Note: I am not using the appropriate number of significant figures to calculate sunrise, sunset, and solar noon. While it may appear that my calculations are accurate to one second, they actually have a precision of closer to 3 minutes (mostly due to approximation). Also, this calculation does not take into account the effect of air temperature, altitude, etc. Together, these may affect the time by 5 minutes or more.

Find today's Julian date (days since Jan 1, 2000 + 2451545):

Now, calculate J_transit at longitude 82.3856, start with n:

Now J_*:

Using J_*, calculate M (mean anomaly) and then use that to calculate C and λ:

We need to calculate the equation of center, C:

We need λ which is the ecliptical longitude of the sun:

Finally, calculate J_transit:

Now, to get an even more accurate number, recursively recalculate M using J_transit until it stops changing. Notice how close the approximation was.

Ok, translate this into something we understand. i.e. When is Solar Noon?

Alrighty, now calculate how long the sun is in the sky at latitude 34.8444:

Now we need to calculate δ which is the declination of the sun:

Now we can go about calculating H (Hour angle):

Just as above, calculate J_*, but this time using hour-angle:

We can use M from above because it really doesn't change that much over the course of a day, calculate J_set in the same way:

Now I'm going to cheat and calculate J_rise:

Using the same idea, figure out when sunrise and sunset are:

A couple anomalies occur. At high latitudes, you will sometimes get H = 0. This means that either the sun does not rise (in the winter) or the sun does not set (in the summer) on that day.