How can i calculate when sunrise and sunset will occur?

Question

How is it possible for scientists to calculate to the minute when the times for sunrise and sunset to happen, and when the equinoxes and solstices to happen? Any helpful info is most appreciated. =)

Answer 1

I think it would be a sine function of increasing amplitude with increasing latitude.  Since the orbit of the earth is elliptical that would probably enter into the calculation too.  You would also have to allow for how many minutes early or late you are depending on the transit of the sun, which in solar time should be 12 noon but seldom is in this world of daylight savings time and time zones.

Answer 2

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.

Answer 3

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).

Answer 4

Here is a web site that will calculate it for any city or location, and for any day of the year.

http://www.cmpsolv.com/los/sunset.html

Answer 5

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 RA = arctan(tan(LT)*sin(23.45)). RA is the same quadrant as LT

Sun's declination DEC = arcsin(sin(LT)*sin(23.45))

Sun's local hour angle LHA = 99.04 + 360.9856*D - RA - LON

Sun's azimuth = arctan(sin(LHA) / (cos(LHA)*sin(LAT) - tan(DEC)*cos(LAT)) + 180

Azimuth reckoned from 0 degrees at north through 90 east, 180 south, etc.

Sun's altitude = arcsin(sin(LAT)*sin(DEC) + cos(LAT)*cos(DEC)*cos(LHA))

Worked example for 2008 Jan 30 at 0h GMT for longitude 115 W Latitude 40 N:

D = 30.0

LM = 308.62

M = 25.54

LT = 309.44

RA = 311.85

DEC = -17.90

LHA = 61.76

AZ = 237.95

ALT = 8.47

This should be OK for an accuracy of 0.05 degrees throughout 2008 but rounding errors in the expressions for LM, M and LHA will degrade the accuracy by about 0.04 degrees per year for subsequent years. An accuracy of 1 minute in sunrise/sunset time requires an error of less than about 0.1 degrees in the sun's position, depending on latitude.

The times of equinoxes and solstices can be obtained from the intermediate result for sun's true longitude, which is 0 degrees for the March equinox, 90 degrees for the June solstice, 180 degrees for the September equinox and 270 degrees for the December solstice. The accuracy of these times will not be so high, however, with 1 hour corrresponding to an accuracy of 0.04 degrees in the sun's true longitude. Calculating equinoxes and solstices to the nearest minute requires many more periodic terms in the sun's longitude to be taken into account.

Add a note to your question if this isn't clear or you want more information.

Answer 6

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.

Answer 7

There are standard formulae which can do this. You just put in the date, longitude, latitude and you can find exactly where the sun will be.