Gravitational acceleration, g

When a mass is close to another mass, they attract one another. The attraction force is called gravitation. The gravitational force, F, depends on the magnitude of the masses, m1 and m2, the distant separating them, r, and the universal gravitational constant, G:

F = G . m1 . m2) / r²

The acceleration exerted on a mass by the mass of the earth is called the “gravitational acceleration”, designated g. 

If the earth were not rotating and if it were just a smooth sphere of constant density, the value of g would be a constant all over the earth. However, the earth is rotating, so objects experience a centripetal acceleration (zero at the poles and a maximum on the equator) that reduces gravity. The earth is also not a sphere, but an oblate spheroid (flatter at the poles and bulging at the equator. The surface also has topography – hills and valleys, mountains and deep ocean trenches. Finally, the rocks of the earth have different densities. (Sensitive gravitometers can map the variation of gravity over an area to locate salt lenses, which indicate the best location to drill an oil well.)

Because of all these effects, the effective gravity on the Earth’s surface varies by around 0.7%, from 9.7639 m/s² on the Nevado Huascarán mountain in Peru to 9.8337 m/s² at the surface of the Arctic Ocean.[4] In large cities, it ranges from 9.766 in Kuala Lumpur, Mexico City, and Singapore to 9.825 in Oslo and Helsinki. The value of g is highest near the earth’s poles. Elsewhere, it is reduced by the centripetal acceleration caused  by the rotation of the earth. Near the equator, the value of g is around 9.806 m/s².

In most engineering calculations, gravity does not need to be known to great accuracy. However, when testing hydro turbines (model turbines in a test laboratory or prototype turbines in a powerhouse) each percentage of efficiency can be worth a lot of money to the turbine manufacturer and Owner, so a very accurate value of g is calculated for the test location using a formula in the International Electrotechnical Commission (IEC) standard.

Published by hydrogray

Hydropower specialist

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