Starting point

This article or the following section is not adequately provided with supporting documents ( e.g. individual evidence ). Information without sufficient evidence could be removed soon. Please help Wikipedia by researching the information and including good evidence.

The point of origin of a star is that point on the eastern horizon where it appears to rise as a result of the earth's rotation and becomes visible to the observer. The direction is usually given as an azimuth and counted from north to east (clockwise). Under constellation the sun, moon, planets, fixed stars and comets are understood, while for artificial earth satellites other conditions here.

The sinking point of a star is analogous to that point on the western horizon where it reaches the end of its apparent arc and becomes invisible to the observer. With an ideal (mathematical) horizon the point of rise and fall are symmetrical to the meridian , i.e. H. their azimuths complement each other to 360 °.

relevance

Where and when the rise of a star is or was important for several reasons:

1. Because of the possibilities of observing the celestial body and its timing
2. because of some methods of orientation , e.g. B. in seafaring
3. for the worldview of earlier peoples and some today's esotericists - for example
   • at sunrise , when it is celebrated as a mythological giver of light and joy
   • when special stars first rise, e.g. B. Sirius as a harbinger of the annual Nile flood .

calculation

The azimuth A of the rise or set can be calculated by spherical trigonometry if several dates are known:

1. the coordinates of the location , in particular its latitude B
2. the declination D of the star, d. H. its distance from the celestial equator
3. at most the height of the landscape horizon above the horizontal.

In order to determine the time of the rise, the right ascension of the star and the sidereal time at the location are also required. For the latter you need the date, the exact time and the geographical length of the location.

To demonstrate the orbit of the sun in the open air, some public observatories have developed methods of horizon astronomy that use horizon marks, obelisks, large sundials or metal arches to represent the seasonal rise and set points as well as the highest levels of the sun and other stars. Some of these processes were implemented in plants like Stonehenge thousands of years ago .

Formulas

Since when a star rises and sets its elevation angle is h = 0 , a cosine law results in the nautical triangle

cos B cos D cos t = 0 - sin B sin D , from which the hourly angle t of rise or set follows:

cos t = -tan B tan D , and from a sine theorem, the azimuth A of the rise :

sin A = cos D sin t .

Because of the ambiguity of arcsin A , the sign of the declination D has to be taken into account:
For D> 0 (star north of the equator) applies 0 <A <90 ° (1st quadrant, A between north and east) and
for D <0 ( Star south of the equator) 90 <A <180 ° (2nd quadrant, A between east and south).

The azimuth of the loss results from 360 - A .

Sun and planets

The declination of the sun can maximally reach the angle of the ecliptic inclination , currently ε = 23.43 ° , which occurs at the solstice : -ε <D <ε

For an observer at the earth's equator ( B = 0 ), the sun always rises between the azimuths
90 ° - ε <A <90 ° + ε (i.e. morning distance < ε ) and crosses the horizon vertically.

For any latitude B , the sun crosses the horizon at an angle ; the morning distance can be much larger than ε , beyond the arctic circle in summer even almost 90 ° (see midnight sun ). In the winter polar night, however , the solution of the equations is imaginary.

For the latitudes of Central Europe , the morning range can reach about 45 °, i. H. the sun rises in the northeast at the summer solstice and in the southeast at the winter solstice . Similarly, the sinking points are between northwest and southwest.

The conditions are similar for the planets , as their orbital planes deviate only slightly from the ecliptic . In contrast, the moon (current orbit inclination approx. 5½ °, therefore D to 29 °) can deviate its morning and evening distances in Central Europe by up to 10 ° from those of the sun.

Stars and Earth satellites

If a fixed star is in the celestial equator ( D = 0 ° ), it rises exactly in the east and sets in the west - just like the sun at equinox . However, the other stars are distributed over the whole sky, which is why declinations between + 90 ° (North Pole) and −90 ° (South Pole) are possible. Therefore, their rise azimuths can be between 0 ° (north point, border of the circumpolar stars ) and 180 ° (south point, invisible part of the sky). For the calculation see the formulas above.

In artificial earth satellites , the point of rise and fall depends on the orbital inclination i . For i <90 ° the satellite moves from west to east, i.e. it rises in the western half of the sky and sets in the eastern half. For orbital inclinations over 90 °, the movement runs from east to west - but still not symmetrical to the meridian. With polar orbits (close to 90 °) the movement is almost north-south or vice versa, with i ~ B it is quite asymmetrical.