1. Extensible Simulation of Planets and Comets Natalie Wiser-Orozco Dr. Keith Evan Schubert Dr. Ernesto Gomez Dr. Richard J. Botting July 22, 2009

2. Exoplanet Discovery ● Dr. Paul Kalas (UC Berkeley) confirms that Fomalhaut b orbits it's parent star 1. ● 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

4. 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.

5. Overview Of The Extensible Simulator ● Numerical Methods and Gravitational Functions ● Project Structure and Management ● Visualizations ● Cameras ● Bodies ● Heuristics ● Results and Future Work

6. 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

7. 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)‏

8. 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.

9. Project Management ● Fashioned after well known Integrated Development Environments (IDEs)‏ Projects Body Configuration Files

10. Project Functions ● Project Functions  Create/Edit New Project  Add/Edit Body Configuration Files  Choose Gravitational Function/Numerical Method  Calculate / Simulate

11. Simulation Screen-shots

12. Visualization and Heuristics ● Application Programming Interface ● Cameras ● Bodies ● Scene Navigation ● Heuristics ● Body Scaling

13. Application Programming Interface ● Base Body and Camera objects ● Body and Camera wrapper objects ● Manager objects ● Work together to help the simulation run smoothly

14. Scene Navigation ● Built in navigation ● Extensible navigation via camera implementation

15. Body Scaling

16. 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

17. Facilitate Future Research ● Programmatic Video Capture ● Additional Numeric Methods ● Additional Dynamics Equations ● GPGPU Integration ● Other general improvements

18. 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 Introductory Survey. McGraw-Hill, Second Edition, 2002. 3.E. Saar I. Suisalu A. Klypin A. Melott, J. Einasto and S. Shandarin. Cluster analysis of the nonlinear evolution of large scale structure in an axion/gravitino/photino dominated universe. Physical Review Letters, (51):935, 1983. 4.Srinivas Aluru. Greengard’s 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 simulation. SIAM J. Sci. Stat. Comput., (6):85–103, 1985. 6.J. S. Bagla. Cosmological N-Body simulation: Techniques, Scope and Status. Current Science, 88:1088–1100, April 2005. 7.J. Barnes. A modified tree code: Don’t laugh; it runs. J. Comput. Phys., (87):161–170, 1990. 8.J. Barnes and P. Hut. A hierarchical o(n log n) force-calculation algorithm. Nature, (324):446–449, 1986. 9.M. Davis, G. Efstathiou, C. Frenk, and S.D.M. White. The evolution of large-scale structure in a universe dominated by cold dark matter. ApJ, (292):371–394, 1985. 10.D. J. D. Earn and J. A. Sellwood. The Optimal N-Body Method for Stability Studies of Galaxies. The Astrophysical Journal, 451:533–+, October 1995. 11.Sergio Gelato, David F. Chernoff, and Ira Wasserman. An adaptive hierarchical particle-mesh code with isolated boundary conditions. ApJ, May 1997. 12.L. Greengard and V. Rokhlin. A fast algorithm for particle simulations. J. Comp. Phys., (73):325–348, 1987. 13.Randall Splinter. A nested grid particle-mesh code for high resolution simulations of gravitational instability in cosmology. MNRAS, (281), 1996. 14.K.F. Sundman. M´emoire sur le probl`eme des trois corps. Acta Math., (36):105–179, 1913. 15.Qiu-Dong Wang. The global solution of the n-body problem. Celestial Mechanics and Dynamical Astronomy, 50(1):73–88, 1991. 16.M.S. Warren and J.K. Salmon. Astrophysical n-body simulations using hierarchical tree data structures. In Proc. Supercomputing ’92, pages 570– 576, 1992. 17.M.S. Warren and J.K. Salmon. A parallel hashed oct-tree n-body algorithm. In Proc. Supercomputing ’93, pages 1–12, 1993. 18.Dr. Bernd Wirsing. Supercomputer simulations explain the formation of galaxies and quasars in the universe, June 2005. 19.F. Zhao and L. Johnsson. The parallel multipole method on the connection machine. SIAM. J. Sci. Stat. Comput., (12):1420–1437, 1991.

19. Q & A Code is open source and can be found here: http://code.google.com/p/extensiblesimulationofplanetsandcomets/