Measuring Titan's Orbital Period
Just got a new telescope and one of my first projects was to measure Titan’s orbital period around Saturn. Titan is Saturn’s brightest moon and should be visible in most small telescopes. All of my measurements were done by sight and estimation of Titan’s distance compared to the horizontal diameter of Saturn. Obviously accuracy could be improved with some actual measurement tools or the use of a camera. Unfortunately it was difficult to get a long string of clear nights, so there is one noticeable 4 day gap in data. I also did not wait for the moon to make it all the way back around to the starting position, I figured I had taken enough data to get a decent fit.
Each night I would observe at roughly the same time, and make a drawing in my notebook. After observing every clear night for 11 days I was able to create the above simulated image (drawn in Photoshop) showing Titan’s change of position. I then measured the coordinates for each night’s measurement and plotted the results in a graph. To make the math a bit easier I assumed that Titan’s orbit was circular, thus the position of the moon along the X axis (the plane of orbit) would vary sinusoidally with time (see Wikipedia’s article on Simple Harmonic Motion). Using scipy and matplotlib I fitted the data to the equation x(t) = A cos(ωt + φ), producing the plot below. The result for the fit indicated a period of 380.4 HRS, off slightly from the known value of 382.68 HRS. Still, not bad for just rough measurements!