Seperti disebutkan dalam http://aa.quae.nl/en/antwoorden/zonpositie.html#14 panjang matahari terbit / terbenam bervariasi dari sekitar 128 / cos (garis lintang) detik di equinoxes hingga sekitar 142 / cos (1,14 * lintang ) di titik balik matahari.
Lebih khusus lagi, inilah panjang matahari terbit / terbenam di berbagai lintang:
Melampaui 65 derajat lintang utara atau selatan, matahari tidak terbit atau terbenam setiap hari, dan panjang matahari terbit / terbenam meningkat secara signifikan.
Data yang diplot di atas adalah panjang matahari terbit, tetapi panjang matahari terbenam sangat mirip.
Semua perhitungan untuk program ini dibuat dengan program ini:
https://github.com/barrycarter/bcapps/blob/master/ASTRO/bc-solve-astro-12824.c
Output mentah dari waktu matahari terbit / terbenam:
https://github.com/barrycarter/bcapps/blob/master/ASTRO/sun-rise-set-multiple-latitudes.txt.bz2
Anda dapat memverifikasi hasil ini di:
http://aa.usno.navy.mil/data/docs/RS_OneYear.php
Matahari terbit terpanjang yang saya temukan untuk tahun 2015 adalah pada 89 derajat 51 menit lintang selatan, 125 derajat bujur timur. Di sana, matahari mulai naik 20 Sep 2015 pukul 2352, berbandul naik turun sedikit (tetapi tidak pernah set cukup), dan akhirnya selesai naik 43 jam dan 21 menit kemudian, pada 22 Sep 2015 pada 1913, tetapi lihat peringatan di akhir jawaban ini.
Anda dapat "memverifikasi" ini dengan mengunjungi
http://aa.usno.navy.mil/data/docs/RS_OneYear.php dengan parameter berikut:
mendapatkan:
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)
Perhatikan bahwa matahari terbit pada 2352 pada 20 September, dan tidak ditetapkan untuk sisa tahun ini, memverifikasi waktu mulai matahari terbit.
Memverifikasi waktu akhir agak sulit. Untuk melakukan ini, kunjungi
http://ssd.jpl.nasa.gov/horizons.cgi dengan parameter berikut:
mendapatkan:
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
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)
Author : Jon.Giorgini@jpl.nasa.gov
*******************************************************************************
Diameter sudut matahari adalah sekitar 32 arcminutes, jadi tungkai bawah matahari adalah 16 arcminutes di bawah pusat matahari. Ketika pusat matahari memiliki ketinggian geometris -18 arcminutes (-0,3 derajat), tungkai bawah memiliki ketinggian geometrik -34 arcminutes. Karena pembiasan dekat cakrawala juga 34 menit, anggota tubuh bagian bawah matahari naik ketika ketinggian geometris matahari -0,3 derajat.
Dalam tabel di atas, ini terjadi antara 1914 dan 1915, tetapi program saya menggunakan data yang sedikit lebih akurat untuk diameter sudut matahari, dan matahari benar-benar selesai naik antara 1913 dan 1914 (dan lebih dekat ke 1913).
Anda kemudian dapat terbang hampir setengah jalan di dunia ke garis lintang 89 derajat 51 menit dan garis bujur -19 derajat untuk melihat matahari terbenam terpanjang satu menit yang lebih pendek, yang dimulai pada 23 Sep 2015 pukul 2128 dan berakhir pada 25 Sep 2015 pukul 1648, panjang 43 jam dan 20 menit.
Dalam hal ini, Anda akan menggunakan
http://aa.usno.navy.mil/data/docs/RS_OneYear.php untuk memverifikasi waktu berakhirnya matahari terbenam, dan HORIZONS untuk memverifikasi waktu mulai matahari terbenam.
Matahari terbit dan terbenam polar jauh lebih pendek:
Di Kutub Utara, matahari mulai terbit pada 18 Maret 2015 pada 2015, dan selesai terbit pada 20 Maret 2015 pada 0441, panjang 32 jam dan 26 menit.
Di Kutub Selatan, matahari mulai terbenam pada 21 Mar 2015 pukul 1650, dan selesai pada 23 Mar 2015 pukul 0117, panjang 32 jam dan 27 menit.
Di Kutub Selatan, matahari mulai terbit pada 21 Sep 2015 pukul 0508, dan selesai naik pada 22 Sep 2015 pukul 1400, panjang 32 jam dan 52 menit.
Di Kutub Utara, matahari mulai terbenam pada 24 Sep 2015 pukul 0243, dan selesai pada 25 Sep 2015 pukul 1131, panjang 32 jam dan 48 menit.
Peringatan utama: Seperti HORIZON dan tabel matahari terbit / terbenam di atas, saya mengasumsikan 34 menit refraksi di cakrawala. Itu masuk akal untuk sebagian besar lokasi, tetapi mungkin tidak masuk akal menutup kutub, di mana matahari terbit dan matahari terbenam terpanjang terjadi. Secara khusus, pembiasan dapat berubah dengan cepat di garis lintang ini, memungkinkan matahari terbit dan terbenam yang jauh lebih lama.
Saya sekarang percaya bahwa http://what-if.xkcd.com/42/ tidak akurat, dan akan melakukan ping ke penulis untuk memberi tahu dia.