浅谈冬至

冬至日不是日出最晚的日期。

和很多人一样，在刚接触冬至这个概念的时候理所当然的也以为是日出最晚的一天。

冬至实际上是一个很有趣的复杂议题。这篇文章是写的时间最长之一。/lh

直观结论

白昼长度极小值由太阳赤纬决定；而日出/日落时刻的表观极值还叠加了时差（Equation of Time，EoT） 的影响。EoT 与赤纬变化的相位不同，结果是：白昼最短通常出现在冬至附近，而最早日落常出现在冬至之前数日，最晚日出常出现在冬至之后数日。

科普性内容

文章中部分内容可能比较难以理解，这一部分可以让你快速读懂发生了什么。

显然，夏至是一年中白昼最长的一天，冬至则是白昼最短的一天。但一年中日出最早的那天并不是夏至，日落最晚的那天也不是夏至。事实上，最早的日出通常在夏至前约一周出现，而最晚的日落则在夏至后约一周才到来。冬季则相反：最早的日落赶在冬至之前，最晚的日出则落在冬至之后。

这种现是地球运行中两种不同节奏综合的结果。

首先，四季和白昼长短变化的根源在于：地球并非直立地围绕太阳公转，而是始终保持着约23.5度的倾角，。这个倾角使得太阳直射点在地球的南北回归线之间来回移动。夏至时，太阳直射北回归线（直射代表垂直于北回归线所在地的地平面），北半球的白昼达到最长；冬至时，太阳直射南回归线，北半球的白昼最短。如果地球只是这样规律地倾斜旋转，那么日出和日落的最早最晚时刻，理应与白昼最长最短的日子完全重合。

但地球的运行还有另一层复杂之处。我们的日常时间是一种均匀流逝的“平太阳时”。它假设地球以恒定速度围绕太阳运行。然而，地球的公转轨道并非正圆，而是一个椭圆形。根据开普勒定律，当地球在1月初运行到离太阳最近的“近日点”附近时，它的公转速度最快；而在7月初运行到离太阳最远的“远日点”附近时，速度最慢。这意味着，以真实的太阳位置为基准的“真太阳时”（例如日晷所显示的时间），与我们使用的均匀钟表时间之间，每天都会产生几分钟的偏差。这个差值被称为“均时差”。

“均时差”，在微妙地调整着太阳每天在天空中出现和消失的具体钟点。

因此，有两种力量在共同决定每天的日出日落时刻：第一股是比较宏大的“季节力量”，由地轴倾斜主导，它从春分开始，稳定地将日出时间逐渐推前，将日落时间逐渐拉后，直至夏至达到顶点。第二股是精细的“时钟差力量”，由地球公转速度的快慢变化主导，它会根据地球在轨道上的位置，将太阳的真实位置相对于我们的钟表或向前推、或向后拉。

在夏至前夕，季节力量推动日出提前，而时钟差力量此时也恰好向前推动太阳的位置。两股力量方向一致，形成合力，使得日出时间被加速推前，从而在夏至之前就达到了“最早日出”的顶点。

夏至过后，季节力量开始转向，试图让日落提前。但此时的时钟差力量依然保持着向前的惯性，继续推迟太阳落山的时间。这两股力量方向相反，相互拉扯，结果就是日落时间并没有立刻提前，反而得以继续推迟一小段时间，直到夏至之后才创造出“最晚日落”的时刻。

冬季的景象是这一过程的对称倒影。冬至前，季节力量和时钟差力量共同将日落时间向后拉，于是“最早日落”提前到来；冬至后，季节力量开始试图让日出提前，但时钟差力量仍在向后拖拽，导致“最晚日出”延迟出现。

因此，我们手中的日历所标记的“夏至”与“冬至”，只是地球倾斜所定义的白昼长短的极值点。而我们所观察到日出和日落的具体时刻，则是地球的“恒定倾斜”与“不匀速度”来构成的。

---

背景

日出/日落的发生既取决于太阳在天球的几何位置（太阳赤纬 $\delta$），也受地球自转与轨道参数的影响（这影响“真太阳时”与“平太阳时”之间的差），即 Equation of Time（EoT）。为便于复现，这里采用常见近似 NOAA / Meeus。

日出 / 日落小时角

设地面纬度为 $\varphi$，太阳赤纬为 $\delta$，天顶角取日出的常用修正 $z = 90.833^\circ$（包含平均大气折射和太阳半径修正）。日出/日落的小时角 H 。

$$\cos H = \frac{\cos z - \sin\varphi\sin\delta}{\cos\varphi\cos\delta}.$$

小时角 H转为时间：每 15° 对应 1 小时。使用 NOAA 的合成公式（分钟制）将小时角与 EoT、经度合成为 UTC 日出/日落时间：

$$\text{sunrise}_{UTC} = 720 - 4(\text{longitude} + H) - \mathrm{EoT},$$ $$\text{sunset}_{UTC} = 720 - 4(\text{longitude} - H) - \mathrm{EoT}.$$

最后再将 UTC 转为本地时（中国为 UTC+8）。

Equation of Time（近似表达）

令 $\gamma = 2\pi (N-1)/365)$，$N$ 为当年日序，则 EoT 的常用近似为：

$$\mathrm{EoT} \approx 229.18\Big(0.000075 + 0.001868\cos\gamma - 0.032077\sin\gamma - 0.014615\cos2\gamma - 0.040849\sin2\gamma\Big),$$

太阳赤纬（弧度）近似：

$$\delta \approx 0.006918 - 0.399912\cos\gamma + 0.070257\sin\gamma - 0.006758\cos2\gamma + 0.000907\sin2\gamma - 0.002697\cos3\gamma + 0.00148\sin3\gamma.$$

计算摘要

伪代码：

Inputs:
  lat   : latitude in decimal degrees (north positive)
  lon   : longitude in decimal degrees (east positive)
  tz    : time zone offset from UTC (hours)
  start_date, end_date

Constants:
  ZENITH = 90.833 deg   // civil sunrise/sunset
  PI = 3.141592653589793

Procedure:
function day_of_year(date):
    return N   // 1..365 (or 366)
function eot_and_declination(date):
    N = day_of_year(date)
    gamma = 2 * PI * (N - 1) / 365
    EoT = 229.18 * (
          0.000075
        + 0.001868 * cos(gamma)
        - 0.032077 * sin(gamma)
        - 0.014615 * cos(2*gamma)
        - 0.040849 * sin(2*gamma)
    )                  // minutes
    decl = 0.006918
         - 0.399912 * cos(gamma)
         + 0.070257 * sin(gamma)
         - 0.006758 * cos(2*gamma)
         + 0.000907 * sin(2*gamma)
         - 0.002697 * cos(3*gamma)
         + 0.001480 * sin(3*gamma)   // radians
    return EoT, decl
function sunrise_sunset(date, lat, lon, tz):
    EoT, decl = eot_and_declination(date)
    φ = lat * PI / 180
    z = ZENITH * PI / 180


    cosH = (cos(z) - sin(φ)*sin(decl)) / (cos(φ)*cos(decl))
    cosH = clamp(cosH, -1, 1)
    H = acos(cosH) * 180 / PI      // degrees

    sunrise_utc = 720 - 4*(lon + H) - EoT
    sunset_utc  = 720 - 4*(lon - H) - EoT
    sunrise_local = sunrise_utc + tz*60
    sunset_local  = sunset_utc  + tz*60
    daylength     = sunset_local - sunrise_local

    return sunrise_local, sunset_local, daylength

Main:
    for date from start_date to end_date:
        sr, ss, dl = sunrise_sunset(date, lat, lon, tz)
        save(date, sr, ss, dl)

代入数据：

LAT = 31.2304
LON = 121.4737

上海地区日照长度：

上海地区时差和太阳赤纬变化曲线：

上海地区日出和日落变化曲线：

 理论太阳正午 与 时差修正后的太阳正午关系图：

冬季时期详细展示图：

准确性对比

以上计算结果都是个人计算得出，准确性可能存在偏差。

中国上海市的日出日落时间表 - MAPLOGS 有着比较权威的数据，有兴趣可以和我附录里面放的数据对比一下，准确性在1分钟以内。

结论

上海地区日出最晚为2026/1/10 的 6:53:27AM

在大多数中纬度城市（包括上海），冬至为白昼最短日，但最晚的日出和最早的日落往往不与冬至同日出现。这是地球轨道偏心与轴倾造成 EoT 与赤纬同台作用的自然结果。以上计算结果已经在图标中呈现。

这么看来冬季赛观测日出还是挺理想的。

鸣谢

在本文的撰写过程中，AI为部分内容的生成与排版提供了重要帮助。

• 本文伪代码由 ChatGPT 生成，完成了为算法部分的表述。

• 附录表格的排版由 DeepSeek 协助完成。

附录

date	sunrise_minutes	sunset_minutes	sunrise	sunset	daylength_minutes
3/20/2025	359.49077691626866	1085.0478126813923	5:59:29	18:05:03	725.5570357651236
3/21/2025	358.22648456328227	1085.7001016807721	5:58:14	18:05:42	727.4736171174899
3/22/2025	356.9595406194203	1086.3489949156506	5:56:58	18:06:21	729.3894542962303
3/23/2025	355.6904728092169	1086.994755202527	5:55:41	18:07:00	731.3042824
3/24/2025	354.4198094313249	1087.6376472573215	5:54:25	18:07:38	733.2178378259966
3/25/2025	353.14807915221013	1088.277936945719	5:53:09	18:08:17	735.1298577935088
3/26/2025	351.87581079869346	1088.915890533985	5:51:53	18:08:55	737.0400797352916
3/27/2025	350.60353314962026	1089.551773941111	5:50:36	18:09:33	738.9482407914907
3/28/2025	349.3317747269324	1090.1858519931548	5:49:20	18:10:11	740.8540772662224
3/29/2025	348.0610636	1090.8183876806318	5:48:04	18:10:49	742.7573240942168
3/30/2025	346.7919271083862	1091.4496414198293	5:46:48	18:11:27	744.6577143114431
3/31/2025	345.52489178858286	1092.0798703189112	5:45:31	18:12:05	746.5549785303283
4/1/2025	344.26048302948936	1092.7093274496883	5:44:16	18:12:43	748.4488444
4/2/2025	342.99922493233964	1093.3382611259367	5:43:00	18:13:20	750.3390362
4/3/2025	341.7416400900061	1093.9669141891573	5:41:44	18:13:58	752.2252740991512
4/4/2025	340.4882493809718	1094.5955233026675	5:40:29	18:14:36	754.1072739216957
4/5/2025	339.23957176455855	1095.2243182549416	5:39:14	18:15:13	755.9847465
4/6/2025	337.9961240775664	1095.8535212731088	5:38:00	18:15:51	757.8573971955424
4/7/2025	336.7584208324468	1096.483346347546	5:36:46	18:16:29	759.7249255150994
4/8/2025	335.52697401711293	1097.1139985684977	5:35:32	18:17:07	761.5870245513847
4/9/2025	334.30229289645695	1097.7456734756793	5:34:18	18:17:45	763.4433805792223
4/10/2025	333.0848838156179	1098.378556421827	5:33:05	18:18:23	765.2936726
4/11/2025	331.8752500050092	1099.0128219511691	5:31:53	18:19:01	767.1375719461599
4/12/2025	330.67389138708484	1099.6486331938095	5:30:40	18:19:39	768.9747418067246
4/13/2025	329.4813043847875	1100.2861412770214	5:29:29	18:20:17	770.8048368922339
4/14/2025	328.2979817	1100.925484754468	5:28:18	18:20:56	772.627503
4/15/2025	327.12441228300963	1101.5667890543714	5:27:07	18:21:34	774.4423767713618
4/16/2025	325.9610808294155	1102.2101659476675	5:25:58	18:22:13	776.2490851
4/17/2025	324.8084679	1102.8557130371905	5:24:49	18:22:51	778.0472451272226
4/18/2025	323.6670496274222	1103.5035132689422	5:23:40	18:23:30	779.8364636
4/19/2025	322.53729746355293	1104.1536344665092	5:22:32	18:24:09	781.6163370029562
4/20/2025	321.41967809489006	1104.8061288896938	5:21:25	18:24:48	783.3864507948037
4/21/2025	320.3146532084322	1105.4610328184312	5:20:19	18:25:28	785.1463796
4/22/2025	319.2226793169721	1106.1183661630694	5:19:13	18:26:07	786.8956868460973
4/23/2025	318.14420757363666	1106.7781321020793	5:18:09	18:26:47	788.6339245284427
4/24/2025	317.0796836	1107.440316748275	5:17:05	18:27:26	790.3606332
4/25/2025	316.0295472238181	1108.1048888445937	5:16:02	18:28:06	792.0753416207756
4/26/2025	314.9942324364131	1108.7717994905033	5:15:00	18:28:46	793.7775670540902
4/27/2025	313.97416705170355	1109.4409819000698	5:13:58	18:29:26	795.4668148483663
4/28/2025	312.9697725838747	1110.1123511927046	5:12:58	18:30:07	797.1425786088299
4/29/2025	311.9814640326618	1110.7858042175994	5:11:59	18:30:47	798.8043401849377
4/30/2025	311.00964967920834	1111.461219412814	5:11:01	18:31:28	800.4515697336057
5/1/2025	310.05473087718053	1112.1384566999595	5:10:03	18:32:08	802.0837258
5/2/2025	309.1171018385959	1112.8173574153798	5:09:07	18:32:49	803.7002555767839
5/3/2025	308.19714941384154	1113.4977442786867	5:08:12	18:33:30	805.3005948648452
5/4/2025	307.29525286535716	1114.1794213994585	5:07:18	18:34:11	806.8841685341014
5/5/2025	306.41178363449126	1114.862174322851	5:06:25	18:34:52	808.4503906883597
5/6/2025	305.5471051	1115.5457701148098	5:05:33	18:35:33	809.9986650137588
5/7/2025	304.7015723351084	1116.2299574874964	5:04:42	18:36:14	811.5283851523881
5/8/2025	303.87553184065985	1116.9144669654727	5:03:53	18:36:55	813.0389351248128
5/9/2025	303.0693213	1117.599011093087	5:03:04	18:37:36	814.5296898
5/10/2025	302.2832692539801	1118.2832846834315	5:02:17	18:38:17	816.0000154294514
5/11/2025	301.5176949115073	1118.966965	5:01:31	18:38:58	817.4492701976128
5/12/2025	300.77290776545044	1119.6497126350441	5:00:46	18:39:39	818.8768048695937
5/13/2025	300.04920733752346	1120.3311707931343	5:00:03	18:40:20	820.2819634556108
5/14/2025	299.3468828585401	1121.0109667990437	4:59:21	18:41:01	821.6640839405036
5/15/2025	298.66621294865456	1121.6887120105284	4:58:40	18:41:41	823.0224990618739
5/16/2025	298.0074652885503	1122.3640024271713	4:58:00	18:42:22	824.3565371
5/17/2025	297.37089628186413	1123.0364192309435	4:57:22	18:43:02	825.6655229490793
5/18/2025	296.7567507092471	1123.705529366956	4:56:45	18:43:42	826.9487786577088
5/19/2025	296.16526137457214	1124.3708861635942	4:56:10	18:44:22	828.2056247890221
5/20/2025	295.59664874393223	1125.0320299910645	4:55:36	18:45:02	829.4353812471322
5/21/2025	295.05112057818985	1125.6884889572289	4:55:03	18:45:41	830.6373684
5/22/2025	294.5288716	1126.3397796394274	4:54:32	18:46:20	831.8109080794544
5/23/2025	294.0300829161432	1126.9854078508267	4:54:02	18:46:59	832.9553249346835
5/24/2025	293.5549220368944	1127.6248694396563	4:53:33	18:47:37	834.0699474
5/25/2025	293.10354209277625	1128.2576511195366	4:53:06	18:48:15	835.1541090267604
5/26/2025	292.6760816510629	1128.8832313289238	4:52:41	18:48:53	836.2071496778609
5/27/2025	292.27266429302585	1129.5010811175448	4:52:16	18:49:30	837.2284168
5/28/2025	291.8933982337855	1130.110665057527	4:51:54	18:50:07	838.2172668237415
5/29/2025	291.53837594654465	1130.7114421767822	4:51:32	18:50:43	839.1730662302375
5/30/2025	291.20767379311553	1131.302866912049	4:51:12	18:51:18	840.0951931189335
5/31/2025	290.9013516627588	1131.8843900788788	4:50:54	18:51:53	840.9830384
6/1/2025	290.6194526214498	1132.4554598557033	4:50:37	18:52:27	841.8360072342535
6/2/2025	290.36200257376834	1133.0155227790265	4:50:22	18:53:01	842.6535202052581
6/3/2025	290.12900993968293	1133.5640247466717	4:50:08	18:53:34	843.4350148069889
6/4/2025	289.9204653485558	1134.1004120259392	4:49:55	18:54:06	844.1799466773834
6/5/2025	289.7363413527378	1134.6241322634528	4:49:44	18:54:37	844.8877909
6/6/2025	289.57659216314835	1135.1346354934285	4:49:35	18:55:08	845.5580433302802
6/7/2025	289.44115340924304	1135.631375141064	4:49:26	18:55:38	846.1902217318209
6/8/2025	289.3299419	1136.1138090177333	4:49:20	18:56:07	846.7838670919723
6/9/2025	289.24285556861605	1136.581400304683	4:49:15	18:56:35	847.3385447
6/10/2025	289.1797730622436	1137.0336185219455	4:49:11	18:57:02	847.8538454597019
6/11/2025	289.1405538806497	1137.4699404792489	4:49:08	18:57:28	848.3293865985992
6/12/2025	289.12503816431564	1137.889851205754	4:49:08	18:57:53	848.7648130414384
6/13/2025	289.13304667500427	1138.2928448555626	4:49:08	18:58:18	849.1597981805584
6/14/2025	289.16438079038403	1138.6784255860348	4:49:10	18:58:41	849.5140447956508
6/15/2025	289.21882254023797	1139.0461084060985	4:49:13	18:59:03	849.8272858658605
6/16/2025	289.2961346858601	1139.3954199918876	4:49:18	18:59:24	850.0992853060275
6/17/2025	289.39606084405295	1139.7258994672034	4:49:24	18:59:44	850.3298386231504
6/18/2025	289.51832565694673	1140.037099146501	4:49:31	19:00:02	850.5187734895544
6/19/2025	289.6626350086376	1140.3285852382965	4:49:40	19:00:20	850.6659502296588
6/20/2025	289.8286762894237	1140.5999385071061	4:49:50	19:00:36	850.7712622176824
6/21/2025	290.01611870816976	1140.8507548922753	4:50:01	19:00:51	850.8346361841055
6/22/2025	290.2246136530913	1141.0806460822778	4:50:13	19:01:05	850.8560324291865
6/23/2025	290.4537951009893	1141.289240043333	4:50:27	19:01:17	850.8354449423437
6/24/2025	290.70328007470954	1141.476182	4:50:42	19:01:29	850.7729014267204
6/25/2025	290.97266914833756	1141.641132	4:50:58	19:01:38	850.6684632287823
6/26/2025	291.261547	1141.7837721726933	4:51:16	19:01:47	850.5222251733132
6/27/2025	291.5694830069216	1141.9037983116111	4:51:34	19:01:54	850.3343153046895
6/28/2025	291.8960318944932	1142.0009264303385	4:51:54	19:02:00	850.1048945358452
6/29/2025	292.2407344161405	1142.0748906229496	4:52:14	19:02:04	849.8341562068091
6/30/2025	292.6031180839388	1142.125443639146	4:52:36	19:02:08	849.5223255552071
7/1/2025	292.9826979349792	1142.1523570365398	4:52:59	19:02:09	849.1696591015606
7/2/2025	293.3789773356292	1142.1554212882963	4:53:23	19:02:09	848.7764439526671
7/3/2025	293.79144882067925	1142.1344458474164	4:53:47	19:02:08	848.3429970267371
7/4/2025	294.21959496479667	1142.0892591691522	4:54:13	19:02:05	847.8696642043556
7/5/2025	294.66288928354874	1142.0197086932149	4:54:40	19:02:01	847.3568194096661
7/6/2025	295.12079716110765	1141.925660787591	4:55:07	19:01:56	846.8048636264832
7/7/2025	295.5927768016253	1141.8070006559337	4:55:36	19:01:48	846.2142238543084
7/8/2025	296.0782802011603	1141.6636322106003	4:56:05	19:01:40	845.585352
7/9/2025	296.57675413695597	1141.4954779135253	4:56:35	19:01:30	844.9187237765693
7/10/2025	297.08764117080295	1141.302478587183	4:57:05	19:01:18	844.2148374163801
7/11/2025	297.6103806631826	1141.0845931979661	4:57:37	19:01:05	843.4742125347835
7/12/2025	298.14440979486255	1140.841798614338	4:58:09	19:00:51	842.6973888194753
7/13/2025	298.6891645926189	1140.574089342143	4:58:41	19:00:34	841.8849247495241
7/14/2025	299.2440809557791	1140.2814772394615	4:59:15	19:00:17	841.0373962836825
7/15/2025	299.8085956803176	1139.9639912133716	4:59:49	18:59:58	840.1553955
7/16/2025	300.38214747729637	1139.621676900962	5:00:23	18:59:37	839.2395294236657
7/17/2025	300.9641779825141	1139.2545963368711	5:00:58	18:59:15	838.2904184
7/18/2025	301.5541327543224	1138.8628276095874	5:01:33	18:58:52	837.3086949
7/19/2025	302.1514622566649	1138.4464645086425	5:02:09	18:58:27	836.2950022519776
7/20/2025	302.75562282452364	1138.0056161647612	5:02:45	18:58:00	835.2499933402376
7/21/2025	303.3660776090759	1137.5404066849214	5:03:22	18:57:32	834.1743290758455
7/22/2025	303.9822975000114	1137.0509747841647	5:03:59	18:57:03	833.0686772841534
7/23/2025	304.60376202260386	1136.5374734158952	5:04:36	18:56:32	831.9337113932913
7/24/2025	305.22996020728874	1136.0000694022633	5:05:14	18:56:00	830.7701091949746
7/25/2025	305.8603914	1135.4389430661176	5:05:52	18:55:26	829.5785516364617
7/26/2025	306.4945662189341	1134.854287865869	5:06:30	18:54:51	828.3597216
7/27/2025	307.13200703320786	1134.246310034484	5:07:08	18:54:15	827.1143030012761
7/28/2025	307.7722489997791	1133.6152282236774	5:07:46	18:53:37	825.8429792238983
7/29/2025	308.41484061925064	1132.961273154267	5:08:25	18:52:58	824.5464325350164
7/30/2025	309.0593444	1132.2846872734895	5:09:04	18:52:17	823.2253428414105
7/31/2025	309.7053376465076	1131.5857244199738	5:09:42	18:51:35	821.8803867734662
8/1/2025	310.3524127269509	1130.8646494969294	5:10:21	18:50:52	820.5122367699785
8/2/2025	311.0001779420642	1130.121738153995	5:11:00	18:50:07	819.1215602119307
8/3/2025	311.6482578718793	1129.3572764780674	5:11:39	18:49:21	817.7090186061881
8/4/2025	312.2962938735369	1128.5715606933345	5:12:18	18:48:34	816.2752668197976
8/5/2025	312.9439445052893	1127.7648968706176	5:12:57	18:47:46	814.8209523653283
8/6/2025	313.59088590857834	1126.9376006460523	5:13:35	18:46:56	813.3467147374739
8/7/2025	314.2368121481227	1126.089996949027	5:14:14	18:46:05	811.8531848009043
8/8/2025	314.8814355100697	1125.2224197392316	5:14:53	18:45:13	810.3409842291619
8/9/2025	315.5244867583775	1124.335212	5:15:31	18:44:20	808.8107249942126
8/10/2025	316.16571534970143	1123.4287242557843	5:16:10	18:43:26	807.2630089060829
8/11/2025	316.80488960715456	1122.5033168090176	5:16:48	18:42:30	805.6984272018631
8/12/2025	317.4417968534021	1121.5593570366184	5:17:27	18:41:34	804.1175601832163
8/13/2025	318.0762435036322	1120.5972204050345	5:18:05	18:40:36	802.5209769014023
8/14/2025	318.7080551190243	1119.6172900077445	5:18:42	18:39:37	800.9092348887202
8/15/2025	319.3370764213969	1118.6199563565647	5:19:20	18:38:37	799.2828799351678
8/16/2025	319.9631712697855	1117.605617	5:19:58	18:37:36	797.6424459090445
8/17/2025	320.58622259975124	1116.5746772198888	5:20:35	18:36:34	795.9884546201376
8/18/2025	321.2061323262692	1115.527548050363	5:21:12	18:35:32	794.3214157240939
8/19/2025	321.82282121108904	1114.4646478776012	5:21:49	18:34:28	792.6418266665122
8/20/2025	322.43622869549597	1113.3864013607676	5:22:26	18:33:23	790.9501726652717
8/21/2025	323.0463126994296	1112.2932394290124	5:23:03	18:32:18	789.2469267295828
8/22/2025	323.65304938794407	1111.185599102172	5:23:39	18:31:11	787.5325497
8/23/2025	324.25643290601784	1110.063923313477	5:24:15	18:30:04	785.8074904074592
8/24/2025	324.8564750827318	1108.9286607337513	5:24:51	18:28:56	784.0721856510195
8/25/2025	325.4532051058501	1107.780265596613	5:25:27	18:27:47	782.3270604907628
8/26/2025	326.0466691678507	1106.6191975242182	5:26:03	18:26:37	780.5725283563675
8/27/2025	326.6369300844493	1105.4459213531038	5:26:38	18:25:27	778.8089912686545
8/28/2025	327.2240668866739	1104.2609069597315	5:27:13	18:24:16	777.0368400730576
8/29/2025	327.80817438753724	1103.0646290853495	5:27:48	18:23:04	775.2564546978122
8/30/2025	328.3893627243605	1101.8575671598396	5:28:23	18:21:51	773.4682044
8/31/2025	328.96775687779063	1100.6402051242376	5:28:58	18:20:38	771.6724482
9/1/2025	329.5434961685529	1099.4130312516572	5:29:33	18:19:25	769.8695350831043
9/2/2025	330.1167337	1098.1765379663868	5:30:07	18:18:11	768.0598042334198
9/3/2025	330.68763597825415	1096.9312216609562	5:30:41	18:16:56	766.2435856827021
9/4/2025	331.25638201864194	1095.6775825110144	5:31:15	18:15:41	764.4212004923725
9/5/2025	331.82316309327416	1094.4161242878934	5:31:49	18:14:25	762.5929611946192
9/6/2025	332.3881819669118	1093.1473541687687	5:32:23	18:13:09	760.7591722018569
9/7/2025	332.95165231440694	1091.8717825443632	5:32:57	18:11:52	758.9201302299563
9/8/2025	333.5137980899134	1090.589922824177	5:33:31	18:10:35	757.0761247342635
9/9/2025	334.0748528817905	1089.3022912392523	5:34:04	18:09:18	755.2274383574618
9/10/2025	334.63505925413926	1088.0094066425308	5:34:38	18:08:01	753.3743473883916
9/11/2025	335.1946681	1086.7117903068702	5:35:12	18:06:43	751.5171222309672
9/12/2025	335.75393783844925	1085.4099657208362	5:35:45	18:05:25	749.6560279
9/13/2025	336.31313396253825	1084.1044583824018	5:36:19	18:04:06	747.7913244198636
9/14/2025	336.87252809557754	1082.7957955907186	5:36:52	18:02:48	745.9232674951411
9/15/2025	337.43239740004026	1081.4845062361442	5:37:26	18:01:29	744.0521088361039
9/16/2025	337.9930238339323	1080.1711205887377	5:38:00	18:00:10	742.1780967548054
9/17/2025	338.5546934241654	1078.8561700854507	5:38:33	17:58:51	740.3014766612853
9/18/2025	339.11769553370107	1077.5401871162642	5:39:07	17:57:32	738.4224915825631
9/19/2025	339.6823221233133	1076.2237048095353	5:39:41	17:56:13	736.5413827
9/20/2025	340.2488670088145	1074.9072568168303	5:40:15	17:54:54	734.6583898080158
9/21/2025	340.81762511458624	1073.5913770975371	5:40:49	17:53:35	732.7737519829509
9/22/2025	341.3888917242474	1072.2765997035553	5:41:23	17:52:17	730.887708
9/23/2025	341.9629617292937	1070.9634585643673	5:41:58	17:50:58	729.0004968350736
9/24/2025	342.5401288765371	1069.652487272806	5:42:32	17:49:39	727.1123583962689
9/25/2025	343.1206850151748	1068.3442188718257	5:43:07	17:48:21	725.2235338566509
9/26/2025	343.7049193443178	1067.0391856425933	5:43:42	17:47:02	723.3342662982756
9/27/2025	344.29311766180996	1065.7379188942011	5:44:18	17:45:44	721.4448012323912
9/28/2025	344.88556161516976	1064.4409487553082	5:44:53	17:44:26	719.5553871401385
9/29/2025	345.4825279554981	1063.1488039680012	5:45:29	17:43:09	717.6662760125031
9/30/2025	346.08428779518977	1061.8620116841576	5:46:05	17:41:52	715.7777238889678
10/1/2025	346.69110587030445	1060.5810972645745	5:46:41	17:40:35	713.8899914
10/2/2025	347.30323980845617	1059.3065840811228	5:47:18	17:39:18	712.0033442726666
10/3/2025	347.92093940308615	1058.038993322145	5:47:55	17:38:02	710.1180539190589
10/4/2025	348.54444589500514	1056.778844	5:48:33	17:36:47	708.2343979063148
10/5/2025	349.1739913	1055.5266517701675	5:49:10	17:35:32	706.3526605080756
10/6/2025	349.8097975180598	1054.2829307343545	5:49:49	17:34:17	704.4731332162947
10/7/2025	350.4520760212072	1053.048191273932	5:50:27	17:33:03	702.5961152527248
10/8/2025	351.10102679409505	1052.8229408675893	5:51:06	17:31:49	700.7219140734942
10/9/2025	351.75683785510165	1051.6076837209962	5:51:45	17:30:36	698.8508458658946
10/10/2025	352.4196846	1050.402920599245	5:52:25	17:29:24	696.9832360364129
10/11/2025	353.0897289743748	1049.2091486633794	5:53:05	17:28:13	695.1194196890046
10/12/2025	353.7671192184199	1048.026861310955	5:53:46	17:27:02	693.2597421
10/13/2025	354.45198888427444	1046.856548	5:54:27	17:25:51	691.4045591362456
10/14/2025	355.14445642783414	1045.698694199879	5:55:09	17:24:42	689.5542377720448
10/15/2025	355.8446245955904	1044.5537810379333	5:55:51	17:23:33	687.7091564423429
10/16/2025	356.55257986777985	1043.4222853598676	5:56:33	17:22:25	685.8697054920877
10/17/2025	357.26839192180046	1042.3046794853767	5:57:16	17:21:18	684.0362875635763
10/18/2025	357.99211311704585	1041.2014310896006	5:58:00	17:20:12	682.2093179725548
10/19/2025	358.72377800233244	1040.113003066364	5:58:43	17:19:07	680.3892250640315
10/20/2025	359.46340284711255	1039.0398533932844	5:59:28	17:18:02	678.5764505461718
10/21/2025	360.2109851976907	1037.9824349982416	6:00:13	17:16:59	676.7714498
10/22/2025	360.96650345968175	1036.9411956266692	6:00:58	17:15:56	674.9746921669876
10/23/2025	361.7299165079601	1035.916577709067	6:01:44	17:14:55	673.1866612
10/24/2025	362.5011633253778	1034.909018228087	6:02:30	17:13:55	671.4078549027092
10/25/2025	363.28016267152657	1033.9189485845047	6:03:17	17:12:55	669.6387859129782
10/26/2025	364.0668128	1032.9467944613348	6:04:04	17:11:57	667.8799816784867
10/27/2025	364.86099110538396	1031.9929756853126	6:04:52	17:11:00	666.1319845799286
10/28/2025	365.6625540614767	1031.057906084929	6:05:40	17:10:03	664.3953520234523
10/29/2025	366.47133685172014	1030.1419933441628	6:06:28	17:09:09	662.6706564924426
10/30/2025	367.28715329345414	1029.2456388510345	6:07:17	17:08:15	660.9584855575804
10/31/2025	368.1097956970885	1028.369237540077	6:08:07	17:07:22	659.2594418429885
11/1/2025	368.93903478151697	1027.5131777277975	6:08:56	17:06:31	657.5741429462805
11/2/2025	369.7746196298583	1026.677840940204	6:09:46	17:05:41	655.9032213103458
11/3/2025	370.6162776867281	1025.8636017314516	6:10:37	17:04:52	654.2473240447234
11/4/2025	371.4637147982025	1025.0708274926794	6:11:28	17:04:04	652.6071126944769
11/5/2025	372.31661529558346	1024.299878250113	6:12:19	17:03:18	650.9832629545296
11/6/2025	373.1746421240151	1023.5511064515339	6:13:10	17:02:33	649.3764643275188
11/7/2025	374.03743701693145	1022.8248567402452	6:14:02	17:01:49	647.7874197233137
11/8/2025	374.90462071723465	1022.1214657157072	6:14:54	17:01:07	646.2168449984727
11/9/2025	375.7757932460098	1021.441261680065	6:15:47	17:00:26	644.6654684340552
11/10/2025	376.6505342194828	1020.7845643698581	6:16:39	16:59:47	643.1340301503753
11/11/2025	377.52840321480954	1020.151684672273	6:17:32	16:59:09	641.6232814574635
11/12/2025	378.4089401851609	1019.5429243253918	6:18:25	16:58:33	640.1339841
11/13/2025	379.2916659244288	1018.9585756019837	6:19:17	16:57:58	638.6669096775549
11/14/2025	380.17608258172834	1018.3989209764997	6:20:11	16:57:24	637.2228383947713
11/15/2025	381.06167422570775	1017.864232775057	6:21:04	16:56:52	635.8025585493492
11/16/2025	381.94790745850725	1017.3547728083313	6:21:57	16:56:21	634.4068653498241
11/17/2025	382.83423207901666	1016.8707919874219	6:22:50	16:55:52	633.0365599084053
11/18/2025	383.7200817948929	1016.412529922917	6:23:43	16:55:25	631.6924481280241
11/19/2025	384.6048749825858	1016.9802145075498	6:24:36	16:54:59	630.3753395
11/20/2025	385.4880154944101	1015.5740614830173	6:25:29	16:54:34	629.0860459886072
11/21/2025	386.36889351147533	1015.1942739917192	6:26:22	16:54:12	627.8253804802439
11/22/2025	387.24688644105595	1014.8410421143695	6:27:15	16:53:50	626.5941556733136
11/23/2025	388.12135985674735	1014.5145423946319	6:28:07	16:53:31	625.3931825378845
11/24/2025	388.9916684795172	1014.2149373521365	6:29:00	16:53:13	624.2232688726193
11/25/2025	389.85715719751147	1013.9423749854417	6:29:51	16:52:57	623.0852177879302
11/26/2025	390.71716212224317	1013.6969882667138	6:30:43	16:52:42	621.9798261444706
11/27/2025	391.5710116785415	1013.478894630105	6:31:34	16:52:29	620.9078829515635
11/28/2025	392.41802772540956	1013.2881954560131	6:32:25	16:52:17	619.8701677306035
11/29/2025	393.2575267	1013.1249755536061	6:33:15	16:52:07	618.8674488489011
11/30/2025	394.0888208143386	1012.9893026441831	6:34:05	16:51:59	617.9004818298445
12/1/2025	394.9112192024751	1012.8812268481274	6:34:55	16:51:53	616.9700076456523
12/2/2025	395.7240291790238	1012.8007801783693	6:35:43	16:51:48	616.0767509993456
12/3/2025	396.52655744052953	1012.7479760434326	6:36:32	16:51:45	615.2214186
12/4/2025	397.31811130440747	1012.7228087632714	6:37:19	16:51:43	614.4046974588639
12/5/2025	398.09799994833224	1012.7252531012158	6:38:06	16:51:44	613.6272531528836
12/6/2025	398.8655356504695	1012.7552638154423	6:38:52	16:51:45	612.8897281649728
12/7/2025	399.6200350261503	1012.8127752334436	6:39:37	16:51:49	612.1927402072934
12/8/2025	400.36082025652337	1012.897700853022	6:40:22	16:51:54	611.5368805964986
12/9/2025	401.0872203046879	1013.009932973335	6:41:05	16:52:01	610.9227126686471
12/10/2025	401.79857211480294	1013.1493423595118	6:41:48	16:52:09	610.3507702447089
12/11/2025	402.49422178970127	1013.3157779443076	6:42:30	16:52:19	609.8215561546062
12/12/2025	403.1735257	1013.5090665701827	6:43:10	16:52:31	609.3355408275897
12/13/2025	403.8358518185398	1013.7290127750875	6:43:50	16:52:44	608.8931609565477
12/14/2025	404.48058038150816	1013.9753986250856	6:44:29	16:52:59	608.4948182435775
12/15/2025	405.1071053629677	1014.2479835967792	6:45:06	16:53:15	608.1408782338116
12/16/2025	405.71483526819384	1014.5465045122894	6:45:43	16:53:33	607.8316692440956
12/17/2025	406.30319413665586	1014.8706755293151	6:46:18	16:53:52	607.5674813926593
12/18/2025	406.8716224531247	1015.2201881885297	6:46:52	16:54:13	607.3485657
12/19/2025	407.4195780064099	1015.594711520284	6:47:25	16:54:36	607.1751335138741
12/20/2025	407.94653669294496	1015.9938922122752	6:47:57	16:55:00	607.0473555193303
12/21/2025	408.4519932627612	1016.4173548395091	6:48:27	16:55:25	606.9653615767479
12/22/2025	408.9354620057383	1016.8647021575256	6:48:56	16:55:52	606.9292401517873
12/23/2025	409.3964773763808	1017.3355154595017	6:49:24	16:56:20	606.9390381
12/24/2025	409.83459455574325	1017.8293549974609	6:49:50	16:56:50	606.9947604417176
12/25/2025	410.2493899495093	1018.3457604674402	6:50:15	16:57:21	607.0963705179308
12/26/2025	410.64046162161713	1018.8842515580747	6:50:38	16:57:53	607.2437899364575
12/27/2025	411.00742966321275	1019.4443285616727	6:51:00	16:58:27	607.4368989
12/28/2025	411.3499364970982	1020.0254730464766	6:51:21	16:59:02	607.6755365493784
12/29/2025	411.66764711822043	1020.6271485884197	6:51:40	16:59:38	607.9595014701993
12/30/2025	411.96024927111387	1021.2488015603366	6:51:58	17:00:15	608.2885522892227
12/31/2025	412.2274535655694	1021.8898619762297	6:52:14	17:00:53	608.6624084106602
1/1/2026	412.4689935	1022.549744387868	6:52:28	17:01:33	609.0807509
1/2/2026	412.6846256193535	1023.2278488306844	6:52:41	17:02:14	609.5432232113309
1/3/2026	412.87412913501663	1023.9235618156581	6:52:52	17:02:55	610.0494326806415
1/4/2026	413.03730613381765	1024.636257	6:53:02	17:03:38	610.5989512297923
1/5/2026	413.1739812542307	1025.3652980781076	6:53:10	17:04:22	611.1913168238768
1/6/2026	413.28400150749695	1026.110036252991	6:53:17	17:05:07	611.8260347454941
1/7/2026	413.36723602185236	1026.869815010347	6:53:22	17:05:52	612.5025789884947
1/8/2026	413.42357574526534	1027.643969464651	6:53:25	17:06:39	613.2203937193857
1/9/2026	413.4529331	1028.4318279086704	6:53:27	17:07:26	613.9788947986003
1/10/2026	413.4552416629638	1029.2327130166768	6:53:27	17:08:14	614.7774714
1/11/2026	413.4304556639001	1030.0459430604733	6:53:26	17:09:03	615.6154873965731
1/12/2026	413.37854965741946	1030.8708331337398	6:53:23	17:09:52	616.4922834763204
1/13/2026	413.29951801996515	1031.7066963802313	6:53:18	17:10:42	617.4071783602661
1/14/2026	413.1933744866894	1032.5528452214205	6:53:12	17:11:33	618.3594707347311
1/15/2026	413.06015166119533	1033.4085925792733	6:53:04	17:12:25	619.3484409
1/16/2026	412.8999005115743	1034.273253089935	6:52:54	17:13:16	620.3733525783607
1/17/2026	412.71268985598675	1035.146144	6:52:43	17:14:09	621.4334544482831
1/18/2026	412.4986058409069	1036.0265878713365	6:52:30	17:15:02	622.5279820304295
1/19/2026	412.2577514149988	1036.913910701061	6:52:15	17:15:55	623.6561592860622
1/20/2026	411.99024580143316	1037.807446102572	6:51:59	17:16:48	624.8172003011388
1/21/2026	411.6962239712711	1038.706534894862	6:51:42	17:17:42	626.0103109235909
1/22/2026	411.37583612035326	1039.6105264866628	6:51:23	17:18:37	627.2346903663096
1/23/2026	411.0292471519404	1040.5187799226542	6:51:02	17:19:31	628.4895327707138
1/24/2026	410.6566362	1041.4306648933532	6:50:39	17:20:26	629.7740287262142
1/25/2026	410.25819596495097	1042.3455627062863	6:50:15	17:21:21	631.0873667413352
1/26/2026	409.8341325535642	1043.2628672162732	6:49:50	17:22:16	632.4287346627091
1/27/2026	409.3846647	1044.1819857129049	6:49:23	17:23:11	633.7973210385989
1/28/2026	408.91002333946506	1045.1023397635395	6:48:55	17:24:06	635.1923164240744
1/29/2026	408.41045138499356	1046.023366010367	6:48:25	17:25:01	636.6129146253734
1/30/2026	407.88620303890207	1046.9445169203414	6:47:53	17:25:57	638.0583138814393
1/31/2026	407.3375435059714	1047.865261486991	6:47:20	17:26:52	639.5277179810196
2/1/2026	406.7647485692269	1048.7850858833417	6:46:46	17:27:47	641.0203373141148
2/2/2026	406.1681042084495	1049.7034940653984	6:46:10	17:28:42	642.5353899
2/3/2026	405.54790623583557	1050.6200083258204	6:45:33	17:29:37	644.0721020899848
2/4/2026	404.9044599487727	1051.534169797626	6:44:54	17:30:32	645.6297098488533
2/5/2026	404.23807979955484	1052.4455389079249	6:44:14	17:31:27	647.2074591
2/6/2026	403.54908908174025	1053.3536957818574	6:43:33	17:32:21	648.8046067001171
2/7/2026	402.8378196327343	1054.258240597054	6:42:50	17:33:15	650.4204209643198
2/8/2026	402.1046115520877	1055.1587938890916	6:42:06	17:34:10	652.0541823370039
2/9/2026	401.3498129348987	1056.0549968085293	6:41:21	17:35:03	653.7051838736306
2/10/2026	400.57377961964187	1056.9465113302435	6:40:34	17:35:57	655.3727317106017
2/11/2026	399.7768749496698	1057.8330204158729	6:39:47	17:36:50	657.0561454662031
2/12/2026	398.9594695475881	1058.7142281302838	6:38:58	17:37:43	658.7547585826957
2/13/2026	398.12194110165376	1059.5898597130545	6:38:07	17:38:35	660.4679186114007
2/14/2026	397.26467416331576	1060.4596616060335	6:37:16	17:39:28	662.1949874427178
2/15/2026	396.3880599549964	1061.3234014381123	6:36:23	17:40:19	663.9353415
2/16/2026	395.49249618718994	1062.1808679683784	6:35:30	17:41:11	665.6883717811884
2/17/2026	394.5783869	1063.0318709888838	6:34:35	17:42:02	667.4534841049239
2/18/2026	393.6461422159075	1063.876241188282	6:33:39	17:42:53	669.2300989723744
2/19/2026	392.69617833970403	1064.713829977622	6:32:42	17:43:43	671.0176516
2/20/2026	391.7289172432887	1065.544509279604	6:31:44	17:44:33	672.8155920363153
2/21/2026	390.7447865958602	1066.3681712826196	6:30:45	17:45:22	674.6233846867594
2/22/2026	389.7442196018176	1067.1847281609037	6:29:45	17:46:11	676.4405085590861
2/23/2026	388.7276548578362	1067.9941117621283	6:28:44	17:47:00	678.2664569042921
2/24/2026	387.69553621230654	1068.7962732637698	6:27:42	17:47:48	680.1007370514633
2/25/2026	386.64831262639757	1069.5911827995649	6:26:39	17:48:35	681.9428701731673
2/26/2026	385.5864380360561	1070.3788290573787	6:25:35	17:49:23	683.7923910213226
2/27/2026	384.5103712142947	1071.1592188497707	6:24:31	17:50:10	685.6488476354759
2/28/2026	383.4205756331702	1071.9323766585533	6:23:25	17:50:56	687.5118010253831
3/1/2026	382.3175193249036	1072.6983441545967	6:22:19	17:51:42	689.3808248296931
3/2/2026	381.20167474164344	1073.4571796941364	6:21:12	17:52:27	691.2555049524929
3/3/2026	380.0735186134226	1074.208957792798	6:20:04	17:53:13	693.1354391793753
3/4/2026	378.9335318039108	1074.953768578543	6:18:56	17:53:57	695.0202367746323
3/5/2026	377.78219916361576	1075.6917172247183	6:17:47	17:54:42	696.9095180611025
3/6/2026	376.6200093802348	1076.4229233643568	6:16:37	17:55:25	698.802914
3/7/2026	375.4474548	1077.1475204868666	6:15:27	17:56:09	700.7000656609596
3/8/2026	374.2650314011652	1077.865655318214	6:14:16	17:56:52	702.6006239170489
3/9/2026	373.0732383754331	1078.577487185685	6:13:04	17:57:35	704.5042488102519
3/10/2026	371.87257822395526	1079.2831873682887	6:11:52	17:58:17	706.4106091443334
3/11/2026	370.66355646109366	1079.9829384338432	6:10:40	17:58:59	708.3193819727495
3/12/2026	369.4466815	1080.6769335637623	6:09:27	17:59:41	710.2302520937993
3/13/2026	368.22246432841484	1081.365375866545	6:08:13	18:00:22	712.1429115381302
3/14/2026	366.99141863142154	1082.0484776809465	6:06:59	18:01:03	714.0570590495249
3/15/2026	365.7540603099377	1082.7264598697939	6:05:45	18:01:44	715.9723995598562
3/16/2026	364.5109074463528	1083.399551105397	6:04:31	18:02:24	717.8886436590442
3/17/2026	363.26248008667943	1084.0679871474827	6:03:16	18:03:04	719.8055070608032
3/18/2026	362.00930004963897	1084.7320101145697	6:02:01	18:03:44	721.7227100649307
3/19/2026	360.7518907328422	1085.3918677496972	6:00:45	18:04:24	723.639977
3/20/2026	359.49077691626866	1086.0478126813923	5:59:29	18:05:03	725.5570357651236

表格说明：

• date: 日期 (月/日/年格式)
• sunrise_minutes: 日出时间（以分钟计，从0:00开始）
• sunset_minutes: 日落时间（以分钟计，从0:00开始）
• sunrise: 日出时间 (HH:MM:SS格式)
• sunset: 日落时间 (HH:MM:SS格式)
• daylength_minutes: 白昼长度（分钟）