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Abstract

With reference to Section 6.1, we have for a conservative field of force
$$ - dV = {F_{x}}dx + {F_{y}}dy + {F_{z}}dz $$
from which it follows that
$$ {F_{x}} = - \frac{{\partial V}}{{\partial x}}{F_{y}} = - \frac{{\partial V}}{{\partial y}}{F_{z}} = - \frac{{\partial V}}{{\partial z}} $$
or, in vector notation,
$$ F = - \nabla V $$
(8.1)
This is a fundamental relation in the consideration of problems in gravitation theory. It states that we may determine the vector quantity F, the gravitational attraction, by first solving for the scalar potential V and then taking the derivative. For most complex gravitational problems, this is often the simplest method of solution.

Keywords

Gravity Anomaly Polar Axis Gravity Measurement Gravitational Attraction Equipotential Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1974

Authors and Affiliations

  • Charles B. Officer
    • 1
  1. 1.Marine Environmental ServicesHanoverUSA

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