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The Physics of Dark Energy
An exploration of a recent discovery in cosmology.

— Copyright © 2007, P. Lutus  Message Page

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Space Applet

NOTE: This Java space applet is supseded by a newer, better one based on the HTML5 canvas tag and JavaScript -- more features, better looking, and no Java applet security concerns. Click here to see it.

Here is an interactive Java applet that models normal orbital dynamics, plus the behavior of dark energy. Because this is a sophisticated 3D orbital simulation, the reader is strongly encouraged to acquire some anaglyphic glasses () to enhance the experience. When you have acquired your 3D glasses, click the "Anaglyphic" checkbox below.


Some suggestions:

  • To make the space applet bigger, click the "Separate" button. This will separate the applet from your browser, put it in a window of its own, and allow you to make it as large as you want.
  • Because the applet is a full 3D gravitational simulation, consider getting a pair of 3D anaglyphic glasses — this will allow you to see the third dimension of depth and properly sort out the moving display of planets and "comets."
  • You can choose to increase the number of "comets," but a large number of "comets" requires more computer power. When running this simulator, for best results always use the fastest computer available to you.
  • Once you have the display set up as you like, press the "Dark energy" button. This automatically changes the equation being solved from the classical gravitational equation listed as (1) on this page to the dark energy equation listed as (6) on this page.
  • To return the simulation to its original state, turn off the dark energy option and press the "Reset" button.
  • To freeze the simulation at any point, click the "Run/Stop" checkbox.

Detailed Notes and Experiments:

  • This simulator is based on a more ambitious simulation project listed here. It is a full 3D simulation, which is why having some way to view in 3D is so important. The Java listing for the applet is here.
  • The simulator is scaled to the dimensions of the solar system, out to about the orbit of Saturn. The default view is set up to show this area. All nine planets are modeled (including the non-planet Pluto), as well as an arbitrary number of "comets" in random orbits.
  • The "comets" feature can be used to create a reasonable simulation of a star cluster or galaxy cluster, but remember that the individual bodies don't all interact with each other, they only interact with the central body, the "sun". This is simply because a symmetrical gravitational simulation would require a huge amount of computer horsepower, much more than exists on a typical home computer. Interacting with a central body produces a reasonable simulation with modest computer power.
  • Some readers may get a mistaken impression resulting from how the simulator is set up. Even though all the orbiting bodies revolve around a central point, this is just a computational convenience and doesn't represent the universe, which has no center and which is much more random in its gravitational behavior.
  • The simulator's default dark energy constant (4e-15) represents a value that is much, much higher than the actual value. This is because the playing field is not a set galaxies separated by billions of light-years, but a model of the solar system, a much smaller scale with much higher gravitational forces. In order to produce a realistic simulation, the dark energy value had to be scaled up to accommodate the shorter ranges.
  • In the default configuration, activating the dark energy option will cause the departure of most of the comets and planets except the inner two (Mercury and Venus). This is meant to reveal something about dark energy physics — that a sufficiently strong gravitational coupling will resist the pull of dark energy. This is true at the cosmological scale as well — galactic clusters are expected to resist the pull of dark energy, even as the distance between groups of galaxies increases over time because of dark energy.
  • As an experiment, create a lot of "comets" and then adjust the dark energy constant value to something smaller than the default (example 4e-16), to see how this causes the outer orbiting bodies to depart while the inner bodies remain gravitationally bound. Remember to disable the dark energy option and then press the "Reset" button to restore things to an initial state. This experiment should graphically demonstrate why Einstein's original application of a cosmological constant could not have achieved the desired result.
  • Under the influence of dark energy, from time to time one sees a "comet" gradually increase the size of its elliptical orbit about the sun, and then depart at an accelerating pace. This is a perfect picture of the characteristic behavior of dark energy, one played out by the universe as a whole.
  • The time step setting, with a default of 64 hours, can be adjusted to suit the reader's preference. Smaller time steps produce more accurate results, but take more computation time. Large steps may produce anomalous, unrealistic behaviors, in particular with planets and "comets" that approach the sun closely. In such a case, numerical errors may cause a body to exit the solar system at high speed. This behavior isn't realistic physics.

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