The movement of planet with eccentric orbit relative to other planet with eccentric orbit

I had written a blog before about the movement of planets relative to other planets, but later I realized that in that blog, I only explained about planets occupying orbits with low eccentricty. The movement of planets with eccentric orbit relative to other planets with eccentric orbits is as interesting, if not more interesting, than if all planets occupy almost circular orbit.

For this experiment lets have a system consisted of a star, a hot jupiter and 3 earth sized planets. The Star is called Vigan ( yellow ), the Hot Jupiter is called Ephemis ( brown ). The three Earth sized planets are Miula ( magenta ), Sihen ( green ) and Altiva ( red ).

Vigan System

The yellow circle is Vigan, the primary star of Vigan system. The brown path is the orbit of Ephemis, the Hot Jupiter. The magenta math is the orbit of Altiva, and the green path is the orbit of Sihen, and the red path is the orbit of Altiva.

movement of planets in Vigan System relative to Ephemis

movement of planets in Vigan System relative to Altiva

movement of planets in Vigan System relative to Sihen

movement of planets in Vigan System relative to Miula

All plot results above show that the retrograde motion of a planets relative to other planets in the system, is more complex than if all planets occupy almost circular orbit.

The movements of planet relative to other planets are interesting things to experiment with. The plot results always show different and interesting new shapes. Whether we can somehow control the shape of the plot result by some kind of mathematic equation, is something I am interested to study.

Download NCGS Program and Source Code here.