CSERD


Extended Example


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Two validation tests were performed on the Windows version of GalaxSee. The first test use GalaxSee to predict the orbital period of an Earth-mass planet orbiting a Sol-mass start at 1 AU. The second test validated that a cluster of stars modeled using GalaxSee satisfied the virial theorem.

(http://scienceworld.wolfram.com/physics/VirialTheorem.html)

Any valid gravitational simulation tool should be able to simulate the movement of the Earth about the Sun. Through trial and error the value of the tangential velocity that would create a stable rotation was found to be approximately 0.172 AU/day, resulting in an orbit of approximately 1 year. The observed value is .01719 AU/day (2 pi AU per year). In addition when the accepted value is filled in the proper field, the orbit is stable and repetitive.

The second test studied the potential and kinetic energy of a simulated galaxy. There is a well known theoretical result, the Virial Theorem, which relates the potential and kinetic energy of a non-rotating gravitationally bound cluster of stars. The Virial Theorem states that for a stable non-rotating cluster of stars the total kinetic energy will be 1/2 of the total gravitational potential energy. A series of galaxies with increasing random velocity were run, and it was found that for models with a ratio of kinetic to potential energy of 1:2 the simulated galaxies maintained their structure. Galaxies with less kinetic energy (slower initial movement) collapsed, while galaxies with higher kinetic energy (faster initial movement) expanded.

Finally, in all models the total energy and momentum were calculated and, to within reasonable precision energy and momentum, were conserved in the test models.

The physics of the model (Newtonian gravity solved using an explicit integration method with forces ignored for extremely close "fly-bys") should be appropriate for the examples listed in the online lesson plans, but would fail for cases of extremely high velocities. Additionally, tests of the accuracy of the models for large masses were not run.


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