Confining Particles with the Motion of Shepherd Moons
I will write a program in Python involving the orbit of two moons around a planet. Many planets in our solar system have moons. Sometimes, when there is excess dust and icy or rocky debris orbiting the planet as well, the moons can help herd this dust into defined rings. For example, two of Saturn’s moons, Prometheus and Pandora, define Saturn’s F ring. They do so by orbiting on either side of the dust ring. Any dust that tries to escape is either absorbed by the moons’ gravitational pulls, or is pushed back into the ring by the different speeds of the moons. The outer moon travels at a relatively fast speed, thus speeding up any stray particles of dust that try to escape the ring, swirling them back towards the ring. Similarly, the inner moon travels slower, slowing down any dust that tries to escape the ring by traveling in towards the planet.
For my project, I will model the shepherd moons Prometheus and Pandora orbiting Saturn and herding dust particles between them into a ring. I will use vpython to create a 3D simulation of the planet and moon system. The moons orbit at slightly different speeds and different distances from the planet. In my model the orbits will be circular, since that is a sufficient approximation of a realistic elliptical orbit for this exercise. I will then model small particles between the moons’ orbits to show the dust ring they help contain. The dust will look like a cloud or ring-shaped plane made up of dots. I will animate them so that they move in or out towards the moons and stick to the moons if they collide due to the moons’ gravitational pulls. I will also attempt to animate the particles so that they can be pushed back into the ring by the moons velocities and motion trajectories. I will include a graph of the moons’ and a dust particle’s motion to show more clearly how they interact with each other.
This simulation and accompanying graphs will illustrate how the motion of shepherd moons help create rings around planets.