Work experience project on celestial mechanics

*** Frequency output ***

Click on diagram to enlarge.

The goal of our project was to plot the frequencies of both Saturn and Jupiter given certain starting semi-major axes of both these bodies (Values such as eccentricity however, were not changed and were kept at a constant value of 0.05 for all the bodies). We also took into consideration the effects of the other massive bodies (Uranus and Neptune) while running these simulations. We plotted the results of the simulation onto a 3-dimensional graph. This graph had the semi-major axis of Jupiter on the X axis, the semi-major axis of Saturn on the Y-axis and the frequency of the two bodies on the Z-axis. The semi-major axis for Jupiter varied between approximately 5.2-5.4, for Saturn this value was between around 8.7 and 9.5. We noticed that in general, the frequency changed smoothly according to the variations in the semi-major axis for both the planets. However at a value of approximately 5.4 AU for Jupiter and 8.7 AU for Saturn, the frequency increased dramatically by a factor of 5. When calculations were done, we discovered that this was because Saturn and Jupiter were very close to a 2:1 mean motion resonance at these values. We ran approximately 40 different simulations with the semi-major axis varied using data on how the orbits had evolved over a 50 million year period in the early solar system. Thus every simulation was run using the semi-major axis form the body approximately 1.25 million years after that used in the previous simulation.

- Shaun

2017 May 4th

Last Revised: 2017 May 12th