Solar Coaster vs CloudLabs celestial body path

Solar Coaster provides accurate position, time, motion and eclipse information for Earth's nearest star, Sol, our Sun, and nearest celestial body, Luna, our Moon. Information includes 3D movement graphs, upcoming eclipses and their circumstances, rise and set times, positions, distances and velocities, moon phase, illumination and crescent rotation. Solar Coaster automatically updates its state every minute, or you can examine minutes randomly. The simulation uses a local horizontal coordinate system when displaying information, which essentially means that your current position is the center of the Universe and all calculated values are relative to you. Sun and Moon positions are also available in equatorial coordinates. Solar Coaster stores enough onboard astronomical data to keep it running through the year 2100 AD, which means that all calculations can be performed locally without the need of a network connection — useful while in the wild chasing an eclipse. Algorithms are accurate at all longitudes, and latitudes between -61° south and +60° north (roughly speaking, locations outside the Polar regions). Of course, you must have Location Services enabled and allow Solar Coaster to access your position for accurate simulation results, and to properly detect eclipses visible at your location. You can also allow Notification Center to keep you informed when those eclipses will occur. Solar Coaster comes in various flavors: for iOS a native App; and for macOS a native App, Screen Saver and Web App.

In this situation, you will see the matrix form of the trajectory of a celestial body. It is necessary to find the determinant and the angle of rotation in order to determine whether the trajectory is an ellipse or a hyperbola. You must also find the equation of the trajectory. The simulation provides a computer and a holoprojector where you can carry out the mathematical analysis.