How Long Does It Take For Sun To Set

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

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

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

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

All calculations for this program were fabricated 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/primary/ASTRO/sunday-rise-fix-multiple-latitudes.txt.bz2

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

The longest sunrise I institute for 2022 was at 89 degrees 51 minutes south latitude, 125 degrees eastward longitude. There, the sun starts ascension xx Sep 2022 at 2352, bobbles up and down a bit (but never quite sets), and finally finishes rising 43 hours and 21 minutes subsequently, at 22 Sep 2022 at 1913, but come across caveat at the end of this answer.

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

to become:

                      Sun or Moon Rise/Set Table for I Year              o  ,    o  ,                                                                              Astronomical Applications Dept. Location: E125 00, S89 51                          Rise and Set for the Dominicus for 2022                   U. S. Naval Observatory                                                                                                                Washington, DC  20392-5420                                                                  Universal Fourth dimension                                                                      January.       February.       Mar.       Apr.       May        June       July       Aug.       Sept.      October.       Nov.       Dec.   Twenty-four hours Rise  Set  Ascent  Set  Ascent  Ready  Rising  Fix  Rise  Set  Rising  Fix  Rise  Set up  Rise  Ready  Rise  Prepare  Rise  Gear up  Rise  Set  Rising  Set up      h 1000  h m   h m  h 1000   h m  h m   h m  h m   h m  h m   h m  h grand   h m  h one thousand   h m  h m   h chiliad  h one thousand   h g  h g   h one thousand  h m   h grand  h m 01  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 02  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 03  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 04  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 05  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 06  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 07  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 08  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 09  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 10  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 11  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 12  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 13  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** xiv  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 15  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 16  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 17  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** eighteen  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 19  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** **** 20  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  2352       **** ****  **** ****  **** **** 21  **** ****  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 22  **** ****  **** ****  1842 1614  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 23  **** ****  **** ****       0708  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 24  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 25  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 26  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 27  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 28  **** ****  **** ****  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 29  **** ****             ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 30  **** ****             ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  ---- ----  **** ****  **** ****  **** ****  **** **** 31  **** ****             ---- ----             ---- ----             ---- ----  ---- ----             **** ****             **** ****  (**** object continuously to a higher place horizon)                                                      (---- object continuously below horizon)                  

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

Verifying the end fourth dimension is a piddling tricker. To practise this, visit http://ssd.jpl.nasa.gov/horizons.cgi with the post-obit parameters:

to get:

                      Revised : Jul 31, 2022                  Sun                                 10   Physical PROPERTIES (revised Jan 16, 2022):   GM (10^11 km^3/s^2)   = one.3271244004193938  Mass (10^30 kg)   ~ one.988544   Radius (photosphere)  = six.963(10^5) km  Angular diam at 1 AU  = 1919.3"   Solar Radius (IAU)    = six.955(ten^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/southward     Adopted sidereal per  = 25.38 d   Pole (RA,December in deg.) =  286.13,63.87   Obliquity to ecliptic = 7 deg 15'           Solar constant (1 AU) = 1367.vi West/m^ii    Solar lumin.(erg/s)   =  iii.846(x^33)   Mass-energy conv rate = iv.3(10^12 gm/south) Constructive temp (Thou)    =  5778   Surf. temp (photosphr)= 6600 G (bottom) Surf. temp (photosphr)=  4400 Chiliad (top)   Photospheric depth    = ~400 km         Chromospheric depth   = ~2500 km   Sunspot cycle         = 11.iv yr         Wheel 22 sunspot min. =  1991 A.D.    Motn. rel to nrby strs= noon : RA=271 deg; Dec=+30 deg                           speed: 19.4 km/south = 0.0112 AU/day   Motn. rel to ii.73K BB = noon : 50=264.seven+-0.8; b=48.2+-0.5                           speed: 369 +-11 km/s  Results  ******************************************************************************* Ephemeris / WWW_USER Fri Jan  1 21:49:19 2022 Pasadena, USA      / Horizons     ******************************************************************************* Target torso name: Sun (10)                        {source: DE431mx} Center trunk name: World (399)                     {source: DE431mx} Heart-site name: (user divers site below) ******************************************************************************* Start fourth dimension      : A.D. 2022-Sep-22 nineteen:00:00.0000 UT       Terminate  time      : A.D. 2022-Sep-22 20:00:00.0000 UT       Step-size       : one minutes ******************************************************************************* Target pole/equ : IAU_SUN                         {East-longitude +} Target radii    : 696000.0 10 696000.0 x 696000.0 1000{Equator, peak, pole}     Center geodetic : 125.000000,-89.850000,7.057E-13 {E-lon(deg),Lat(deg),Alt(km)} Center cylindric: 125.000000,xvi.7540774,-6356.730 {E-lon(deg),Dxy(km),Dz(km)} Center pole/equ : High-precision EOP model        {East-longitude +} Center radii    : 6378.1 ten 6378.1 ten 6356.8 km     {Equator, summit, pole}     Target primary  : Dominicus Vis. interferer : MOON (R_eq= 1737.400) km        {source: DE431mx} Rel. calorie-free curve : Sun, EARTH                      {source: DE431mx} Rel. lght bnd GM: ane.3271E+11, 3.9860E+05 km^3/south^ii                               Atmos refraction: NO (AIRLESS) RA format       : HMS Time format     : CAL  RTS-only print  : NO        EOP file        : eop.160101.p160324                                            EOP coverage    : Information-BASED 1962-JAN-20 TO 2022-Jan-01. PREDICTS-> 2022-MAR-23 Units conversion: i au= 149597870.700 km, c= 299792.458 km/s, 1 24-hour interval= 86400.0 s  Table cut-offs one: Elevation (-90.0deg=NO ),Airmass (>38.000=NO), Daylight (NO ) Tabular array cut-offs ii: Solar Elongation (  0.0,180.0=NO ),Local 60 minutes Angle( 0.0=NO ) *******************************************************************************  Date__(UT)__HR:MN     Azi_(a-appr)_Elev **************************************** $$SOE  2022-Sep-22 19:00 *m  128.1772  -0.3117  2022-Sep-22 19:01 *m  127.9272  -0.3109  2022-Sep-22 nineteen:02 *m  127.6771  -0.3101  2022-Sep-22 19:03 *m  127.4270  -0.3093  2022-Sep-22 nineteen:04 *m  127.1770  -0.3085  2022-Sep-22 xix:05 *thou  126.9269  -0.3077  2022-Sep-22 19:06 *m  126.6769  -0.3069  2022-Sep-22 19:07 *m  126.4268  -0.3061  2022-Sep-22 nineteen:08 *m  126.1767  -0.3053  2022-Sep-22 19:09 *k  125.9267  -0.3045  2022-Sep-22 nineteen:x *thousand  125.6766  -0.3037  2022-Sep-22 19:11 *m  125.4266  -0.3029  2022-Sep-22 19:12 *m  125.1765  -0.3021  2022-Sep-22 19:13 *m  124.9264  -0.3013  2022-Sep-22 19:14 *thou  124.6764  -0.3005  2022-Sep-22 xix:15 *m  124.4263  -0.2997  2022-Sep-22 19:16 *yard  124.1762  -0.2989  2022-Sep-22 19:17 *k  123.9262  -0.2981  2022-Sep-22 19:xviii *grand  123.6761  -0.2973  2022-Sep-22 19:19 *m  123.4261  -0.2964  2022-Sep-22 nineteen:20 *g  123.1760  -0.2956  2022-Sep-22 19:21 *m  122.9259  -0.2948  2022-Sep-22 19:22 *g  122.6759  -0.2940  2022-Sep-22 nineteen:23 *grand  122.4258  -0.2932  2022-Sep-22 19:24 *m  122.1757  -0.2923  2022-Sep-22 19:25 *m  121.9257  -0.2915  2022-Sep-22 19:26 *m  121.6756  -0.2907  2022-Sep-22 19:27 *1000  121.4256  -0.2899  2022-Sep-22 19:28 *m  121.1755  -0.2890  2022-Sep-22 nineteen:29 *thou  120.9254  -0.2882  2022-Sep-22 19:thirty *yard  120.6754  -0.2874  2022-Sep-22 xix:31 *one thousand  120.4253  -0.2865  2022-Sep-22 nineteen:32 *m  120.1753  -0.2857  2022-Sep-22 19:33 *m  119.9252  -0.2849  2022-Sep-22 19:34 *grand  119.6751  -0.2840  2022-Sep-22 19:35 *m  119.4251  -0.2832  2022-Sep-22 19:36 *one thousand  119.1750  -0.2823  2022-Sep-22 19:37 *thousand  118.9250  -0.2815  2022-Sep-22 xix:38 *m  118.6749  -0.2807  2022-Sep-22 19:39 *k  118.4248  -0.2798  2022-Sep-22 19:forty *chiliad  118.1748  -0.2790  2022-Sep-22 nineteen:41 *m  117.9247  -0.2781  2022-Sep-22 19:42 *m  117.6746  -0.2773  2022-Sep-22 19:43 *thousand  117.4246  -0.2764  2022-Sep-22 19:44 *m  117.1745  -0.2756  2022-Sep-22 19:45 *m  116.9245  -0.2747  2022-Sep-22 xix:46 *chiliad  116.6744  -0.2739  2022-Sep-22 nineteen:47 *chiliad  116.4243  -0.2730  2022-Sep-22 19:48 *m  116.1743  -0.2721  2022-Sep-22 nineteen:49 *g  115.9242  -0.2713  2022-Sep-22 19:l *grand  115.6742  -0.2704  2022-Sep-22 19:51 *m  115.4241  -0.2696  2022-Sep-22 19:52 *grand  115.1740  -0.2687  2022-Sep-22 19:53 *k  114.9240  -0.2678  2022-Sep-22 19:54 *chiliad  114.6739  -0.2670  2022-Sep-22 nineteen:55 *one thousand  114.4239  -0.2661  2022-Sep-22 19:56 *m  114.1738  -0.2652  2022-Sep-22 xix:57 *chiliad  113.9237  -0.2644  2022-Sep-22 19:58 *grand  113.6737  -0.2635  2022-Sep-22 19:59 *m  113.4236  -0.2626  2022-Sep-22 twenty:00 *m  113.1735  -0.2618 $$EOE ******************************************************************************* Column meaning:  Fourth dimension    Prior to 1962, times are UT1. Dates thereafter are UTC. Any 'b' symbol in the 1st-column denotes a B.C. appointment. Showtime-column blank (" ") denotes an A.D. date. Calendar dates prior to 1582-October-15 are in the Julian calendar organisation. Afterward agenda 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 calibration is used internally. It is equivalent to the current IAU definition of "TDB". Conversion between CT and the selected non-compatible UT output scale has not been determined for UTC times after the next July or January 1st.  The last known jump-2d is used over whatsoever future interval.    NOTE: "n.a." in output means quantity "not available" at the print-fourth dimension.  SOLAR PRESENCE (OBSERVING SITE)   Time tag is followed by a blank, and so a solar-presence symbol:          '*'  Daylight (refracted solar upper-limb on or above apparent horizon)         'C'  Ceremonious twilight/dawn         'Northward'  Nautical twilight/dawn         'A'  Astronomical twilight/dawn         ' '  Nighttime OR geocentric ephemeris  LUNAR PRESENCE WITH TARGET RISE/TRANSIT/Fix MARKER (OBSERVING SITE)   The solar-presence symbol is immediately followed by another marker symbol:          'k'  Refracted upper-limb of Moon on or above apparent horizon         ' '  Refracted upper-limb of Moon below credible horizon OR geocentric         'r'  Rising    (target body on or above cut-off RTS elevation)         't'  Transit (target torso at or by local maximum RTS elevation)         's'  Fix     (target body on or beneath cut-off RTS acme)  RTS MARKERS (TVH)   Ascension and set are with respect to the reference ellipsoid true visual horizon defined by the summit cut-off angle. Horizon dip and yellowish-low-cal refraction (Globe only) are considered. Accurateness is < or = to twice the requested search step-size.   Azi_(a-appr)_Elev =    Airless credible azimuth and elevation of target center. Adjusted for calorie-free-fourth dimension, the gravitational deflection of light, stellar aberration, precession and nutation. Azimuth measured Due north(0) -> East(90) -> South(180) -> West(270) -> Northward (360). Elevation is with respect to plane perpendicular to local zenith management.  TOPOCENTRIC Only. Units: DEGREES    Computations past ...      Solar System Dynamics Group, Horizons On-Line Ephemeris Organization      4800 Oak Grove Drive, Jet Propulsion Laboratory      Pasadena, CA  91109   Usa      Information: http://ssd.jpl.nasa.gov/      Connect    : telnet://ssd.jpl.nasa.gov:6775  (via browser)                   telnet ssd.jpl.nasa.gov 6775    (via command-line)      Writer     : Jon.Giorgini@jpl.nasa.gov  *******************************************************************************                  

The sun's athwart diameter is about 32 arcminutes, so the sunday'southward lower limb is 16 arcminutes beneath the sunday's eye. When the center of the sun has geometric superlative -18 arcminutes (-0.iii degrees), the lower limb has geometric elevation -34 arcminutes. Since refraction near the horizon is as well 34 arcminutes, the sunday's lower limb rises when the sun's geometric height is -0.3 degrees.

In the table in a higher place, this occurs between 1914 and 1915, but my program uses slightly more than accurate data for the sun's angular diameter, and the dominicus really finishes rising between 1913 and 1914 (and closer to 1913).

You can and so wing well-nigh halfway across the world to latitude 89 degrees 51 minutes and longitude -nineteen degrees to encounter the one-minute-shorter longest sunset, which starts at 23 Sep 2022 at 2128 and ends at 25 Sep 2022 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 catastrophe 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 2022 at 2022, and finishes rising at 20 Mar 2022 at 0441, a length of 32 hours and 26 minutes.

• At the South Pole, the sun starts setting at 21 Mar 2022 at 1650, and finishes setting at 23 Mar 2022 at 0117, a length of 32 hours and 27 minutes.

• At the South Pole, the sun starts ascension at 21 Sep 2022 at 0508, and finishes rising at 22 Sep 2022 at 1400, a length of 32 hours and 52 minutes.

• At the Northward Pole, the lord's day starts setting at 24 Sep 2022 at 0243, and finishes setting at 25 Sep 2022 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 about locations, but may be unreasonable shut the pole, where the longest sunrises and sunsets occur. In particular, refraction tin change rapidly at these latitudes, assuasive 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.

Source: https://astronomy.stackexchange.com/questions/12824/how-long-does-a-sunrise-or-sunset-take

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