Equivalently, it suffices that the curl of the force field F is zero; using the formula for the curl in spherical coordinates, ∇ ∇ × × F = 1 r sin ⁡ ⁡ θ θ ( ∂ ∂ F ∂ ∂ φ φ ) θ θ ^ ^ − − 1 r ( ∂ ∂ F ∂ ∂ θ θ ) φ φ ^ ^ = 0 because the partial derivatives are zero for a central force; the magnitude F does not depend on the angular spherical coordinates θ and φ.