Solar system (Solar system 2009)
This simulation (Solar system 2009) can be used to calculate the trajectories of planets and other objects in a solar system. The program is designed for educational purposes. It can be used, for example, to demonstrate the motion of a planet on an elliptical orbit and to investigate the relationship between orbital period and major semi-major axis according to Kepler's law. Velocities, accelerations and forces can be displayed as vector arrows and the current vector components of position, velocity, acceleration, force and angular momentum can be taken from a table.
The precise three-dimensional calculation is based on input data from NASA. The accuracy is high enough to calculate the orbital periods of the planets to the nearest second. The simulation also allows you to calculate the orbits of famous satellites such as the Voyager and Pioneer probes or even self-created objects by simply specifying the initial conditions for location and velocity.
The calculation can be either classical (Newtonian) or relativistic with corrections due to special and general relativity. The graphical display allows the image to be rotated and zoomed in on particularly interesting events, such as the flyby of the Voyager probes on Jupiter. The precise position and speed of all known bodies in our solar system can be retrieved from the NASA Horizons web interface. Instructions on how to use this database can be found under Horizons instructions.
New: The program now displays the currently calculated time as date and time if the start date is noted in the imported data set. Download the new program version from 22.11.2013...
Current: There is a data set for the comet Ison, which will pass very close to the sun.
Operation
The program consists of a single exe file that can be run on Windows computers. After starting the program, approximate data for the movement of the earth around the sun is set. The calculation can be started directly by pressing the "Start" button. However, other prepared data files can also be downloaded (see below) and read in using the menu item "File" ? "Open solar system" menu item. The start parameters of the celestial bodies can be read, changed or entered on the left-hand side of the window. To do this, the relevant celestial body must first be selected (top left of the window). The color of the celestial body can be changed by clicking on the colored square. The data can be entered and displayed either in SI units or in astronomical units (selection below the input fields). An additional celestial body can be created using the "Create new celestial body" button. Do not forget to enter the initial conditions for the new celestial body before you start the calculation. If you take the data from the NASA information system, please note that all celestial body data must refer to the same reference system (e.g. barycenter of the solar system).
The "Display speed" slider can be used to set how quickly the display should take place. The slider does not affect the calculation accuracy, which is automatically ensured by an adaptive step size procedure. The buttons under Zoom can be used to adjust the image section for a suitable display. The 0 button centers the image on the coordinate origin. The image can be rotated using the sliders to the right of the graphic and below the graphic. The image section can be moved simply by left-clicking in the image and holding the mouse button down while moving the mouse. The orbital curves of the celestial bodies can be displayed as lines by ticking the "Draw orbital curves" box. The orbital curves of the planets are stored temporarily in the program so that different views of the orbital curves can be called up even after the calculation has been stopped. For special purposes, e.g. for printing images, the representation of the orbital curves can also be calculated with the correct representation of the intersection of lines. This calculation can be very time-consuming and is therefore only triggered when required via the "Draw correct intersections" button. The current velocities, accelerations and forces can be displayed as vector arrows. The corresponding selection must be made. The length of the arrows can be adjusted for an appropriate display using the slider below.
The "Show window with figures" button opens a window in which all current values of the individual celestial bodies and the overall system are displayed. The x, y and z components and the magnitude are shown for the location r, the velocity v, the acceleration a, the force F and the angular momentum L. The mass m, the potential energy Epot and the kinetic energy Ekin can also be read off for each celestial body. The "RelCorr" factor indicates the correction factor for relativistic corrections. Here, 1.0 means no corrections.
The potential energy Epot, the kinetic energy Ekin and the total energy E are given for the overall system. The total energy is a conservation variable. The total angular momentum is also a conserved quantity whose three components Lx, Ly and Lz are obtained. For some applications, it is helpful to examine the angular momentum in relation to the center of gravity. You can therefore choose between displaying the angular momentum in relation to the coordinate origin or to the center of gravity. The elapsed time t is displayed in days, hours, minutes and seconds. If only two celestial bodies are calculated (e.g. sun and earth), the orbital period and the major semi-axis are displayed after a full orbit. In any case, the minimum and maximum distance between two celestial bodies can be displayed. To do this, the two celestial bodies must be selected at the bottom right. A minimum or maximum distance is then displayed as soon as a minimum or maximum distance is observed. This function is particularly suitable for comparing orbital data of planets and moons with literature data or for reading the closest approach of an object to a planet during a flyby.
In the menu you will find functions to save the data of the solar system or to load other data. The currently displayed graphic can also be saved in a graphic format or printed directly.