I am working on a mathematical investigation for my school work and in my investigation, I am trying to model Mercury's velocity around the sun. I picked up data for the velocity from the NASA Horizons System and the data is for 1 whole year starting at the 1st of January. Can someone suggest what sort of equations can model the graph images below?
Since I cannot add the actual image of the graph (due to my reputation level), I have added it as a hyperlink: X-Component of Velocity Y-Component of Velocity Z-Component of Velocity
I tried to search up the models up on the internet; however, I am not sure what I can go by. The internet is giving me an equation for relating velocity and radius but not velocity and time. Also, I tried to mathematically find an equation; however, I am ending up at an integral which I think is not solvable. I hope all this information is enough, thank you.