How can I compute sunrise/sunset times? [closed]

Answer 1

In Ruby I wrote this for equation of time.

include Math

# degrees to radians = PI/180
to_r = PI/180.0

#radians to degrees = 180/PI
to_d = 180.0/PI

puts "Day, Declination, EofT"

# test a celestial year worth of values.
for jday in 1..366

  et = -7.633 * sin(jday * (2 * PI)/365.24) + 9.65 * sin((jday - 78) * 180/92 * to_r)
  a_sin = sin(23.433 * to_r) * sin((2 * PI/366) * (jday - 81))
  declination = asin(a_sin) * to_d
  puts "#{jday}, #{declination}, #{et}"

end

Then for the above equation:

# center disk and refraction factor have been considered.
cos_omega = sin(-0.83 * to_r) - tan(latitude * to_r) * tan(declination * to_r)
semi_diurnal_arc = acos(cos_omega)

There is a whole website devoted to this at http://www.analemma.com/

• The key to these calculations are good libraries like the one for python above.
• Also usage of Date and Time classes. I would look on rubyforge for something like ephem.

Answer 2

Definitions of what constitutes sunrise/sunset can vary. For example, in ephem "rising and setting are defined as the moments when the upper limb of the body touches the horizon (that is, when the body’s alt plus radius equals zero)" [PyEphem Quick Reference].

#!/usr/bin/env python
import datetime
import ephem # to install, run `pip install pyephem`

o = ephem.Observer()
o.lat, o.long, o.date = '34:3', '-118:15', datetime.datetime.utcnow()
sun = ephem.Sun(o)
print "Los Angeles"
print "sunrise:", o.next_rising(sun), "UTC"
print "sunset:",o.next_setting(sun), "UTC"

Output

Los Angeles, CA
sunrise: 2010/3/30 13:42:43 UTC
sunset: 2010/3/30 02:11:50 UTC

If it is open-source library then you could fix it instead of creating a new one with new bugs.

Answer 3

I did see some interesting things on this NOAA page under the Technical Definitions and Computational Details heading, but I'm sure you've read that already.

The answer to the SO question "Position of the sun given time of day, and lat/long" and the above may actually be all you need.

As a side note (it doesn't answer your question directly), is there a reason you can't pull the NOAA data and use it as a lookup table instead of calculating it? Storage tends to be relatively cheap these days.

Answer 4

For accuracy in the 5min range you have to consider 'which' sunset.
Do you want the time the bottom of the sun touches the horizon or the time the top of the sun passes below the horizon?

It takes 2mins for the sun to cross the horizon.
Below the 1min level you also need to take into account atmospheric refraction.

Answer 5

You may consider reading Wikipedia's article on sunrise equations. The lead paragraph gives the equation:

where:

• ω_o is the hour angle in degrees at either sunrise (when negative value is taken) or sunset (when positive value is taken) in degree (°)
• φ is the latitude of the observer on the Earth in degrees
• δ is the sun declination in degrees

Answer 6

Have a look at this book:
"Practical Astronomy with your Calculator (Paperback)" by Peter Duffett-Smith.
It is quite old but still in print... link