Finding every light threshold by numerical search
The poster starts from the same low-precision solar theory used for the star maps — the Meeus VSOP-style series that returns the Sun's apparent right ascension, declination and ecliptic longitude for any Julian Day. For your chosen date and latitude, the tool walks the local day in two-minute steps, from one local midnight to the next. At every step it combines the Sun's position with the Earth's rotation angle to form the local hour angle, then converts equatorial coordinates into the Sun's altitude above the horizon. Rather than solving a single sunrise formula, it watches for the moments the altitude crosses four meaningful thresholds: minus six degrees, where deep night ends and the blue hour begins; minus four degrees, where the first warm golden light appears; minus zero point eight three three degrees, the official sunrise and sunset altitude that includes atmospheric refraction and the Sun's finite disk; and plus six degrees, where the warm directional light gives way to ordinary daylight.
Each crossing is refined by linear interpolation between the two surrounding samples, so the printed times are accurate to a fraction of a minute. Solar noon is found independently as the highest altitude of the day, which is the meridian transit. The four bands are then simple: night below minus six degrees, blue hour between minus six and minus four on both sides of darkness, golden hour between minus four degrees and plus six degrees around sunrise and sunset, and plain white daylight whenever the Sun climbs above six degrees. In polar latitudes a threshold may never be crossed on a given date; the calculator detects that and renders an all-day or all-night ring instead of inventing a time.
The 24-hour arc poster and your time zone
The canvas turns those numbers into a ring covering a full day: noon at the top, midnight at the bottom, sunrise on the left limb and sunset on the right. Every minute of the ring is colored by its light band — deep navy for night, cool blue for the blue hour, warm gold for the golden hour and bright cream for daylight — and each event is marked with a dot, a short tick and its time. The center carries the city name, the date and solar noon, while a legend explains the four colors. All clock times are expressed in your browser's local time zone, which is named explicitly both in the settings panel and on the poster itself; if your browser zone differs from the city's zone, apply the displayed UTC offset mentally, or type the city's custom coordinates and set your device to the destination zone. Download redraws the whole timeline at 300 DPI, privately and without a watermark.
用数值搜索找出每一个光线分界时刻
这张海报的计算基础与星空地图相同：采用 Meeus 的 VSOP 风格低精度太阳级数，对任意儒略日返回太阳的视赤经、赤纬与视黄经。针对你选定的日期与纬度，工具以两分钟为步长，从当地午夜走到次日午夜，遍历一整天。每一步都把太阳位置与地球自转角合成为地方时角，再把赤道坐标换算为太阳的地平高度角。它不依赖单一的日出公式，而是监测高度角穿越四个关键阈值的瞬间：负六度，黑夜结束、蓝调时刻开始；负四度，第一道温暖金光出现；负零点八三三度，即包含大气折射与太阳视圆面的官方日出日落高度；以及正六度，温暖的方向性光线让位于普通白昼。
每个穿越点都会用前后两个采样做线性插值精修，因此印出的时间误差远小于一分钟。太阳正午则单独取全天高度角的最大值，即太阳上中天的时刻。四个光带随之确定：高度低于负六度为夜，蓝调时刻位于黑暗两侧的负六度到负四度之间，黄金时刻环绕日出日落、介于负四度与正六度之间，太阳高于六度即为明亮的纯白日光。在极地纬度，某些分界在特定日期可能永不出现；计算器会识别这种情况，直接绘制全天白昼或全天黑夜的色环，而不会编造一个时间。
24 小时圆环海报与你的时区
画布把这些数字变成覆盖一整天的圆环：正午在顶部、午夜在底部，日出在左侧弧、日落在右侧弧。环上每一分钟都按其光带着色——深夜蓝代表夜、冷蓝代表蓝调时刻、暖金代表黄金时刻、亮米白代表日光；每个事件都用圆点、短刻度与具体时间标出。圆心写有城市名、日期与太阳正午，下方图例解释四种颜色。所有钟表时间都按你浏览器的本地时区呈现，设置面板与海报上都会明确标注该时区名称；若你的浏览器时区与城市实际时区不同，可自行按显示的 UTC 偏移换算，或填入该城市的自定义坐标并把设备时区设为目的地时区。下载时整条时间轴会以 300 DPI 重绘，过程私密且无水印。
Why is sunrise computed at −0.833° instead of zero?
At the geometric instant the Sun's center crosses the horizon, its upper limb is already visible because atmospheric refraction lifts the disk by roughly half a degree and the Sun itself spans about half a degree. Almanacs therefore define sunrise and sunset at a center altitude of −0.833°, which is exactly the threshold this tool searches for.
为什么日出按 −0.833° 而不是零度计算？
当太阳中心几何上恰好经过地平线时，由于大气折射把日轮抬升约半度、太阳视圆面本身也约占半度，太阳上缘其实已经可见。因此天文年历把日出日落定义为太阳中心高度 −0.833°，本工具搜索的正是这个阈值。
What exactly are golden hour and blue hour here?
Golden hour is the warm, low-angle window between −4° and +6° of solar altitude around sunrise and sunset; blue hour is the cooler window between −6° and −4° when blue wavelengths dominate. The boundaries are photographic conventions, so treat the minutes as smooth transitions rather than hard switches — the gradient on the ring hints at that.
这里的黄金时刻和蓝调时刻具体指什么？
黄金时刻是日出日落前后太阳高度在负四度到正六度之间、光线温暖低斜的窗口；蓝调时刻则是负六度到负四度之间、蓝色波长主导天空的清冷窗口。这些分界是摄影惯例，时间应理解为平滑过渡而非硬切换——环上的渐变色也在暗示这一点。
Which time zone are the listed times in?
Always the local time zone reported by your own browser and operating system; the panel and poster print its name and UTC offset so there is no ambiguity. For a city in another zone, set your device to that zone temporarily or enter custom coordinates, and interpret the ring against the zone shown.
列表里的时间是哪个时区的？
始终是你自己浏览器与操作系统报告的本地时区；面板与海报都会印出时区名称和 UTC 偏移，避免歧义。若要计算另一时区城市的时刻，可临时把设备时区切换到该时区，或填入自定义坐标后按所显示的时区解读圆环。
