Kepler's Orbital Motion Examined in Comparison with the Methods of Mechanics Developed by Stanescu and Tabacu

A new method developed by Stanescu and Tabacu to study the mechanics of a particle moving along a definite curve is compared with the well-known approach applied in calculating the Kepler's orbital motion. A particular effect of the rate of change of the kinetic energy of a body with respect to the change of a parameter defining the body position on the orbit is examined as an example. A comparison of the two methods shows only a slight numerical difference between the results of the Stanescu-Tabacu method and the traditional formalism. The components of the body acceleration are calculated along the orbit as an application of the new approach.