Contents
Synopsis:
ShepherdSim is a Matlab program that simulates a much simpler system of Shepherd Moons in Saturn’s orbit. Two test particles are positioned with an initial velocity to observe their paths under the influence of two satellites. These satellites are referred to shepherding satellites because they maintain Sautrn’s rings by keeping the particles in place (refer to Background) using their gravitational influence. For this project, the program defaults to the moons, Pandora and Prometheus to observe their gravitational effects, but the user can set the satellite’s distance from the planet and mass to play with the paths of the test particles. The initial positions and velocities of the test particles can also be changed for the same purpose.
This webpage was created by Omar Garcia (Class of 2020) as the conclusion to the final project for ASTR 350 – Intro to Stars. Code can be downloaded here. ShepherdSim-1umt7fb
Background and Motivation:
Shepherding satellites are small natural satellites of a planet that clears a gap in planetary ring material or maintains the structure of the rings by keeping the material in place. While this project observes the effects of shepherding moons in the most prominent example, Saturn , it is important to note that this purpose of satellites can be observed in the all of the Solar System’s gas giants.
The default moons in this program are Prometheus and Pan.
Pan |
Prometheus |
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Mass: | 4.95*10^15 kg | Mass: | 1.595*10^17 kg |
Semi-major Axis: | 133,584 km | Semi-major Axis: | 139,380 km |
Code Breakdown:
ShepherdSim is composed of three primary functions that calculate the position of the moons and test particles based on their position relative to each other and the planet Saturn. These are elliptical, Acceleration, and MoonAccel, which function in a loop to get a fluid path for the objects involved.
Elliptical
This function finds the path of the objects through a time stepping method provided the size of the time step and records them in a movie. The constants and initial conditions are provided to set up the orbits of all objects. This is the part where the user can attempt to position the various test particles as well as satellites to observe the paths. The position of the objects are calculated in two different functions based on what object they are. The Moons are run through the MoonAccel function while the test particles are run through the Acceleration function. Additionally, the program displays the paths on a plot which is changing with time. What the user will see when the program is executed is that the moons do not leave a trail on the plot unlike the test particles because it is assumed that the satellites will remain on the same path. This allows us to focus on the path of the test particles much more clearly and observe the effects of gravity from the satellites.
Acceleration
The function for the test particles, Acceleration, calculates the next position of a test particle by computing the acceleration vector which is dependent on the particle’s position relative to Saturn as well as the satellites. Given enough time, small shifts can be observed as a result of getting close to either one of the satellites.
MoonAccel
The function for the satellites, MoonAccel, calculates the next position of a the satellites by computing the acceleration vector which is dependent on the particle’s position relative to Saturn. With the provided velocity and distances relative to Saturn, the satellites will take on a consistent circular or elliptical orbit. As a result, the program shouldn’t display a trail for them.
Results
The effects of the shepherding satellites becomes obvious in these simulations:
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