Question

Is gravitational force a vector ?justify ?​

Answer 1

Answer:

The gravitational force, as any force, is a vector.

The gravitational field is actually a tensor field. However, in most common applications, relativity theory contributes only a tiny correction and it can be safely ignored. Which means that most of the components of this tensor field are so small that they contribute very little to the motion of a test particle. The only term that remains relevant, then, is one component of that tensor field, which will behave (approximately) as a scalar field.

The gradient of that scalar field is, in fact, the gravitational acceleration. Multiplied by the mass of a test particle, it yields the (vector) force on that particle.

In terms of the most relevant equations using the language of vector calculus, the (nonrelativistic) gravitational field ϕ is the solution to Poisson’s equation for gravity, ∇2ϕ=4πGρ , where ρ is the mass density and G is Newton’s constant. When ρ is a point mass of mass M , the solution becomes ϕ=−GM/r , where r is the radial distance from that mass. The gravitational acceleration of a test particle is a=−∇ϕ=−GMr/r3 where r is the vector pointing from the source to the test particle (i.e., r=|r| ). The force on a particle of mass m is given by Newton’s second law: F=ma .

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