Name: Yang “Fish” Yu

Major: Physics

Minor: Mathematics

Advisors: Dr. John F. Lindner, Dr. Cody Leary

We simulated Sol’s apparent motion as observed from tumbling asteroids. If all the mass of the asteroid is concentrated at a point, it will move in an elliptical orbit, like Earth. To account for the tumbling of the asteroid, we extend the point into a dumbbell. We forced the center of mass to move elliptically, and then the asteroid itself tumbled, according to Newton’s second law.

We calculated Sol’s apparent motion by numerical integration of Kepler and dumbbell’s orbital equations and changeable parameters. Our system is very sensitive to initial conditions, and hence is chaotic.

We simulated Sol’s movement in skies under different conditions from observer’s perspective. Sol is able to move irregularly in the skies; it may move back and forth in the sky or stay below the horizon for days.

Yang will be online to field comments on April 16:

4-6 pm EDT (PST 1pm-3pm, Africa/Europe: late evening)

Very interesting and cool project! Thank you for sharing it here. Congratulations, Fish!

Thank you Dr. Pierce!

I love the coil and ball plots! Could we next numerically integrate the dumbbell asteroid orbits for rotation and translation simultaneously (without the two-step process of elliptic orbit first and the chaotic tumbling second)?

Thank you Dr. Lindner! I think it’s workable if we represent dumbbell’s position with respect to Sol. In our case, the position of dumbbell \delta r is relative to center of mass (points from center of mass to two ends), if we represent it with respect to Sol (points from Sol to two ends), we might be able to integrate them simultaneously!

Very interesting work Fish! What did you use to run/generate your simulations?

Great job and congratulations!

Thank you Dr. Guarnera! We used Mathematica to do all the calculation and and simulations.

Great project Fish! Who is Sol? I love your poster. It’s very creative.

Thank you Carlos! “Sol” can be any center giant star that dominates asteroids in their system. For example, the sun in Sun-Earth-Moon system; Saturn in Saturn-Titan-Hyperion system.

I like your Little Prince graphic! It looks like the Prince sees Sol change direction form time to time. What are the possible causes of this physically?

Yes! In figure in 2D Polar coordinate, we represent the direction of zenith as red dashed line along dumbbell’s rod. The direction of it will change as dumbbell tumbles. Some reasons to cause dumbbell doing tumbling motion are: asteroids’ highly irregular shape, gravity force caused by other neighbor planets. For example, Hyperion is sponge like with highly irregular shape, and Titan, one of the largest Saturn’s moons, has strong gravity force acting on Hyperion.

Hello Fish! Congratulations on doing this work, and thank you for sharing it here today, so that others can benefit from it. Because I don’t know enough about your subject to ask any questions, you are saved from that experience! But I really appreciate catching up with you at this point, to see some of your work in your major, and to think back to being in FYS, which seems a very long time ago! Again, congratulations and thank you!

Hi Professor Graham! Thank you so much for stopping by! Thank you so much for your encouragement and supports from day 1 I came to Wooster. I wouldn’t choose physics major without you! (So does this poster and IS!)