Paris_Example

Been working through the actual math of using a formula on a sphere

to solve a daylight hours problem. Using Paris, France as the example.

Paris sits at Latitude 48.9 degrees N and Longitude 2.2 degrees E.

                                                             

Calculating for the Summer Solciste ie, longest day of the year...

https://share.gemini.google/6GfkuFKVc0r9

My calculations:

tan(48.9) = 1.146

tan(23.5) = 0.434

1.146 x 0.434  = 0.497

I want to calculate arccos(0.497) - (arccos is the angle for a given arc length) - but my 

Windows machine will only do this if I am working in rads...

(There are 2 pi rads in 180 degrees.)

arccos(0.497) is 1.05 rads.

pi - 1.5 is 2.09 rads

Or more directly, I run arccos on -0.497:

(minus because the tilt is giving me more hours!... while the numbers run counter clockwise on the sphere!))

                                                                             

To get hours, I divide 24 hours by pi rads.

I then multiply by 2.09, which gives 15.9 hours.

                                                                    

I am free to add more minutes, as per the Gemini solution!