Transcript Creating a 2-D Model of the Solar System using Physics

Creating a 2-D Model of the Solar
System using Physics-Based
Geometries in Java.
Brian Tubergen
Purpose/Subject/Goals
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Create a working simulation of the Solar System
Implement Keplerian/Newtonian models to control
planetary motion
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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
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Transition 2-D simulation into 3-D
Scope of Study
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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
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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
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that I’ve seen allow user interaction to the extent
I’d like to with user addition of solar bodies
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My program could be modified in future to do this
Theory/Design
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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)
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Create a class that can represent a planet and
contains data on that planet’s position, velocity,
etc. (Sprite class)
Theory/Design cont.
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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
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a = G*m/r^2
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Every solar body’s acceleration is calculated based on
every other body, if that makes sense
Testing
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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
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Issues with iterative calculation of forces
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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
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Necessary to calculate accelerations correctly
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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
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to compare position data from my program to
position data from NASA
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Decided to simply output data and do basic analysis in
spreadsheet program
Timeline
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1st quarter:
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2nd quarter:
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Fix bugs with said calculations and resulting motion
3rd quarter:
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Get iterative force/acceleration calculations working
for multiple bodies interacting
Verify that the equations actually work based on solar
system data
4th quarter:
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Wrap up/conclude project; Implement user interaction
with simulation if I have time
Results
Results cont.
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Solar bodies appear to move elliptically,
hyperbolically, parabolically, etc. as they should
Real initial position/velocity values have been
assigned
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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.
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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?
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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
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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
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Fair predictor of planetary positions for small
increments of time
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Better for outer planets
Possibility for modification
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User interaction with simulation
Intrusive body testing – What would solar system’s
reaction be to a massive asteroid passing through it, for
instance?