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,
$$ F = - \nabla V $$
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.


Gravity Anomaly Polar Axis Gravity Measurement Gravitational Attraction Equipotential Surface 
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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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