Creating a 2-D Model of the Solar System using Physics-Based Geometries in Java. Brian Tubergen

Purpose/Subject/Goals Create a working simulation of the Solar System Implement Keplerian/Newtonian models to control planetary motion Allow for development of user interaction with simulation: ability to add customizable solar bodies (comets, planets, etc.) at a given location and see what reaction of Solar System is Transition 2-D simulation into 3-D

Scope of Study Program “action at a distance” gravitation force: F = G*m*M/r^2 Acquire real world position/velocity planetary data or find an equation that can give it to me and compare it with simulation Allow for future implementation of non-coplanar orbits (ie: program a z component of position, velocity, etc.) for 3-D purposes

Similar Projects The basic Solar System part of the project is a visual recreation of the Keplerian model of planetary motion Other Solar System simulations exist, but none that I’ve seen allow user interaction to the extent I’d like to with user addition of solar bodies  My program could be modified in future to do this

Theory/Design Program written in Java (for now, for 2-D) Create a class that essentially handles the creation and management of the panel itself (Display class) Create a class that can represent a planet and contains data on that planet’s position, velocity, etc. (Sprite class)

Theory/Design cont. Update the positions of the planets one at a time and iteratively, where at each step the planet’s acceleration is updated based on the position of each other body  a = G*m/r^2  Every solar body’s acceleration is calculated based on every other body, if that makes sense

Testing Acquire real world (or equation based) position and velocity data after one year has passed for each planet and compare to my simulation’s output Verify that my simulation runs more or less correctly (matches real world position data)

Testing Cont.

Problems I ran into Issues with iterative calculation of forces  Solved, although Mercury’s orbit seems to be incorrect Issues handling how to let each planet know about the other planets/bodies in the system  Necessary to calculate accelerations correctly  Solved, although I had to send/receive a lot of data and this probably caused rounding errors

Problems cont. Determining the most intelligent and easiest way to compare position data from my program to position data from NASA  Decided to simply output data and do basic analysis in spreadsheet program

Timeline 1 st quarter:  Get iterative force/acceleration calculations working for multiple bodies interacting 2 nd quarter:  Fix bugs with said calculations and resulting motion 3 rd quarter:  Verify that the equations actually work based on solar system data 4 th quarter:  Wrap up/conclude project; Implement user interaction with simulation if I have time

Results

Results cont. Solar bodies appear to move elliptically, hyperbolically, parabolically, etc. as they should Real initial position/velocity values have been assigned Planetary orbits are mostly circular (as they should be), although Mercury’s appears slightly incorrect

Position Data (my simulation and NASA)

Percent Error

Results cont. Predicted data from my simulation compares favorably to actual data from NASA Inner planets are worse; their movement is a rougher estimate because they move more/faster than outer planets Good predictor for outer planets, however

Causes of error Why are planets closer to the sun “worse” than planets farther from the sun?  They move more in a given time interval than planets farther from the sun  Ultimately means that their accelerations are adjusted less per distance traveled than other planets This is an issue since acceleration depends on location (distance)  This means their accelerations are more incorrect more often, which entails more error

Conclusion Valuable tool for basic visualization of planetary motion Fair predictor of planetary positions for small increments of time  Better for outer planets Possibility for modification  User interaction with simulation  Intrusive body testing – What would solar system’s reaction be to a massive asteroid passing through it, for instance?