Sunrise equations from the matlab code

Generaaly, Daytime is from sunrise to sunset. But, in my research, I will define the daytime is from civil dawn to civil dusk. My research area is South Korea. Time zone is GMT+9 hour I can get the time about civil dawn and civil dusk from the matlab code. I could get the matlab code from the [login to view URL] ([login to view URL]) I’d like to make some equations(less than 10 equations) about civil dawn and dusk from the matlab code. In the end, I’d like to write down the equations on my research When you make some equations, please annotate where did you refer from the line number of the matlab scripts. You can use the formula symbol. You can also refer various materials such as wikipedia or references. please remark the references. [login to view URL]