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Optimising the acceleration due to gravity on a planet's surface

  • Michael Jewess (a1)
Abstract

The Earth (more precisely, the ‘geoid’ thereof) is known to approximate closely to a slightly oblate spheroid whose unique axis coincides with the Earth's axis of rotation [1,2]. (By ‘spheroid’ is meant is an ellipsoid of revolution, i.e. one with two semi-axes equal; a slightly oblate one has these two semi-axes slightly longer than the unique one.) To the nearest km, the diameter of the ‘geoid’ pole-to-pole is 43 km less than the equatorial diameter of 12756 km. There is a reduction of practical significance (0.527%) in the acceleration of free fall" at sea level between the poles and the equator, and therefore in the weight of objects. Of this, 0.345% derives directly from the rotation of the Earth; the balance of 0.182% results from the purely gravitational effect of the Earth's deviation from sphericity.

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The Mathematical Gazette
  • ISSN: 0025-5572
  • EISSN: 2056-6328
  • URL: /core/journals/mathematical-gazette
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