Extensible Simulation of Planets and Comets

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Extensible Simulation of Planets and Comets

• Natalie Wiser-Orozco
• Dr. Keith Evan Schubert
• Dr. Ernesto Gomez
• Dr. Richard J. Botting
• July 22, 2009

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Exoplanet Discovery

• Dr. Paul Kalas (UC Berkeley) confirms that
  Fomalhaut b orbits it's parent star1.
• Increased frequency of discoveries of this
  nature.
• Questions that arise as a result.

3
Movement of Objects In Space

• Carl Sundman 3-body
• Qiu-Dong Wang n-body
• Solar system stability

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Simulation of Objects In Space

• Computational power
• Existing simulators focus on
• Pre-determined sets of bodies
• Specific algorithm or method
• Extensible Simulator
• Arbitrary number of bodies
• Choose different numerical methods and
  gravitational functions.

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Overview Of The Extensible Simulator

• Numerical Methods and Gravitational Functions
• Project Structure and Management
• Visualizations
• Cameras
• Bodies
• Heuristics
• Results and Future Work

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Numerical Methods

• Taylor Series derivatives of original function
• Runge-Kutta finite difference approximations
• Extrapolation very accurate, inefficient
• Multistep needs help of a single-step method
• Multivalue easy to change step size

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Gravitational Solutions

• Law of Universal Gravitation (Newton)?
• General Relativity (Einstein)?
• Quantum Gravity (String Theory, M Theory)?
• Solar Wind
• Different classes of numerical techniques
• Particle-Particle
• Particle-Mesh
• Particle-Particle/Particle-Mesh (P3M)?
• Particle-Multi-Mesh(PM2)?

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Simulation Flexibility

• No one technique handles all
• Try different techniques on the same data
• Extensible Simulator allows for any technique
• Limited only by what is implemented, therefore
  limitless.

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Project Management

• Fashioned after well known Integrated Development
  Environments (IDEs)?
• Projects
• Body Configuration Files

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Project Functions

• Project Functions
• Create/Edit New Project
• Add/Edit Body Configuration Files
• Choose Gravitational Function/Numerical Method
• Calculate / Simulate

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Simulation Screen-shots
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Visualization and Heuristics

• Application Programming Interface
• Cameras
• Bodies
• Scene Navigation
• Heuristics
• Body Scaling

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Application Programming Interface

• Base Body and Camera objects
• Body and Camera wrapper objects
• Manager objects
• Work together to help the simulation run smoothly

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Scene Navigation

• Built in navigation
• Extensible navigation via camera implementation

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Body Scaling
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Results

• Error analysis yielded accuracy to an average of
  2 significant digits
• Aim of research
• Extensibility of numerical methods, gravitational
  functions, cameras and bodies
• Appeal to all levels of knowledge
• Convey ideas and discoveries with confident
  results

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Facilitate Future Research

• Programmatic Video Capture
• Additional Numeric Methods
• Additional Dynamics Equations
• GPGPU Integration
• Other general improvements

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References

1. Paul Kalas et al. Optical Images of an Exosolar
   Planet 25 Light-Years from Earth Science
   (322)1345-1348, November 2008
2. Michael T. Heath. Scientific Computing, An
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   2002.
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   nonlinear evolution of large scale structure in
   an axion/gravitino/photino dominated universe.
   Physical Review Letters, (51)935, 1983.
4. Srinivas Aluru. Greengards n-body algorithm is
   not order n. SIAM Journal on Scientific
   Computing, 17(3), May 1996.
5. A.W. Appel. An efficient program for many- body
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6. J. S. Bagla. Cosmological N-Body simulation
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   White. The evolution of large-scale structure in
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10. D. J. D. Earn and J. A. Sellwood. The Optimal
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14. K.F. Sundman. Memoire sur le probleme des trois
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15. Qiu-Dong Wang. The global solution of the n-body
    problem. Celestial Mechanics and Dynamical
    Astronomy, 50(1)7388, 1991.
16. M.S. Warren and J.K. Salmon. Astrophysical n-body
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18. Dr. Bernd Wirsing. Supercomputer simulations
    explain the formation of galaxies and quasars in
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19. F. Zhao and L. Johnsson. The parallel multipole
    method on the connection machine. SIAM. J. Sci.
    Stat. Comput., (12)14201437, 1991.

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Q A

• Code is open source and can be found here
• http//code.google.com/p/extensiblesimulationof
  planetsandcomets/