# Day sheet

Variation range of the day arcs of the sun in northern Central Europe (for latitude 56 ° N , around Copenhagen )

In astronomy, the part of the apparent star orbit that lies above the mathematical horizon, calculated for a certain (geographical) location and a certain date , is called the day arc , or more rarely the day arc . Ideally, its length corresponds to the period between the rise and fall of a star - but without taking into account the astronomical refraction , which is why the actual duration is a few minutes longer.

The “true day curve” also takes into account the given topographical conditions, i.e. the height of the location and the course of the landscape horizon or the depth of the keel on the sea .

As the apparent star or solar orbit in Meridian peaked and is symmetrical, is expected in astronomy usually with the half-diurnal arc , followed with T referred. The day arc depends on the geographical latitude B of the location and on the declination D of the star and can be estimated using formulas of spherical trigonometry :

${\ displaystyle \ cos T = - \ tan B \ cdot \ tan D}$

If B or D = 0, cos T = 0 and therefore T = 90 °, which corresponds to 6 hours. At the equator the day arc ( 2T ) for all stars, including the sun, is exactly 12 hours. At the poles , however, it is 24 hours or 0 hours, because rising and setting are not formally defined here.

Variation of the day arc of the sun in Central Europe (calculated for 52 ° N , around Rotterdam )

In mid-northern latitudes, the day arcs of the sun vary between 8 hours (December / January) and 16 hours (June / July), and the day length accordingly . The day arc is shortest around the winter solstice and the longest around the summer solstice . At the equinox date, the day arc has 12 hours, then the difference between the azimuth of the sunrise exactly in the east and that of the sunset in the west is exactly 180 °.

The circumpolar stars near the celestial poles ( D > 90 ° - B ) are above the horizon all year round, so their diurnal arc is 24 hours - regardless of the fact that they are outshone by the sun during the day.