Measurement of Gravity for Study of Figure of the Earth

Abstract

Ever since 1687 when Sir Issac Newton gave his famous law of gravitation scientists all over the world have used it to study the figure of the earth. The law can be written as follows,

$$F = G \cdot \frac{{{m_1}{m_2}}}{{{r^2}}}$$

((1.1))

Where F is the force of attraction between two point masses m₁ and m₂ and r is the distance between them, G is the universal gravitational constant. The value of G has been determined by several workers including Henry Cavendish in 1798 and its latest value adopted is (6.673 ± 0.003) X 10⁻⁸ c.g.s. units (IUGG, 1967). In Equation (1.1) if we substitute m ₁ = 1 unit, m₂ = M, the mass of the earth, R- the distance from the centre of gravity of the earth to its surface, we can write,

$$g = \frac{{GM}}{{{R^2}}}$$

((1.2))

Where g is the acceleration due to gravity. It is expressed in ft sec ⁻² or cm sec ⁻². Geophysicists generally use a unit of ‘gal’ which is defined as an acceleration of 1 cm sec⁻². One milligal is 1/1000 of a gal.