# How long does a sunrise or sunset take?

From the time that the sun appears on the horizon, or meets it on its setting, to the time that it is fully visible, or no longer visible on its setting, how much time passes? Secondly, is there a place in the world where a sunrise/sunset occurs over a period of a few days? Meaning, that from the time it begins to appear over the horizon until it is fully visible, a period of a few days pass without night intervening (and the same for the opposite with sunset)?

• what-if.xkcd.com/42 may help – user21 Dec 10 '15 at 19:11
• At the equator, the sun seems to rise and set quickly - as Rudyard Kipling says, "On the road to Mandalay, Where the flyin'-fishes play, An' the dawn comes up like thunder outer China 'crost the Bay!" While the farther North or South you go, sunset lingers more and more. Summer sunsets in Georgia seem to take 15 minutes or so to ease under the covers of the darkening land. – Howard Miller Jan 4 '16 at 1:25

The time it takes depends on various factors: the angle that the path of the sun makes with the horizon is the main one, though there are also optical effects caused by the atmosphere have an effect too.

Generally the closer to the equator you live, the steeper is the angle, and so the faster is the sunset.

Using Stellarium I did a couple of tests:

• In the UK (50 degrees North) on 10th December, it took the sun 4min 47s seconds to sink below a simulated horizon.
• In Angloa (10 degrees south), on the same day it took 2min 26s for the sun to set.

It seems that in most populated regions, a sunset takes between 2 and 5 minutes.

There are locations, close to the Antarctic circle at this time of year, at which the sun merely partially sets, and then rises again. And at the Pole, the sun moves around in horizontal circles in the sky each day. During summer there is a permanent sun, as winter approaches the sun gets closer to the horizon, and then sets over several days. (Randall calculates 38 to 40 hours in the blog that Barry links)

• Actually, the ecliptic is the Sun's yearly path, not daily. – AstroFloyd Dec 12 '15 at 18:02

As noted in http://aa.quae.nl/en/antwoorden/zonpositie.html#14 the length of sunrise/sunset varies from approximately 128/cos(latitude) seconds at the equinoxes to approximately 142/cos(1.14*latitude) at the solstices.

More specifically, here's the length of sunrise/sunset at various latitudes:

Beyond 65 degrees north or south latitude, the sun does not rise or set daily, and the length of sunrise/sunset increases significantly.

The data plotted above is the length of sunrise, but the length of sunset is very similar.

All calculations for this program were made with this program:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-12824.c

The raw output of sunrise/sunset times:

https://github.com/barrycarter/bcapps/blob/master/ASTRO/sun-rise-set-multiple-latitudes.txt.bz2

You can verify these results at: http://aa.usno.navy.mil/data/docs/RS_OneYear.php

The longest sunrise I found for 2015 was at 89 degrees 51 minutes south latitude, 125 degrees east longitude. There, the sun starts rising 20 Sep 2015 at 2352, bobbles up and down a bit (but never quite sets), and finally finishes rising 43 hours and 21 minutes later, at 22 Sep 2015 at 1913, but see caveat at the end of this answer.

You can "verify" this by first visiting http://aa.usno.navy.mil/data/docs/RS_OneYear.php with these parameters:

to get:


Sun or Moon Rise/Set Table for One Year
o  ,    o  ,                                                                              Astronomical Applications Dept.
Location: E125 00, S89 51                          Rise and Set for the Sun for 2015                   U. S. Naval Observatory
Washington, DC  20392-5420
Universal Time

Jan.       Feb.       Mar.       Apr.       May        June       July       Aug.       Sept.      Oct.       Nov.       Dec.
Day Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set  Rise  Set
h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m   h m  h m
01  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
02  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
03  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
04  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
05  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
06  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
07  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
08  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
09  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
10  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
11  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
12  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
13  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
14  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
15  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
16  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
17  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
18  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
19  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****
20  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  2352       **** ****  **** ****  **** ****
21  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
22  **** ****  **** ****  1842 1614  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
23  **** ****  **** ****       0708  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
24  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
25  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
26  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
27  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
28  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
29  **** ****             ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
30  **** ****             ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** ****
31  **** ****             ---- ----             ---- ----             ---- ----  ---- ----             **** ****             **** ****

(**** object continuously above horizon)                                                      (---- object continuously below horizon)


Note that the sun rises at 2352 on September 20th, and doesn't set for the rest of the year, verifying the sunrise start time.

Verifying the end time is a little tricker. To do this, visit http://ssd.jpl.nasa.gov/horizons.cgi with the following parameters:

to get:


Revised : Jul 31, 2013                  Sun                                 10

PHYSICAL PROPERTIES (revised Jan 16, 2014):
GM (10^11 km^3/s^2)   = 1.3271244004193938  Mass (10^30 kg)   ~ 1.988544
Radius (photosphere)  = 6.963(10^5) km  Angular diam at 1 AU  = 1919.3"
Solar Radius (IAU)    = 6.955(10^5) km  Mean density          = 1.408 g/cm^3
Surface gravity       =  274.0 m/s^2    Moment of inertia     = 0.059
Escape velocity       =  617.7 km/s     Adopted sidereal per  = 25.38 d
Pole (RA,DEC in deg.) =  286.13,63.87   Obliquity to ecliptic = 7 deg 15'
Solar constant (1 AU) = 1367.6 W/m^2    Solar lumin.(erg/s)   =  3.846(10^33)
Mass-energy conv rate = 4.3(10^12 gm/s) Effective temp (K)    =  5778
Surf. temp (photosphr)= 6600 K (bottom) Surf. temp (photosphr)=  4400 K (top)
Photospheric depth    = ~400 km         Chromospheric depth   = ~2500 km
Sunspot cycle         = 11.4 yr         Cycle 22 sunspot min. =  1991 A.D.

Motn. rel to nrby strs= apex : RA=271 deg; DEC=+30 deg
speed: 19.4 km/s = 0.0112 AU/day
Motn. rel to 2.73K BB = apex : l=264.7+-0.8; b=48.2+-0.5
speed: 369 +-11 km/s

Results

*******************************************************************************
Ephemeris / WWW_USER Fri Jan  1 21:49:19 2016 Pasadena, USA      / Horizons
*******************************************************************************
Target body name: Sun (10)                        {source: DE431mx}
Center body name: Earth (399)                     {source: DE431mx}
Center-site name: (user defined site below)
*******************************************************************************
Start time      : A.D. 2015-Sep-22 19:00:00.0000 UT
Stop  time      : A.D. 2015-Sep-22 20:00:00.0000 UT
Step-size       : 1 minutes
*******************************************************************************
Target pole/equ : IAU_SUN                         {East-longitude +}
Target radii    : 696000.0 x 696000.0 x 696000.0 k{Equator, meridian, pole}
Center geodetic : 125.000000,-89.850000,7.057E-13 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 125.000000,16.7540774,-6356.730 {E-lon(deg),Dxy(km),Dz(km)}
Center pole/equ : High-precision EOP model        {East-longitude +}
Center radii    : 6378.1 x 6378.1 x 6356.8 km     {Equator, meridian, pole}
Target primary  : Sun
Vis. interferer : MOON (R_eq= 1737.400) km        {source: DE431mx}
Rel. light bend : Sun, EARTH                      {source: DE431mx}
Rel. lght bnd GM: 1.3271E+11, 3.9860E+05 km^3/s^2
Atmos refraction: NO (AIRLESS)
RA format       : HMS
Time format     : CAL
RTS-only print  : NO
EOP file        : eop.160101.p160324
EOP coverage    : DATA-BASED 1962-JAN-20 TO 2016-JAN-01. PREDICTS-> 2016-MAR-23
Units conversion: 1 au= 149597870.700 km, c= 299792.458 km/s, 1 day= 86400.0 s
Table cut-offs 1: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO )
Table cut-offs 2: Solar Elongation (  0.0,180.0=NO ),Local Hour Angle( 0.0=NO )
*******************************************************************************
Date__(UT)__HR:MN     Azi_(a-appr)_Elev
****************************************
$$SOE 2015-Sep-22 19:00 *m 128.1772 -0.3117 2015-Sep-22 19:01 *m 127.9272 -0.3109 2015-Sep-22 19:02 *m 127.6771 -0.3101 2015-Sep-22 19:03 *m 127.4270 -0.3093 2015-Sep-22 19:04 *m 127.1770 -0.3085 2015-Sep-22 19:05 *m 126.9269 -0.3077 2015-Sep-22 19:06 *m 126.6769 -0.3069 2015-Sep-22 19:07 *m 126.4268 -0.3061 2015-Sep-22 19:08 *m 126.1767 -0.3053 2015-Sep-22 19:09 *m 125.9267 -0.3045 2015-Sep-22 19:10 *m 125.6766 -0.3037 2015-Sep-22 19:11 *m 125.4266 -0.3029 2015-Sep-22 19:12 *m 125.1765 -0.3021 2015-Sep-22 19:13 *m 124.9264 -0.3013 2015-Sep-22 19:14 *m 124.6764 -0.3005 2015-Sep-22 19:15 *m 124.4263 -0.2997 2015-Sep-22 19:16 *m 124.1762 -0.2989 2015-Sep-22 19:17 *m 123.9262 -0.2981 2015-Sep-22 19:18 *m 123.6761 -0.2973 2015-Sep-22 19:19 *m 123.4261 -0.2964 2015-Sep-22 19:20 *m 123.1760 -0.2956 2015-Sep-22 19:21 *m 122.9259 -0.2948 2015-Sep-22 19:22 *m 122.6759 -0.2940 2015-Sep-22 19:23 *m 122.4258 -0.2932 2015-Sep-22 19:24 *m 122.1757 -0.2923 2015-Sep-22 19:25 *m 121.9257 -0.2915 2015-Sep-22 19:26 *m 121.6756 -0.2907 2015-Sep-22 19:27 *m 121.4256 -0.2899 2015-Sep-22 19:28 *m 121.1755 -0.2890 2015-Sep-22 19:29 *m 120.9254 -0.2882 2015-Sep-22 19:30 *m 120.6754 -0.2874 2015-Sep-22 19:31 *m 120.4253 -0.2865 2015-Sep-22 19:32 *m 120.1753 -0.2857 2015-Sep-22 19:33 *m 119.9252 -0.2849 2015-Sep-22 19:34 *m 119.6751 -0.2840 2015-Sep-22 19:35 *m 119.4251 -0.2832 2015-Sep-22 19:36 *m 119.1750 -0.2823 2015-Sep-22 19:37 *m 118.9250 -0.2815 2015-Sep-22 19:38 *m 118.6749 -0.2807 2015-Sep-22 19:39 *m 118.4248 -0.2798 2015-Sep-22 19:40 *m 118.1748 -0.2790 2015-Sep-22 19:41 *m 117.9247 -0.2781 2015-Sep-22 19:42 *m 117.6746 -0.2773 2015-Sep-22 19:43 *m 117.4246 -0.2764 2015-Sep-22 19:44 *m 117.1745 -0.2756 2015-Sep-22 19:45 *m 116.9245 -0.2747 2015-Sep-22 19:46 *m 116.6744 -0.2739 2015-Sep-22 19:47 *m 116.4243 -0.2730 2015-Sep-22 19:48 *m 116.1743 -0.2721 2015-Sep-22 19:49 *m 115.9242 -0.2713 2015-Sep-22 19:50 *m 115.6742 -0.2704 2015-Sep-22 19:51 *m 115.4241 -0.2696 2015-Sep-22 19:52 *m 115.1740 -0.2687 2015-Sep-22 19:53 *m 114.9240 -0.2678 2015-Sep-22 19:54 *m 114.6739 -0.2670 2015-Sep-22 19:55 *m 114.4239 -0.2661 2015-Sep-22 19:56 *m 114.1738 -0.2652 2015-Sep-22 19:57 *m 113.9237 -0.2644 2015-Sep-22 19:58 *m 113.6737 -0.2635 2015-Sep-22 19:59 *m 113.4236 -0.2626 2015-Sep-22 20:00 *m 113.1735 -0.2618$$EOE
*******************************************************************************
Column meaning:

TIME

Prior to 1962, times are UT1. Dates thereafter are UTC. Any 'b' symbol in
the 1st-column denotes a B.C. date. First-column blank (" ") denotes an A.D.
date. Calendar dates prior to 1582-Oct-15 are in the Julian calendar system.
Later calendar dates are in the Gregorian system.

Time tags refer to the same instant throughout the universe, regardless of
where the observer is located.

The dynamical Coordinate Time scale is used internally. It is equivalent to
the current IAU definition of "TDB". Conversion between CT and the selected
non-uniform UT output scale has not been determined for UTC times after the
next July or January 1st.  The last known leap-second is used over any future
interval.

NOTE: "n.a." in output means quantity "not available" at the print-time.

SOLAR PRESENCE (OBSERVING SITE)
Time tag is followed by a blank, then a solar-presence symbol:

'*'  Daylight (refracted solar upper-limb on or above apparent horizon)
'C'  Civil twilight/dawn
'N'  Nautical twilight/dawn
'A'  Astronomical twilight/dawn
' '  Night OR geocentric ephemeris

LUNAR PRESENCE WITH TARGET RISE/TRANSIT/SET MARKER (OBSERVING SITE)
The solar-presence symbol is immediately followed by another marker symbol:

'm'  Refracted upper-limb of Moon on or above apparent horizon
' '  Refracted upper-limb of Moon below apparent horizon OR geocentric
'r'  Rise    (target body on or above cut-off RTS elevation)
't'  Transit (target body at or past local maximum RTS elevation)
's'  Set     (target body on or below cut-off RTS elevation)

RTS MARKERS (TVH)
Rise and set are with respect to the reference ellipsoid true visual horizon
defined by the elevation cut-off angle. Horizon dip and yellow-light refraction
(Earth only) are considered. Accuracy is < or = to twice the requested search
step-size.

Azi_(a-appr)_Elev =
Airless apparent azimuth and elevation of target center. Adjusted for
light-time, the gravitational deflection of light, stellar aberration,
precession and nutation. Azimuth measured North(0) -> East(90) -> South(180) ->
West(270) -> North (360). Elevation is with respect to plane perpendicular
to local zenith direction.  TOPOCENTRIC ONLY. Units: DEGREES

Computations by ...
Solar System Dynamics Group, Horizons On-Line Ephemeris System
4800 Oak Grove Drive, Jet Propulsion Laboratory
Information: http://ssd.jpl.nasa.gov/
Connect    : telnet://ssd.jpl.nasa.gov:6775  (via browser)
telnet ssd.jpl.nasa.gov 6775    (via command-line)
Author     : Jon.Giorgini@jpl.nasa.gov

*******************************************************************************


The sun's angular diameter is about 32 arcminutes, so the sun's lower limb is 16 arcminutes below the sun's center. When the center of the sun has geometric elevation -18 arcminutes (-0.3 degrees), the lower limb has geometric elevation -34 arcminutes. Since refraction near the horizon is also 34 arcminutes, the sun's lower limb rises when the sun's geometric elevation is -0.3 degrees.

In the table above, this occurs between 1914 and 1915, but my program uses slightly more accurate data for the sun's angular diameter, and the sun actually finishes rising between 1913 and 1914 (and closer to 1913).

You can then fly almost halfway across the world to latitude 89 degrees 51 minutes and longitude -19 degrees to see the one-minute-shorter longest sunset, which starts at 23 Sep 2015 at 2128 and ends at 25 Sep 2015 at 1648, a length of 43 hours and 20 minutes.

In this case, you would use http://aa.usno.navy.mil/data/docs/RS_OneYear.php to verify the ending time of the sunset, and HORIZONS to verify the start time of the sunset.

Polar sunrises and sunsets are considerably shorter:

• At the North Pole, the sun starts rising at 18 Mar 2015 at 2015, and finishes rising at 20 Mar 2015 at 0441, a length of 32 hours and 26 minutes.

• At the South Pole, the sun starts setting at 21 Mar 2015 at 1650, and finishes setting at 23 Mar 2015 at 0117, a length of 32 hours and 27 minutes.

• At the South Pole, the sun starts rising at 21 Sep 2015 at 0508, and finishes rising at 22 Sep 2015 at 1400, a length of 32 hours and 52 minutes.

• At the North Pole, the sun starts setting at 24 Sep 2015 at 0243, and finishes setting at 25 Sep 2015 at 1131, a length of 32 hours and 48 minutes.

Main caveat: Like HORIZONS and the sunrise/sunset tables above, I assume 34 arcminutes of refraction at the horizon. That's reasonable for most locations, but may be unreasonable close the pole, where the longest sunrises and sunsets occur. In particular, refraction can change rapidly at these latitudes, allowing for potentially much longer sunrises and sunsets.

I now believe that http://what-if.xkcd.com/42/ is inaccurate, and will ping the author to let him know.

OK, lets start with the simplest mathematical approach to illustrate the path to a fully analytical answer. The sun presents an angular width of 32 arcminutes to any point on earth. That is 32/60 or 0.533 degrees of arc or angular span. Lets assume the Earth does not have its 23 degrees of tilt, for this first approximation. Then as a second approximation lets assume the Earth rotates around the sun in 24 hours, you are still on the equator. Our calculation is as follows;

0.533 degrees/360 degrees) = (hours sunset/24 hours).

Solve for hours sunset and you get,

24 hrs X (0.533/360) = 0.0355 hrs, which is

0.0355 hrs X 60 min/hrs = 2.13 minutes, which is

2.13 min X 60 secs/min = 128 seconds

OK, now that is the first order approximation only and explains the minima of the nice charts previously provided.

The first and trivial correction would be to notice that the 24 hour assumption is not accurate, hence leap years! Beyond that we have actually 23:56 per year. That will get you 127.56 seconds for sunset.

The real solution for the deep divers out there is to understand that the angular width of the sun in the sky is 32 arcminutes but only for any one instant in time for any one point on the Earth. So the next calculation would be to integrate over the diameter of the earth to incorporate the angular width of you are traversing during the sunset traverse time. You the observer are moving, rotating with the surface of the Earth, and hence you are spreading out the apparent angular size of the sun to the extent you are traversing during that sunset period, and this will add time to the sunset period.

Now that is the easier side of all of this. The next calculation would add the geometric correction for latitude which the observer is located in. This introduces horizontal relative component of motion of the sun to the observer, greatly increasing the time when one is not at the summer or winter equinoxes. (The prior calculations had the sun directly perpendicular to the rotation of the Earth.) In the titled Earth Sun systems, this effect is minimized at the equinox positions of the earth sun system and asymptotes toward the prior calculation if one is on the equator and on the equinox twice per year. Again, this is seen nicely in the charts of the previous answers.

I hope that help folks understand some of basic underpinnings of the math and geometry which the actual calculations must take into effect.

No calculators allowed and you can still get there.

• Can you clarify what you mean by "the 24 hour assumption is not accurate, hence leap years". The length for 1 year is not related to the length of 1 day regardless of how you measure a day (assuming you want "noon" to be when the Sun or arbitrary star crosses the meridian). Also, I think your statement "Beyond that we have actually 23:56 per year" should read "actually 23:56 per DAY", not year. – JohnHoltz Jul 6 '18 at 4:08

The Sun's diameter being ½ degree out of 360, I figure it is 2 minutes. Very even precisely two, because the division of time as into minutes, very very long ago, was designed with the movement of the Sun as its base.

• Downvote: at the poles, the sun can take a long time to sink 1/2 degree. The time it takes the sun to sink 1/2 degree at the horizon is dependent on the observer's latitude and isn't a constant. – user21 Dec 10 '15 at 17:34
• @barrycarter I agree, I was thinking strictly ecliptical. I tried to downvote my own post, but that is not allowed. I should know better, I've lived in strange places where the Sun never sets, or worse, never rises. Artists have painted themselves to great careers using the strange light that the Sun shows when in limbo at its horizon in between its seasons. – LocalFluff Dec 10 '15 at 17:43
• You could redeem yourself by computing the time it takes for the sun to go from +.25 degrees declination to -.25 degrees declination (or, actually, a little different, to account for refraction at the horizon), which would give you the maximum possible length of sunrise/sunset. – user21 Dec 10 '15 at 17:45
• There is also refraction - it is quite often possible to see the Sun, or part of it, when technically it's elevation is below 0 degrees as a result of this - as the atmosphere is thickest at the horizon and the degree of refraction greatest. – adrianmcmenamin Dec 10 '15 at 21:21
• Elevation would also have an effect. – user21 Dec 10 '15 at 21:42