How Do You Calculate the Sunset Time on the Winter Solstice at 40 Degrees North?

[smmSTV]

Hi everyone, new member here. Anyway, for my astronomy class my professor wants us to calculate the zone time the center of the sun sets on the winter solstice, at 40 degrees north latitude, and I'm a bit stuck. I know on the winter solstice, the declination of the sun is -23.5 degrees and the right ascension is 18h, and since it would be setting the altitude would be zero. I figured out that I need to find the hour angle of the sun at that exact moment, and use this as the local apparent solar time, and correct to make it mean solar time. I think the objective is to use spherical trigonometry and set up a triangle in the sky, but I'm at a loss of how to set it up, so if anyone could give me a few pointers, that would be great. Thanks.

 

[jim mcnamara]

You want to find this book somewhere:
https://www.amazon.com/dp/0943396352/?tag=pfamazon01-20

Sounds like your prof is going to have you doing lots of these kinds of things. This book gives hand calculation methods (you can use a calculator or write simple code, too)