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The gravitational force fields are both scalar and vector. The forces are the first derivative of the energy.

The derivative is a Quaternion derivative X=[d/dr,Del].


The total energy is W = -mGM/r + cP and there are five forces,

F = XW= [d/dr,Del][-mGM/r, cP] = [vp/r -cDel.P, cdP/dr - Del mGM/r + cDelxP]


The scalar forces are :

vp/r centripetal scalar force

-cDel.P= -cp/r cos(PR) centrifugal scalar force


the vector forces are:

cdP/dr = -cp/r R/r tangent force

Del -mGM/r = vp/r R/r gradient force

cDelxP = RxP cp/r sin(PR) Curl force.

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More answers

Vector. Its forces not only have magnitude (strength), but also have direction.

The force on each member of the pair of objects is directed toward the center

of mass of the other one.
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Q: Is gravitational field scalar or vector?
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