Gee

:This article is about the unit of acceleration. GEE is also the name of a WWII radio navigation device built and implemented by the RAF for use in night bombing. For the Latin alphabet letter, see G.

Calculated value of g

Given the law of universal gravitation, g is merely a collection of terms in that equation:

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:F = G rac{m_1 m_2}{r^2}=(G rac{m_1}{r^2}) m_2 where g is the bracketed terms and thus:

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:g=G rac {m_1}{r^2}

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We can plug in values of G and the mass and radius of the Earth to obtain the calculated value of g:

Related Topics:
Mass - Radius - Earth

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:g=G rac {m_1}{r^2}=(6.6742 imes 10^{-11}) rac{5.9736 imes 10^{24}}{(6.37101 imes 10^6)^2}=9.822 mbox{m/s}^2

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This agrees approximately with the measured value of g. The difference may be attributed to several factors:

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• The Earth is not homogeneous
• The Earth is not a perfect sphere
• The choice of a value for the radius of the Earth (an average value is used above)
• The normal measured g also includes the centrifugal force effects due to the rotation of the Earth

There are significant uncertainties in the values of G and of m1 as used in this calculation. However, the value of g can be measured precisely and in fact, Henry Cavendish performed the reverse calculation to estimate the mass of the Earth.

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