1721. The Variation of Gravity and Its Application to the Measurement of Weight

Paper

Abstract

The measurement of the weight of a stationary object on the surface of the Earth is the measurement of a force. This force is the sum of the gravitational attractions of the Earth, Moon and Sun and the centrifugal force caused by the rotation of the Earth. Because the acceleration of gravity varies over the Earth, the weight of an object also varies from place to place. The variations in the acceleration of gravity due to changes in height above sea level and to changes in latitude can be expressed by simple formulas. The magnitude of these variations is slightly less than 11 of the total gravitational acceleration over the surface of the Earth, and is about 0.2% over the contiguous United States. Variations due to other causes are smaller, but may be significant in high-precision weight measurements. The variations due to the tidal accelerations of the Sun and the Moon (which may reach approximately 0.003% of the total acceleration of gravity) can be calculated by complex formulas or can be derived from continuous observations. The changes due to all other causes (such as mass density changes within the crust of the Earth) cannot be calculated by theory alone. The gravitational variations due to these causes must be directly measured or be estimated using deterministic formulas based on the statistical reduction of measured data. Thus, equipment used for precise weight measurements and moved after being calibrated may be in error by a significant amount.