Direct gravity formula for the Geodetic Reference System 1967
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A Direct Gravity Formula, polynomial in latitude, has been obtained from the series expansion of the closed gravity formula of Somigliana by a telescoping procedure. The use of the 7 coefficient formula gives a result as accurate as the closed expression. With 6 coefficients it gives an order of magnitude better accuracy than that of the widely used Chebyshev approximation and with 5 coefficients a result that is accurate to better than that of the conventional form of computing theoretical gravity. The derived approximation is not only simpler than other forms, but also at least 11 and 17 times faster on the CDC CYBER 74 computer than the Chebyshev approximation and the closed gravity formula respectively.
KeywordsPower Series Chebyshev Polynomial Require Accuracy Conventional Form Economical Form
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