Suncalc [1] is the library I use to calculate the position of the sun. Mapzen [2] host public elevation tile data. This blog post [3] is a good overview of the calculations involved.

[1] https://github.com/mourner/suncalc

[2] https://www.mapzen.com/blog/terrain-tile-service/

[3] http://www.liedman.net/2014/06/25/sunshine/