Sunrise and sunset are daily occurrences that can be enjoyed forever. Taking it for granted, you are rarely interested in what algorithm the celestial body moves, what affects the trajectory, why unusual things happen: polar days and nights, northern lights or an eclipse.

## The occurrence of sunset and sunrise of the heavenly body

The earth is in constant motion both around the sun and around its own axis. Once a day, with the exception of the polar latitudes, one can observe how the fireball disappears beyond the horizon and reappears there a day later, but from the other side. Sunrise and sunset is the time when the "burning" disk of the celestial body disappears from the field of view, and the highest point is completely hidden or appears (at the moment of dawn).

There is a concept of "borders of day and night". This parameter significantly affects the zenith. The latter means a line directed from a point to the surface of the earth perpendicular to it. The zenith angle is the distance between the direction of the beam to the center of the earth and the vertical. Depending on thethe size of the angle can tell if the sun has fully risen. The same determines the end of dusk and the beginning of night.

In astronomy there is a concept of twilight:

1. For high latitudes in winter and summer, the sun may not set or rise. Twilight is considered zero.
2. The duration of the day in such latitudes will be indicated by either 24 hours or 00 hours.
3. Twilight lasts from 15-25 minutes in different parts of the world.

The conclusion follows: twilight has a beginning and an end. Their duration depends on the position of the sun at sunset. If the earth had no atmosphere and the sun were a point, the zenith angle would be 90 degrees. Since the sun has no angular diameter, light is reflected by solid particles. Therefore, the upper edge of the disk depends on the movement of the center of the star. In a normal atmosphere, a 90 degree angle is converted into a straight line in 50 minutes. Accordingly, if the sunset would begin with a decrease in the right angle, twilight would last longer.

As soon as the sun has disappeared behind the horizon, the second stage of twilight begins - the civilian view. The zenith angle is less than 96 degrees to the opposite side of the hemisphere. Further, the angle increases to 102 degrees. This is navigational twilight. It is still light, the horizon line is visible on the water. Then comes astronomical twilight: the angle is 108 degrees, and the visibility of objects becomes weak.

Important! Such calculation algorithms are not suitable for those cities where the time does not change between summer and winter. Also, the result will not be correct, for example, for New Zealand.Summer time is valid from May to September. Therefore, the time of sunrise and sunset is different everywhere.

## Why does the sun turn red?

Sunrise and sunset create an optical effect. The rays of the sun illuminate the earth's surface, painting the sky in different colors. At dawn, we see more delicate shades of red, yellow. At sunset, red and burgundy colors predominate.

The fact is that in the evening the surface of the earth warms up, the humidity decreases, and the speed of air flows increases. Color difference varies by location:

1. Sunset will be less intense on flat terrain.
2. Along the coastal horizon - brighter.
3. And in the northern latitudes - more colorful, but not so bright.

The disk of the sun is far from the horizon. Rays are reflected from the surface. In the western part of the horizon, the colors are not so bright. They are orange, red or yellow.

The closer to the horizon, the more red we see. On both sides of it runs a golden edge. There is a radiance above the dawn. On the other side of the earth, a bluish tint appears in the sky. This is the shadow of the earth. Above it, a segment of the sky is painted in ashy color - the Belt of Venus. Occurs above the horizon at 10 to 20°.

Interesting! The red rays of the sun are the longest, they are noticeable even at sunset. The yellow and white rays are the shortest, so they are not visible when the sun sets below the horizon.

## How does the phase of the moon affect?

The moon does not always appearas a full disk. At first it looks like a crescent, then it begins to increase. When it becomes full again, it decreases. This process affects several phases, forming a cycle of 29.5 days:

1. First phase - the area of ​​the illuminated disk is less than half of the total disk of the moon.
2. Second phase - the end of the new moon and the transition to the full moon.
3. The third phase is characterized by the appearance of a full disk.
4. The fourth phase is the final stage of the full moon, turning into a new moon.

Sunrise and moonrise are linked. The surface of the satellite reflects sunlight, showing the amplitude of movement around the Earth.

## Calculation of sunrise and sunset

To calculate when the sun rises and sets, astronomers use a formula taking into account the declination of the heavenly body. The latitude value can be found on the world map, and the height of the pole - according to the geographical latitude (one value).

For example:

cos(t)=-(0.0148 + sin(f)sin(d)) / (cos(f)cos(d)),

• where t is the hour angle,
• f - latitude,
• d - declination.

0.0148 (this is the sine of 51') is the contribution from refraction and disk size. If it were not there, the formula would be much prettier, on the right side it would be: tg(f)tg(d).

So, in the limiting case where day equals night at the solstice, obviously: t is 6 hours (90°), cos(t)=0. We get a simple equation: sin(f)sin(-23.5 °)=-0.0148, whence f=2.1° (approximately). At this latitude December 21day equals night, i.e. 12 hours.

Now the schedule of sunrise and sunset can be found by downloading a special application, referring to calendar sources. Various calculation options are also available on the Internet, simplified and expanded, and taking into account corrections, the movement of the sun and the location of a person. Sunrise and sunset are interesting phenomena, but besides this, there are many mysteries in the world, the scientific nature of which is broken by the reality of information perception.

## Why are the day lengths different?

When information about the time of sunset and sunrise appeared on the front pages of The Quiet Don, readers had questions. For example, why is the length of the day different from what is stated in the calendars?

Length of the day - the period between sunrise and sunset. But it is not always possible to calculate even the approximate time of this process. The fact is that the angle of declination of the luminary has a certain value. It affects seasonal changes in the weather, the length of the day. Sunrise and sunset determine how many hours will be day, how many - night. Nights are longer in winter, days are longer in summer.

But geographic latitude affects the length of daylight hours. The farther from the equator, the shorter the day in winter and the longer in summer.

Here is a simple example:

Moscow is approximately 55o s. sh. (northern latitude), the village of Veshenskaya - 49o s. sh., and Rostov-on-Don - 47o s. sh. The longitude of the day, depending on the latitude, changes as follows: on the same day, January 22, in Moscow, it is 8h. 01 min., in the village of Veshenskaya - 8 h. 54 min., and in Rostov-on-Don - 9 h. 10 min.

In summer, the opposite is true: while in the south of Russia at the end of June the day length is 15 hours, in St. Petersburg it reaches 18 hours, i.e. the farther north, the longer the summer day.

The longest day is on the summer solstice (around June 22) and the shortest is on the winter solstice (around December 22).

One thing can be said about calendars: they basically print the longitude of the day for a latitude of approximately 55-56o. This is the latitude of Moscow. And in the newspaper "Quiet Don" the length of the day is indicated specifically for Veshenskaya. Therefore, the numbers differ.

## Interesting facts: polar days, equinoxes, northern lights

Besides the schedule of sunrise and sunset, the inconsistency of the movement of light rays, there are many interesting facts about celestial bodies. Recently, astronomers decided to show what the Earth looks like from the moon. And this is what happened:

Earthrise is a common thing for guests of the moon's satellite. Did you know that:

1. The Spirit rover captured the sunset on Mars. He is amazingly beautiful in blue-gray shades.
2. Northern Lights are not only on Earth. On Jupiter, it will be purple.
3. Polar nights are inevitable in Murmansk. In Alaska, about a ton of large pumpkins grow during polar days.
4. The shortest polar night lasts 2 days (at the latitude of the Northern Hemisphere). The longest is at the South Pole. It lasts almost half a year.

All scientific research thatknown to mankind, does not cover even 1% of knowledge about the cosmos, planets and their behavior in the universe. What other secrets does the Earth keep, how long will the Sun shine and how much energy does our galaxy have?