Find the duration of astronomical and civil twilight and dawn on any day of the year and anywhere on Earth. For example

Find the duration of astronomical and civil twilight and dawn on any day of the year and anywhere on Earth. For example, what is the duration of astronomical twilight in Petrograd on January 21st?

To do this, you only need to know the declination of the Sun on a given day, the latitude of the place of observation, and remember that the moment when the Sun is 18њ below the horizon is taken as the end of astronomical twilight or the beginning of an astronomical dawn – from this moment all the stars visible to the naked eye become visible , i.e. stars up to 6th magnitude.
The beginning of the civil dawn and the end of the civil twilight is the moment when the Sun is 6њ below the horizon; then planets and stars of the 1st magnitude are made visible.
Therefore, in order to determine the duration of dawn or twilight, it is only necessary to determine the hour angle of the Sun at the time of its rising or setting and the hour angle of the Sun at the moment it is under the horizon at 18њ or 6њ. The difference between these, respectively, taken, hour angles of the Sun, found with the help of the planisphere, will give us the duration of dawn and twilight. For this case, with the help of the celestial planisphere, it is easy to find that the duration of the astronomical twilight in Petrograd on January 21 is 1 1/2 hours.

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