For the problem below, the expectation is that you submit a standalone HTML file (any images should be embedded) back to GitHub. Data for this problem is provided in the starting repository, which you should accept by following the below link. Don’t forget that you are working in groups, which were posted in class. The first person to accept the assignment should form an easily identifiable group name (likely using the names of your group members). Others in the group should also accept the assignment, and then they can just join the existing group. If you accidentally join the wrong group, I need to fix it manually! So try not to join the wrong group, but if it happens just let me know.
Accept AssignmentThe Problem: Belt Resonance
The file asteroids.csv contains some orbital information (eccentricity and semi-major axis) about over 1 million measured asteroids in our Solar System. Your task in this problem is to plot the distribution of asteroids as a function of their average distance from the Sun (their semi-major axis). You can use either a histogram or a KDE plot, whichever you prefer, but you should ensure that your bins or kernels are narrow enough so that you can make out 5 major dips or drops between the range of 1.75 to 3.5 AU (which is generally where the main portion of the asteroid belt resides).
These areas of relatively few asteroids are caused by orbital resonance with Jupiter over many millennia. If an asteroid is a distance from the Sun that results in its period lining up with some multiple of Jupiter’s period, then that asteroid feels a little extra “push” from Jupiter’s gravity each orbit, like a child being pushed on a swing. Over a large enough time, Jupiter has pushed out all the asteroids in these gaps. You can look up that Jupiter has a period of 11.86 years.
The 5 main gaps that you initially see are caused by the 2:1, 5:2, 3:1, 7:3, and 4:1 resonances, proceeding from left to right. That is to say, asteroids in the 2:1 gap would have completed exactly 2 orbits every time Jupiter completed one. Of course, it is easy to think of other simple ratios that may be valid as well (3:2, for instance). For all irreducible rational numbers with numerator and denominator less than 10 and greater than or equal to 1, determine where that gap would or should be appearing in your asteroid distribution. Plot where the gaps should appear in your distribution for all gaps that should appear within the 1.75 to 3.5 AU range. For each of these points, discuss whether you can see any sign of a dip at that point in your distribution. Maybe if you recompute some of your bins or try zooming in?