Simulating planetary orbits with programming language Python

U ovom radu ćemo prikazati računalnu simulaciju Keplerovog problema i diskutirati njenu primjenu u istraživački usmjerenoj nastavi fizike. Keplerov problem je specijalan slučaj problema dvaju tijela gdje tijela međudjeluju centralnim silama koje opadaju s kvadratom udaljenosti. U tom slučaju problem dvaju tijela možemo svesti na problem jednog tijela u centralnom polju koji možemo riješiti analitički, a potom koristeći to rješenje možemo rekonstruirati orbite zasebnih tijela. Uz pomoć vis-viva jednadžbe i činjenice da je kutna količina gibanja konstantna u slučaju da na tijelo djeluje samo centralna sila, možemo izračunati iznose relativnih brzina tijela na bilo kojem položaju u orbiti. Da bi bila primjenjivija u obrazovne svrhe, simulacija prikazuje grafove ovisnosti iznosa relativnih brzina i udaljenosti između tijela o kutu kojeg vektor položaja planeta formira s pozitivnom x osi te po potrebi demonstrira drugi i treći Keplerov zakon. Da bi što manje ovisila o vrsti računala i instaliranim programskim paketima, za izradu simulacije koristili smo VPython (verzija 7) te Glowscript (verzija 2.8) u Glowscript IDE razvojnom okruženju.In this thesis we demonstrate a computer simulation of Kepler problem and discuss its application for educational purposes. Kepler problem is a special case of two body problem where bodies interact exclusively by a central force that declines in strength as the inverse square of the distance. In this case, the two body problem can be reduced to one body acted on by an external central gravitational force whose analytical solution can be used to return to the real two-body problem and solve for the actual motion of the two original bodies. Using the vis-viva equation and a fact that in the case when the only force on the body is a central force, angular momentum with respect to the origin is a constant of motion, we can calculate relative speed of the two bodies and angular speed of the individual bodies at any position in orbit. In order to make the simulation more useful for educational purposes, it shows diagrams of relative speeds and distances between bodies with respect to the angle which the position vector of the bodies makes with the positive x axis. Simulation, if necessary, can also demonstrate second and third Kepler law, and was programmed using VPython (version 7) and Glowscript (version 2.8) in Glowscript IDE integrated development environment to minimize the dependence on operating systems and installed packages