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Sunrise equation
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Sunrise equation : ウィキペディア英語版
Sunrise equation

The sunrise equation as follows can be used to derive the time of sunrise and sunset for any solar declination and latitude in terms of local solar time when sunrise and sunset actually occur:
:\cos \omega_\circ = -\tan \phi \times \tan \delta
where:

:\omega_\circ is the hour angle at either sunrise (when ''negative'' value is taken) or sunset (when ''positive'' value is taken);
:\phi is the latitude of the observer on the Earth;
:\delta is the sun declination.
== Theory of the equation ==
The Earth rotates at an angular velocity of 15°/hour, therefore the expression \omega_\circ \times \frac^\circ} gives the interval of time before and after local solar noon that sunrise or sunset will occur.
The sign convention is typically that the observer latitude \phi is 0 at the Equator, positive for the Northern Hemisphere and negative for the Southern Hemisphere, and the solar declination \delta is 0 at the vernal and autumnal equinoxes when the sun is exactly above the Equator, positive during the Northern Hemisphere summer and negative during the Northern Hemisphere winter.
The expression above is always applicable for latitudes between the Arctic Circle and Antarctic Circle. North of the Arctic Circle or south of the Antarctic Circle, there is at least one day of the year with no sunrise or sunset. Formally, there is a sunrise or sunset when -90^\circ+\delta < \phi < 90^\circ - \delta during the Northern Hemisphere summer, and when -90^\circ - \delta < \phi < 90^\circ + \delta during the Northern Hemisphere winter. Out of these latitudes, it is either 24-hour daytime or 24-hour nighttime.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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