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.
Link: http://people.physics.tamu.edu/krisciunas/ra_dec_sun_2014.html
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.
Link: http://www.wsanford.com/~wsanford/exo/sundials/DEC_Sun.html
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
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.
Link: http://people.physics.tamu.edu/krisciunas/ra_dec_sun_2014.html
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.
Link: http://www.wsanford.com/~wsanford/exo/sundials/DEC_Sun.html
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