A visualizer for Lagrange points, a physical phenomenon, made as a team project for the 2022 McGill Physics Hackathon. See the video demo.
- Visualize Lagrange points in a system of two astral bodies.
- Control simulation speed, mass of bodies, distance between masses, velocity of the third object and velocity angle.
We were intrigued by the numerous applications of Lagrange points in real-world contexts such as space exploration, satellites, and telescopes. As such, we wanted to gain a better intuitive and visual understanding of Lagrange points by developing an interactive application to facilitate their vizualisation.
Welcome to our Lagrange point simulator for the McGill Physics Hackathon 2022. It calculates the five Lagrange points of two massive objects and the trajectories of small-mass bodies in such a system. Within our interactive application, you may modify the mass of the two massive objects and the distance between them. The speed of the simulation can also be changed to see how small-mass bodies are affected by the gravity of the two large bodies over a long period of time.
The mathematical backend behind the visualizer is in Python, whereas the accompanying graphical user interface is written in QML and powered by Qt's stable and performant GUI technology. Interfacing between the UI and business logic is achieved thanks to the PySide6 bindings.
Implementing 5 Lagrange point equations was quite a challenge, as it required the solving of a quintic function. We overcame this challenge by finding an approximation for each Lagrange point, that is valid as long as the mass ratio between the two masses did not reach a certain limit.
Centering the simulation around the barycenter (which is the center of mass of two bodies that orbit one another) was challenging, as the Lagrange point locations found with the equations are with respect to one of the masses, and not the barycenter.
We are proud that we succeeded in creating a simulator that allowed us to understand in an intuitive way what Lagrange points are, which were previously a nebulous math-heavy, hard-to-imagine, concept. We are proud that we pulled together our barebones knowledge of coding and learned new languages and new methods to create something we can actually concretely see and use.
Although we all had a rough idea of what Lagrange points were, we deepened our understanding on the subject by diving into what exactly governed the motion of objects in a two-mass-body system through extensive research on Newtonian physics. We gained an intuition on how Lagrange points actually work.
We also learned how to create a project under time-sensitive constraints. We figured out of to allocate tasks equally so that each team member could fulfill their role to the best of their abilities. For example, physics-oriented team members focused on the backend of the project, calculating the Lagrange points, whereas more proficient programmers focused on the frontend and built the GUI and the simulator interface.
The choice of what framework to use for building the graphical component of our visualizer was also a hard one to make. We had originally planned to use pygame for that purpose, but decided to go for Qt Quick using QML as it is a more mature and high-level framework for designing performant and appealing GUIs.
We thus learned how to use QML to visualize the objects. We had no experience with the language but believe we did a good job utilizing the 24h to implement as best we could the features we wanted using this novel language for us. Qt/QML is now a new tool we have at our disposal when we will code in the future.
- Enhancing stability of the simulation
- Adding better collision handling
- Adding an arbitrary number of objects to the scene
- Re-writing in Qt C++
Open a command line prompt in the project's directory.
pip install pyqt6
pip install pyside6
python main.py- Uses Qt Quick with PySide6 bindings for Python