The “Figure eight” orbit.

By Aldo Vitagliano, 2018, 12, 11

Solex is not just useful for modelling the Solar system, but it can be used to investigate any N-body configuration your imagination might devise.

This can be done by building up the appropriate SLF file, containing the starting conditions, i.e. the initial positions and velocities (the so-called status vectors) of all the bodies involved, and loading it to the program.

Here are the instructions for modelling a famous 3-body system, made up by three bodies of equal masses stably moving along an 8-shaped path.

A 3-body system is generally unstable, not giving rise to periodic orbits but normally ending up with a binary system plus an ejected body flying away on his own. However, apart those configurations in which a single mass largely predominates, there are a few ones that are stable even when submitted to small perturbations of the initial starting conditions.

Here is the transcription of an appropriate input file (you can also download it and then rename the extension to .slf):

2451545

10 150000  .1  -10  0   Body1

0  0  0

-9.3240737  -8.6473146 0

150000 .1  -10  0   Body2

97.00436  -24.308753  0

4.66203685  4.3236573  0

150000  .1  -10  0   Body3

-97.00436  24.308753  0

4.66203685  4.3236573  0

Here is the sequence of command for running the simulation:

-       - Load the file to the program with option F (Full N-body file).

-       - Make sure to set Orthogonal coordinates (toggle O).

-       - Set the Barycenter as the origin (commands C, -1, then enter 0, 0, 0).

-       - Set the time step to 10 days (command S).

--         - Move 1 step forward (spacebar).

- Turn on the Graphic output (command W).

-       - Set the appropriate window amplitude (zooming in or out with commands + or - ).

-       - Chose the display (moving dots or traces, toggle Trace [.]).

-       - Run the simulation (spacebar for slow step motion, toggle C for continuous motion).

After that, you might investigate what happens after perturbing the system to some extent.

One simple suggestion is just to edit the SLF file and change all the masses by the same amount, for example from 150000 to 155000. Or to change just one of the masses, and so on…

Enjoy!

Page latest update:   December 11, 2018

Any comment, inquiry or suggestion is appreciated:  alvitagl@unina.it

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