The Kepler problem: the Newtonian and the relativistic (Special Theory) point of view
Kostas Papamichalis Dr. of Theoretical Physics

Theoretical analysis and Activities

In this application we simulate the motion of a particle in a Newtonian gravitational field. In the left window the motion is determined in the context of the Newtonian Mechanics, and in the right window in the context of the Einstein's Special Theory of Relativity. In both models, the initial position and velocity of the particle are identical (for an analytic presentation of each theoretical model, see the attached pdf-file).
In the virtual environment of the simulation, the light velocity equals to 1 sim-units and the gravitational constant G to 0.01 sim-units. The center of the star that generates the gravitational field, is located at the origin O of the coordinate system. The user controls the mass M of the star, and the initial velocity of the moving particle which in any case is of the form: (0,v₀,0). Moreover, the initial position of the particle is always at the point (x₀,0,0), where: x₀=1 sim-units.
The limits of the parameters have been chosen so that the orbit of the particle, in both models, is always bounded in a region of the Oxy plane of the coordinate system (see the attached file).
The user can play or pause the simulation by double clicking on the virtual environment.

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