r/astrophysics • u/Allah_Gaming1 • 7h ago
Eccentricity dynamics of the solar system
I have plotted the orbital dynamics of the Solar System over three timescales in: 10,000 years, 100,000 years, and 1,000,000 years in Python and factoring in the gravitational interactions between the planets using the newtonian model of gravitation.
The metric plotted is eccentricity (e), which describes how elliptical an orbit is. A higher value indicates a more elliptical orbit, while e=0 represents a perfectly circular orbit.
In plots 2 and 3, Jupiter and Saturn's eccentricities oscillate almost periodically, largely out of phase with each other. As the two most massive planets, they exert strong gravitational perturbations on each other, influencing their orbital shapes over time.
At a given semimajor axis, higher eccentricity corresponds to a lower orbital angular momentum. Their gravitational interactions allow angular momentum to be exchanged between their orbits, so one planet's eccentricity can increase while the other's decreases. This exchange is constrained by the conservation of the Solar System's total angular momentum, with all the planets contributing to the overall dynamics of the solar system.
Images 2 and 3 are the eccentricity plots of the gas giants over timescales of 100,000 years and 2 million years. Note that the gas giant eccentricity plots are validated but the inner planet plots aren’t fully validated.
Sources:
Image 2: Overlong simulations of the solar system dynamics with two alternating step-lengths by Seppo Mikkola and Harry J Lehto
Image 3: The orbital evolution of the Sun–Jupiter–Saturn–Uranus–Neptune system on long time scales by Alexander Perminov and Eduard Kuznetsov (2020)