Updated: Jul 31, 2020
Hello! Anything fun going on in my life? These days, I am so much into physics. In fact, physics is now on the verge of trumping mathematics in "my list of top priorities." My love for physics abruptly began as I started to study more about electromagnetics these days. Last year, I was watching the same lectures but they all sounded like nonsense; this year, after completing the MIT multivariable calculus course, now it seems that I understand all the gaps in my knowledge from last year, and that is probably why my love for physics revived.
And also, KSEF--one of the biggest science fairs in South Korea-is approaching; hence, I decided to apply my knowledge in Mathematica and physics to investigate about this very interesting celestial body here:
https://en.wikipedia.org/wiki/10199_Chariklo
Photo taken by Hubble telescope (left)
An artist's rendering of Chariklo (right)
This asteroid, 10199 Chariklo, is an asteroid; yet, surprisingly, it has not even one ring, but two rings! This is quite remarkable, as all minor planets known to us did not have a ring. There are a couple of competing theories in academia, with one of those related to Lindblad resonance. Sorry for chemistry geeks--resonance in astronomy is quite different from resonance in chemistry or other normative meanings. Orbital resonance is when two orbiting bodies exert regular gravitational influence on each other. An apt analogy to draw here would be pushing a child on a swing. The child will be pushed periodically, while it also pushes the person behind as the child comes back. A real-life example is Pluto and Neptune, where they have a 2:3 resonance. One notable feature that links this phenomenon back to Chariklo is that this type of resonance increases as the eccentricity (how much the celestial body is un-spherical) increases. So considering the high eccentricity of Chariklo, the high resonance could cause such a body with small mass to possess a ring as well.
My speculation, on the other hand, is that the ring was formed temporarily due to particles that lifted off from the surface of the asteroid after a collision. Then, after the individual particles collided with one another, they got into orbit and later formed a ring.
Using Mathematica, I plan to construct a simulation that shows my hypothesis is plausible. I am using lots of differential equations and naturally NDSolve[]. I am currently on working with two particles, and I will increase the number of particles as I progress.
Ending this post, I wish to post a picture of the two-particle simulation, which I feel particularly proud about after wrestling with NDSolve for several hours today. Let us all take some time to appreciate this piece of intellectual labor.
Beautiful.