世界各地の日の出・日の入り時刻 — 太陽運行計算機

天文学的太陽エフェメリス解析

大気差補正、太陽赤緯、均時差、観測地点の高度を厳密に考慮した高精度な太陽位置計算を実施。

The Science of Sunrise, Sunset & Twilight Phases

Sunrise and sunset times are dictated by spherical trigonometry, the Earth's 23.44° axial tilt, and atmospheric optics. The NOAA astronomical engine calculates exact solar zenith thresholds to model each phase of daylight and dusk:

Atmospheric Refraction & Zenith Thresholds

• Official Sunrise & Sunset (Zenith 90.8333°): The precise moment the upper limb of the Sun aligns with the true horizon. Earth's atmosphere refracts light rays upward by ~34 arcminutes, combined with the Sun's 16 arcminute semi-diameter. Thus, the center of the solar disk is actually 50 arcminutes (0.8333°) below the true horizon when sunrise appears.
• Civil Twilight (Zenith 90.8333° to 96°): The Sun is 0° to 6° below the horizon. Terrestrial objects are clearly distinguishable, streetlights remain off, and outdoor activities can proceed without artificial lighting.
• Nautical Twilight (Zenith 96° to 102°): The Sun is 6° to 12° below the horizon. At sea, the horizon remains sharp enough for mariners to take celestial sights against navigational stars.
• Astronomical Twilight (Zenith 102° to 108°): The Sun is 12° to 18° below the horizon. The faint atmospheric skyglow completely fades, opening full astronomical darkness for deep-sky observation.

Earth's Axial Tilt & Seasonal Day Length Variation

Because Earth is tilted at 23.44° relative to its orbital plane, day length varies dramatically with latitude throughout the year. At the Equator (0°), day length remains nearly constant at 12 hours year-round. Moving toward polar latitudes, summer solstices produce the Midnight Sun (24 hours of continuous sunlight), while winter solstices result in Polar Night.

To view the real-time curved terminator boundary separating day and night across the continents, explore our World Day & Night Map, or track celestial cycles on our Moon Phase Calendar.