Alien Sunsets on Tumbling Asteroids

Yang (Fish) Yu

2021

Because of Earth’s periodic rotating and revolving, we experience regular day and night that makes Earth habitable for multiple lives, including humans. However, planets like Earth are rare in the Universe compared to asteroids, which are different sized and shaped rock bodies. These asteroids’ motion are not periodic, but tumble due to their irregular shapes, and we would like to know the pattern of Sol in the sky of these asteroids. In this thesis, we mathematically simulate the motion of asteroids in 2D and 3D, and we are able to change parameters of asteroids to study more general cases.

Inspired by Hwan Bae and Cyrus Screwvala’s Senior theses in 2019 and 1996, we first represented irregular asteroids that tumble as a dumbbell in 2D: two point masses connected by a massless rod. Next, we added one more dimension to create 3D single dumbbell models. Then we added one more dumbbell to represent asteroids as crossed dumbbells.

We simulated Sol’s motion as observed on asteroids by numerical integration of Kepler and dumbbell’s orbital equations and changeable parameters. Under different revolving orbits, dumbbells are more likely to undergo chaotic motion with larger eccentricity e and semi-major axis a. For eccentric orbits, dumbbell’s tumbling motion is more violent. Changing energy and angular momentum also influence asteroids’ movements. 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 horizon for days.

To show our asteroids are chaotic systems that are highly sensitive to initial conditions, we changed one part of parameters each time by 0.1%. The path of Sol in skies was the same at the beginning, but it changed dramatically after a few days; path under different conditions went in different directions. Applications of this thesis include sunrises and sunsets on Hyperion, a tiny irregular moon of Saturn.