Given a table of sunset times, such as:

Day # Sunset (H:M):
--------- ----------
1 17:10
2 17:11
.. . .
180 20:21
....
365 17:10

and plotting this data (of course converting H:M to Decimal hours), we
get a somewhat sinusoidal relationship between the Day and time of
Sunset: Sunset = f(Day); or more specifically: Sunset = f(A*sin(k*D-
P) This of course is not a pure sinusoid. Observation shows that it
has a significant 2nd harmonic component.

My application is that I have an automation controller that has a
calendar, can do calculations (including trig), but is rather memory
limited. Thus I would like to calculate time of sunset 'on the fly'
rather than store the data table.

I would like an equation that yields Sunset as a function of day
number. I would like to keep it simpler than the generic formula
given latitude and longitude. I would like the formula from the
tabular data.

It appears to have the form:

Sunset = K + A1*sin(k*D-P1) + A2*sin(2*k*D-P2) + ???
Whe
D = Day number
K, A1, A2, k, P1, P2 are constants determined by Long/Lat.

Has anyone determined the basic functions contained within this
'Sunset function'? Given the basic functions, I can then calculate the
constants.
Thanks in advance for your help,
TomCee