While I am conducting my research, I thought that it would be nice to keep a record of the progress that I am making, and hence decided to upload some of the codes that I've written and what they do. The report will be submitted to KSEF, so I cannot release all the specifics, but I will briefly outline what I am doing for people who are interested in student physics research.
First, the most obvious bit: entering the data. SpeedLowest refers to the lowest tangential velocity for a particle lifting from the surface for it to form an elliptical orbit. Same applies for speedHighest.
I then make a 3D rendering of Chariklo! It would be better if I can actually render the rough surface and high eccentricity, but that's too hard for me.
This is perhaps the main part. I set a function particleSolve, which will tell me the location of a particle at time t if I input the initial position, velocity, starting time, and ending time. Using this function, I can create a parametric plot of the particle's location after lifting from the surface of Chariklo.
Setting up the function itself is not that hard, as it just involves three lines of equations:
The initial location, that is, p
The initial tangential velocity, that is, p'
The acceleration at time t, which would be p''[t]=GM/(length of p[t] to (0,0)) * (unit vector of p[t] to (0,0)).
Using NDSolve, we can easily obtain the solution for this set of differential equations.
Now I am trying to incorporate collision detection into the code.