Solar System Orbital Dynamics from Secular Theory


Orbital and rotational evolution of the Solar System.




Russell Deitrick


DistOrb DistRot

Approx. runtime

116 seconds (
112 seconds (womoon/)
25 seconds (marshnb/)
110 seconds (marsvpl/)

This example uses DistOrb to model the orbits of the solar system planets and DistRot to model the obliquity evolution of Earth and Mars. In this main directory, the precession of the Earth’s spin axis is forced to its present day value to emulate the effect of the Moon. In the womoon directory, the same simulation is run, but without this precessional forcing. The directory marsvpl contains a simulation of Mars’ obliquity backward in time using DistOrb and DistRot. This result can be compared to marshnb output, which utilizes orbital data from HNBody (Rauch & Hamilton 2002) to demonstrate the effects of secular resonances not resolved by DistOrb. Note that DistRot can use orbital elements generated by non-VPLanet sources.

To run this example

python <png | pdf>

Expected output


Eccentricity evolution (left) and inclination evolution (right) for the inner solar system planets over the next 1 Myr. Initial condition are taken from Appendix A of Murray & Dermott (1999).


Absolute errors in the eccentricity (left) and inclination (right) between 4th order DistOrb and HNBODY over 5 Myr. Upper panels show the inner solar system planets and lower panels show the outer planets.


Obliquity evolution of Earth with and without the Moon over the next Myr (left) and Mars using secular and N-body models for the orbit over the last 10 Myr (right).