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Orbit of a test particle around a central mass.
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Can do this in two ways: Impose an external potential or put two particles in a box but fix one of them in place.
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Difference between the two cases is that the latter includes softening and a different time-step condition.
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Here I show plots of the orbits, comparing to the analytic case.
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Semi-major axis is fixed to be 1AU, and eccentricity varies.
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Softening is 0.01 AU and 'eta' is 0.01
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Evolved for 100 orbits
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![orbit_plot_11](/uploads/4a0a68e5fa4a387ecfa2cf61476ed4c0/orbit_plot_11.png)
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![orbit_plot_14](/uploads/29057b568f49fc5199048bd743db5573/orbit_plot_14.png)
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If we reduce the semi-major axis for the highly eccentric orbit, then things go a bit crazy for the 'self-gravity' case.
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Could be due to softening or the different time step condition.
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![orbit_plot_16](/uploads/3defb52207e33275ca272404c6e49c04/orbit_plot_16.png)
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Reducing the softening to 0.001 AU does not seem to fix the issue
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![orbit_plot_17](/uploads/2b60bf26f29d45f0a3b08fea372468a0/orbit_plot_17.png)
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