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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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.Vector.
A scalar times a vector is a vector.
A magnetic field is neither: it is a vector field with both direction and quantity.
When one refers to the strength of a magnetic field, they're usually referring to the scalar magnitude of the magnetic field vector, so no.
In mathematics, a field is a set with certain operators (such as addition and multiplication) defined on it and where the members of the set have certain properties. In a vector field, each member of this set has a value AND a direction associated with it. In a scalar field, there is only vaue but no direction.