Last semester in my astronomy class, we tried to find an equation that would fit the path of the sun based on measurements we took, but we realized that due to the change in the tilt of the earth, it wouldn't be a simple sine or cosine graph, and we dropped the subject. I was wondering if there is any simple way, using spherical trigonometry, calculus, or something to calculate the equation Thanks in advance
It really comes down to how accurate you want your equation to be, and over what scale of time. For the day-to-day, a sin function wouldn't be too bad (considering only the regions where it is daylight). To take into account the yearly oscillation of tilt, you would (I think) have to modulate your initial sin function (with a period of a day), with another smaller-amplitude sin function (with a period of a year). If you looked at the situation in more detail (e.g. the geometry) you might find that simply 'sin' isn't the best function. Perhaps sin raised to some power would be better etc etc. I'm sure the answer is readily available out there. Have you tried a google search? Hopefully an observational astronomer will chime in---I'm sure they have the specific answer.
I've done a google search, but I didn't find anything. When we tried to find the equation, we tried just using a normal sine equation over the period of a day, not taking the oscillation of tilt into account Thanks