## Monday, October 20, 2014

### Quick Approximation: Declination and Right Ascension of the Sun

CAUTION:  The formulas presented provide a quick, but crude approximation of the position of our sun.  Search for astronomical algorithms if you want more accurate formulas and algorithms.

I thought it would be fun if I could try to use the curve fitting features of a calculator to obtain an approximate formula of the position of the sun.  Like longitude and latitude on Earth, the celestial objects (planets, stars, comets, asteroids, etc...) are mapped using a system of coordinates:

Right Ascension - measured in hours-minutes-seconds (0:00:00 to 23:59:59.99)
Declination - measured in degrees-minutes-seconds (0° to 359°59'59.99")

I used an HP Prime to take a sample of points and used the curve-fitting features in the Statistics 2Var app.

The sources are:

Right Ascension:

Right Ascension Table - 2014. Data calculated by Kevin Krisciunas - Texas A&M University.  Webpage retrieved October 15, 2014.

For the approximation formula, I chose 100 random points.

Declination:

"Table of the Declination of the Sun.   Mean Value for the Four Years of a Leap-Year Cycle"
Data compiled by Walter Sanford.  Webpage retrieved October 16, 2014.

For the approximation formula, I chose 120 random points.

These formulas are based on the 365-day calendar, where x is the number of days from March 21.  Use radians mode:

Right Ascension (100 random points):
a = 0.0659021173575*x - 0.0873505413785

Declination (120 random points):
d = 23.2834823404 * sin(0.0171866755814*x - 0.0283271293265) + 0.391501633262

This blog is property of Edward Shore.  2014