Is Newton's third law sufficient for electrical or gravitational forces between two objects to be a central force? (In the classical scale)

Question

I hope my question have captured concisely what I am asking about.

Answer 1

Newton's third law is basically just conservation of linear momentum, and it arises from a fundamental symmetry called spatial shift symmetry using Noether's theorem. This symmetry basically says that if we move the system we ar looking at by some distance in space then the physics is not affected. The actual statement is that the action is invarient under spatial translations. see Conservation of Momentum for a discussion of what this means.

A central force means that the force is spherically symmetric, and this is also a symmetry. Noether's theorem tells us that this symmetry also gives rise to a conservation law but this time it is the conservation of angular momentum rather than linear momentum. So if you have a system where angular momentum is conserved that means any forces must be central.

So no, Newton's third law isn't directly related to the existance or otherwise of a central force, but there is a connection in that both the third law and the existance of a central force are related to conservation of momentum.