A study of the apsidal angle and a proof of monotonicity in the logarithmic potential case

This paper concerns the behaviour of the apsidal angle for orbits of central force system with homogeneous potential of degree − 2 ⩽ α ⩽ 1 and logarithmic potential. We derive a formula for the apsidal angle as a fixed end-points integral and we study the derivative of the apsidal angle with respect to the angular momentum ℓ. The monotonicity of the apsidal angle as function of ℓ is discussed and it is proved in the logarithmic potential case.