Planetary system
This is the older 2-dimensional version for calculating planetary orbits. The current, more powerful 3-dimensional version can be found under Solarsystem2009.
This program can be used to realistically calculate the movement of celestial bodies. Up to 6 bodies (sun, planets, moons and comets) can be entered. The sun is also freely movable so that the reaction force of the planets can be studied. The parameters for the sun and earth are preset at the start of the program, but can be changed. Further orbital data of our solar system can be found, for example, under Astronomia Solar System. It is also possible to investigate other interesting constellations, e.g. planetary orbits around a double star system or instability caused by a very heavy planet. To study Kepler's laws, the orbital period T and the major semi-axis a of the orbit are displayed. It is also possible to study what the orbits would look like if the law of gravity had an exponent slightly different from 2.
Operation
To enter the parameters of the celestial bodies, they can be selected individually and then the start coordinates, components of the start speed and mass can be entered for the currently selected body. The celestial body is only taken into account for the movement if the "Active" box is ticked. Pressing "Start" starts the movement with the initial conditions of all bodies. The display can be changed and an exponent other than 2.0 can be selected by ticking the corresponding box. If the display of the orbital data is selected, the current coordinates(x,y), the velocity components(vx,vy), the amount of velocity |v|, the angular momentum L, the components(Fx, Fy) of the total force on the respective celestial body and its amount |F| are displayed for each body. Kinetic energy(Ekin), potential energy(Epot), total energy(Eges) and total angular momentum(Lges) are displayed for the entire system. The angular momentum can be calculated either with respect to an axis through the coordinate origin or with respect to an axis through the center of gravity (selection button in the window with the path data at the bottom right). The major semi-axis of the orbit(a) and the orbital period(T) are only displayed for two-body systems, as closed orbits can no longer be expected for more than two bodies.
Numerical realization
Newton's equations of motion are solved using the 4th order Runge-Kutta method (step size 200 sec). The bodies are assumed to be point-shaped.