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L02_GravTheoryMeasurement-page3

L02_GravTheoryMeasurement-page3 - Applied Geophysics –...

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Applied Geophysics – Gravity theory and measurement Gravity and potentials 1 2 r g E E R GM = where r 1 is the unit vector pointing toward the center of the Earth r Gm U = Gravitational potential: U is a scalar field which makes it easier to work with g is a vector field: Definition: The gravitational potential, U, due to a point mass m, at a distance r from m, is the work done by the gravitational force in moving a unit mass from infinity to to a position r from m.
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Unformatted text preview: Applied Geophysics – Gravity theory and measurement Relating g to U 2 r Gm r U = ∂ ∂ − = g It follows that: For smaller scale problems we usually deal with g, and sum the vertical component of g… r Gm U = Given: U is a scalar field which makes it easier to work with: • Potentials are additive • Gravity is a conservative force • And gravitational acceleration can be easily determined from the potential…...
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