I am reading Mathematical Methods of Classical Mechanics by Arnold. I got stucked on a problem about central fields. Usually in literature central fields are given by $\mathbf{F} = \Phi(r) \mathbf{e}_r$, where $\mathbf{e}_r$ is the radial unit vector.
However, Arnold asks to derive this form by imposing the invariance of the field with respect to the group of motions of the plane which fix $0$. Can somebody give a hint?