I have one solution of this problem
Great Comet of 1811 - Wikipedia
But my solution is in XY-coordinares and a nee in polar coordinates.
See pictures and the Prime 6 sheet
More interesting picture and Prime 6 sheet. Can you point Earth here?
Here's a different way of looking at this (ODE's already solved analytically, as it's a two-body problem).
But the numerical solution more simple for the undestending.
Solution without animation is not solution
[War & Peace] Prologue from Natasha, Pierre and the Great Comet of 1812 - Яндекс.Видео (yandex.ru)