Kepler's laws for a hypothetical gravitational force

Cilj ovoga rada jest ispitati ponašanje Keplerovih zakona za gravitacijsku silu u kojoj je funkcionalna ovisnost udaljenosti različita od \(r^{-2}\). Matematičkom pripremom same simulacije te izradom računalne simulacije u programskom jeziku C moguće je analizom podataka doći do željenih zaključaka vezanih za Keplerove zakone. Pokazano je da za potencije udaljenosti koje su približno jednake dva ponašanje Keplerovih zakona postaje sve sličnije ponašanju za kvadratnu potenciju. Kada bi sustav činile samo Zemlja i Sunce putanja Zemlje bila bi u potpunosti stabilna, no postojanje ostalih planeta u sustavu uzrokuje nestabilnosti i pertubacije Zemljine putanje pa je promatranje u ovom radu točno samo za problem dvaju tijela.The aim of this paper is to examine the behavior of Kepler laws for gravitational force in which the functional dependence of distance is different from \(r^{-2}\). By mathematical preparation of the simulation itself and computer simulation in the C programming language, it is possible to reach the desired conclusions regarding Kepler's laws by analyzing the data. It has been shown that for distance potentials approximately equal to two, the behavior of Kepler's laws becomes increasingly similar to the behavior for quadratic potency. If the system consisted only of the Earth and the Sun the Earth's trajectory would be completely stable, but the existence of other planets in the system causes instabilities and pertubations of the Earth's trajectory, so the observation in this paper is correct only for the two-body problem