How can i calculate when sunrise and sunset will occur?
See reference for details. The general plan is to first calculate the value of the equation of time for the date in question, which will give you the time of local solar noon; you can then do some spherical trig to calculate the times of sunrise and sunset. You will need to use the exact latitude and longitude of the location in question to do this. I wrote a program to do this when I was in Arabia and needed to know when prayer time is, since the stores are closed then. You need to use 64-bit arithmetic to get sufficient precision.
If you just want to know when sunrise and sunset will occur, your newspaper will list it every day, and a “farmer’s” almanac will list values for an entire year. If there is an astronomical observatory nearby, they will probably keep very accurate tables on their website. If you want to figure it out by yourself based on your position on the Earth, it can be very tricky. You have to know exactly where you are on the Earth, exactly how the Earth is oriented in space as a function of time, and exactly how high your horizon is. Sunrise and sunset times are also complicated by tatmospheric refraction and the “equation of time”, which can change the answer by many minutes. The US Naval Observatory has been doing these calculations for many years, and might be a good place to start looking if you want more information. If you want to try the calculations yourself you could look up the Explanatory Supplement to the Astronomical Almanac, which has many of the relevant equations.
Astronomers use the imaginary celestial sphere which has two poles and an equator, the ecliptic (the path of the Sun through the sky) and the meridian an imaginary line through the celestial poles. The equinoxes are where the ecliptic intersects the celestial equator and the solstices are the two points on the ecliptic at which the sun is at its greatest declination of 23.5 deg north or south of the celestial equator. The positions of the Sun are usually given in equatorial co-ordinates, that is declination and right ascension. Since we know all these points (including precession which takes about 28,000 years) it is relatively easy to calculate sunrise and sunset or any other astronomical event such as eclipses to the second (not minutes).
Here are the formulae I provided for a previous question about how to calculate the sun’s altitude and azimuth. At sunrise or sunset, the sun’s altitude is -0.83 degrees, so the time of sunrise or sunset could be derived from these formulae. The time of sunrise/sunset is defined as the time when the sun’s upper limb is on the horizon. Refraction raises the sun’s altitude by 34 arcminutes and 16 arcminutes is added for the sun’s semidiameter, so the sun’s altitude at this time is -50 arcminutes or -0.83 degrees. The formulae are as follows: * denotes multiplication Observer’s longitude = LON (positive to west) Observer’s latitude = LAT Day of year (2008) = D (measured in Greenwich Mean Time), so for noon on January 15th, D = 15.5. You can alter D for your own time zone, so for noon CST on January 15th, D = 15.75 Sun’s mean longitude LM = 279.05 + 0.9856*D (L in degrees) Sun’s mean anomaly M = 355.97 + 0.9856*D (M in degrees) Sun’s true longitude = LT + 1.91*sin(M) Sun’s right ascension
