polar diameter" is 12,711 kilometers (7,900 miles).

The difference between the longest and shortest diameters is 44 kilometers (27 miles), and that means that the "oblateness" of the Earth (its departure from true sphericity) is 44/12,755, or 0.0034. This amounts to 1/3 of 1 percent.

To put it another way, on a flat surface, curvature is 0 per mile everywhere. On Earth's spherical surface, curvature is 0.000126 per mile everywhere (or 8 inches per mile). On Earth's oblate spheroidical surface, the curvature varies from 7.973 inches to the mile to 8.027 inches to the mile.

The correction in going from spherical to oblate spheroidal is much smaller than going from flat to spherical. Therefore, although the notion of the Earth as sphere is wrong, strictly speaking, it is not as wrong as the notion of the Earth as flat.

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