# Solar Declination Part 2

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

### Solar Declination Part 2

My first question about solar declination was not answered, but I've fleshed out the problem some more and come up with a solution:

solar declination = 23.5*Sin(0.01721*d)

where d = 0 when the date is March 21st.

0.01721 is gotten by finding when 91.25*x is equal to $$\pi$$/2. That also finds when sin(91.25*x) equals one which would be approximately during the summer solstice.
91.25 is simply 365/4 so that the seasons are even.
My equation is not exact, but is an approximation, which is not an issue for my purposes.
This equation seems to find the right answer within an acceptable range of error, but why is it that this equation is in wider use:
Declination is calculated with the following formula:
d = 23.45 * sin [360 / 365 * (284 + N)]
Where:
d = declination
N = day number, January 1 = day 1

from this website:
http://www.usc.edu/dept-00/dept/archite ... basic.html

That equation simply gives me the wrong answer.

Thanks for any explanation as to what I'm not understanding.
Guest

### Re: Solar Declination Part 2

As explained in a previous post you are confusing degrees and radians.

Your new formula is essentially the same as the formula on the website, the difference is you've replaced 360 with $$2\pi$$ (so now sin should be calculated using radians) and by re-defining that N starts at the equinox, you've gotten rid of the 284 offset.

You should also be aware that the formulas you've described are approximations, see
https://en.wikipedia.org/wiki/Position_ ... lculations

Hope this helped,

R. Baber.
Guest

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