The Structure, Stability, and Dynamics
of Self-Gravitating Systems

Joel E. Tohline
tohline@rouge.phys.lsu.edu

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Application III.G.1

Through the following application, you may construct a table that details the properties of models along the Maclaurin spheroid sequence for any chosen range of spheroid eccentricities, as prescribed by the analytical expressions in the accompanying discussion. In the following boxes, enter, respectively:
  1. elow the lowest value of the eccentricity for which you want to construct a model.
    0.0 < elow < 1.0;

  2. ehigh the highest value of the eccentricity for which you want to construct a model.
    elow < ehigh < 1.0;

  3. The number of different models you want to construct, evenly spaced in e, over the range elow e ehigh.
    Selected number of models must be ‹ 100.

<== Press this button after you've selected a desired range of eccentricities.

With the default values given, the following table will be produced:


Maclaurin Output

Computed Properties of Maclaurin Spheroids

e w2/ pGr J/Jnorm w2/ 2pGr Erot |Egrav| t
0.200000 0.021470 0.051454 0.010735 0.003265 0.599978 0.005441
0.300000 0.048613 0.078817 0.024307 0.007525 0.599882 0.012544
0.400000 0.087269 0.108458 0.043635 0.013874 0.599596 0.023138
0.500000 0.137995 0.141634 0.068997 0.022782 0.598903 0.038040
0.600000 0.201353 0.180375 0.100676 0.035047 0.597374 0.058669
0.700000 0.277341 0.228336 0.138671 0.052069 0.594072 0.087648
0.800000 0.363159 0.293453 0.181579 0.076575 0.586583 0.130544
0.900000 0.440529 0.399939 0.220264 0.114943 0.566017 0.203073


THE END