If the Earth’s axis were directed perpendicular to the plane of the ecliptic, then the Sun’s altitude above the horizon at noon would be the same throughout the Earth’s globe, all year round. However, the Earth’s axis is tilted at an angle of 66°33′ to the plane of the orbit and directed toward the Pole Star. As a result, the Earth’s motion along its orbit causes constant changes in the Sun’s height above the horizon. A consequence of the tilt of the Earth’s axis to the plane of the ecliptic is also changes in the locations of sunrise and sunset. For example, in Cracow in June the Sun rises in the northeast and sets in the northwest.
In December, on the other hand, it rises in the southeast and sets in the southwest. Only on March 21 and September 23 does the Sun both in Krakow and all over the Earth (except at the poles) rise exactly in the east and set exactly in the west. The phenomenon of rising is encountered when the Sun, or any other celestial body, rises from below the horizon. After rising, the Sun increases its observed height above the horizon up to a certain maximum value, which it reaches at the moment of rising. After the top, the height of the celestial body decreases and at the moment when it reaches zero the phenomenon of sunset occurs.
After sunset, the celestial body continues to decrease its altitude until a certain minimum value, which it reaches at the time of docking. After docking, the height of the celestial body continues to increase and when it rises to zero value we have another sunrise. For an observer at the pole, the phenomenon of sunrises and sunsets in this sense does not occur. An observer located at the equator sees that virtually all celestial bodies rise and set.
For intermediate latitudes, celestial bodies can be divided into those that never rise, never set, and those that enter and set. Twilight begins when the Sun sets and lasts until the Sun’s altitude assumes a certain conventional value. Thus, it is the period after sunset during which the Earth is illuminated by sunlight scattered in the atmosphere. Astronomical twilight can be spoken of when the Sun is 18° below the horizon. Astronomical dawn also begins when the Sun’s altitude is 18° below the horizon and ends at sunrise. Over the course of the year, not only the locations of the Sun’s rising and setting change. The path of its spectral journey above the horizon also changes.
During spring and summer, this path is much longer than during autumn and winter. Twice a year on March 21 and September 23 we have the equinox. This is a time spanning one Earth day, in which the center of the solar disk is present the same amount of time below and above the horizon Night and day then last the same length of time throughout the globe o that is, 12 hours each. The sun’s rays fall on the equator at an angle of 90º. There is a sub-solar point at the equator.
Observing outer space from the Earth’s rotating axis, we succumb to the illusion that all celestial bodies are at an equal distance from us, the so-called celestial sphere, and that they make a rotation from east to west around a common axis. This axis, is called the celestial axis and is an extension of the earth’s axis on the celestial sphere. The points of intersection between the celestial axis and the sphere are the celestial poles; they are the only stationary points on the sphere, just as the Earth’s poles are the only stationary points on the Earth. In turn, the plane of the Earth’s meridian marks the celestial meridian on the celestial sphere. During the course of the day, all celestial bodies change altitude above the hory zont; they reach their greatest altitude when they cross the po łudnik – this is the high point. Thus, the mountaintop of a celestial body is its attainment of the greatest possible height above the horizon in its apparent motion during the day.
The Sun’s altitude is equal to the right angle minus the angle of the difference between the latitude of a given point and the parallel on which the Sun tops at zenith. At the time of the Sun’s rising we observe solar noon. The mountaintop is also called the upper climax. The altitude of a given celestial body at the time of the uppering depends directly on latitude, and on declination (the coordinate of the position of bodies in the celestial systems).
A sub-solar point is a point on the Earth’s surface over which the sun is at zenith at any given time. At each parallel we observe a different altitude of the Sun. In the northern hemisphere, March 21 is the beginning of calendar spring, in the southern hemisphere on this day calendar autumn begins. On September 23, vice versa, in the northern hemisphere calendar autumn begins, while in the southern hemisphere we observe the beginning of calendar spring. Over the course of three consecutive months starting from the equinoxes, the sub-solar point moves northward. On the days of the equinoxes (March 21 and September 23), the Sun is in the plane of the equator.
Thus, if we know the height of the Sun mad the horizon (h) then h= 90°-φ, where φ is the latitude, which, after the transformation, is φ = 90°-h, because on March 21 and September 23 the height of the Sun at the time of the top on the equator is 90°. On June 22, the latitude at which the Sun tops with a known altitude is calculated from the formula: φ= 90°-h+ 23°27′, while on December 22 in the northern hemisphere the formula is used: φ= 90°-h- 23°27′. The value of 23°27′ is the latitude of the parallels over which, on June 22 and December 22, the Sun tops at the zenith, namely the Tropic of Cancer and the Tropic of Capricorn.
To determine the latitude in the southern hemisphere on these days, the following formulas are used: for June 22: φ= 90°-h- 23°27, while for December 22: φ= 90°-h+ 23°27′. Changing the latitude at which the sun tops at the zenith causes a change in lighting conditions on Earth. At different latitudes, the amount of solar energy reaching the Earth’s surface changes. The sun’s altitude increases, or decreases. These changes are the cause of astronomical seasons, which are accompanied by changes in the duration of day and night on Earth.
Table 1 Sun’s altitude above the horizon on the first days of the seasons (φ= 50°N)
| Dates | Patterns for the Northern Hemisphere | Calculations |
| 21 III and 23 IX | h= 90°-φ | h= 90°-50°= 40° |
| 22 VI | h= 90°-φ+ 23°27′ | h= 90°-50°+23°27’= 63°27′ |
| 22 XII | h= 90°-φ- 23°27′ | h= 90°-50°-23°27’= 16°33′ |
In the northern hemisphere, astronomical seasons coincide with calendar ones. In the southern hemisphere, on the other hand, the calendar ones are shifted by 6 months with respect to the astronomical ones. This means that the astronomical winter in the northern hemisphere corresponds to the calendar summer in the southern hemisphere. The calendar seasons are most clearly marked in temperate latitudes. The polar day is a phenomenon that occurs in the polar zones, i.e. in areas bounded by the Arctic Circle. It is a period when the sun is above the horizon for more than 24 hours.
The length of the polar day varies. The polar day lasts the shortest 24 hours in areas located at latitudes marking the Arctic circles. This phenomenon is observed longest at the poles – 6 months. Polar night, on the other hand, is a period when the sun remains hidden below the horizon for more than 24 hours. In spring summer in the polar zones, and parts of the temperate zones located near the Arctic Circle, the phenomenon of white nights occurs. At that time, the sun’s disk does not hide deep below the horizon, so that dusk passes directly into dawn. Despite the fact that the sun is below the horizon, a typical night does not fall, as there is a scattering of the sun’s rays.
Earth’s illumination during the year
March 21
The Sun’s altitude at the time of its elevation at the equator is 90°. The Earth’s globe is illuminated uniformly, but the height of the Sun above the horizon depends on latitude: it decreases with distance from the equator. At the poles, the Sun’s height above the horizon is 0° on this day. Uniform illumination of the globe makes the day equal to night, and lasts 12 hours. This day was called the day of the vernal equinox. Beginning March 21, the northern hemisphere is increasingly warmed and illuminated and the sub-solar point begins to move toward the Tropic of Cancer. At the North Pole, the polar day begins and the polar night ends. In the southern hemisphere, astronomical autumn begins on this day, and at the south pole the beginning of polar night is observed with the end of the polar day.
June 22
The sun’s rays on this day fall perpendicularly on the Tropic of Cancer. At this point the Sun shines at the zenith. On this day, the northern hemisphere, where the calendar summer begins, is more illuminated. The northern hemisphere also records the longest day of the year, and the shortest night. This day is called the summer solstice. The length of the day increases with increasing northern latitudes. In the southern hemisphere, we observe the beginning of calendar winter. The sun’s rays on this day illuminate the north pole, while in the southern hemisphere they reach only the southern polar circle. From June 22, the sun’s subsolar point begins to move toward the equator. Beyond the northern Arctic Circle, the sun is constantly above the horizon, so the polar day continues there. Behind the southern Arctic Circle, it observes the polar night.
September 23
On this day, the sun’s rays fall at right angles to the equator as they do on March 21. The entire globe is evenly lit, with day and night lasting 12 hours each again. This day is called the moment of the autumnal equinox. Beginning on September 23, the southern hemisphere becomes increasingly warmed and illuminated. In the northern hemisphere the calendar autumn begins, while in the southern hemisphere spring begins. From September 23, the sub-solar point begins to move toward the Tropic of Capricorn. At the North Pole, the polar night begins, while at the South Pole the beginning of the polar day is observed.
December 22
The sun’s rays fall perpendicularly on the Tropic of Capricorn, so the sun shines at the zenith over this parallel. The southern hemisphere is more illuminated. This day is called the winter solstice. The northern hemisphere then has the longest night and shortest day of the year. In the northern hemisphere, calendar winter begins, while in the southern hemisphere it is the first day of calendar summer. Beyond the northern Arctic Circle, the polar night begins. From December 22, the sun’s low point begins to move toward the equator. Beginning on this day, the illumination and warming of the southern hemisphere decreases. The Earth in its orbital journey begins to turn towards the Sun again with the northern hemisphere.
Zonal illumination of the Earth
Taking into account the differences in the Earth’s illumination throughout the year at different latitudes, five zones have been distinguished. The boundaries of these zones are the Tropics, and the Arctic Circle. Between the Tropic of Cancer and the Tropic of Capricorn extends the intertropical zone. In this zone, the sun tops twice at the zenith, so the sun’s rays fall perpendicular to the Earth’s surface. Only on the tropics does the sun peak at the zenith once a year. In this zone, day and night last the same amount of time, so about 12 hours. The differences in the duration of day and night are greatest at the tropics and amount to two hours. This zone receives the most solar energy, evenly distributed. Between the tropics and the Arctic Circle extend two zones of temperate latitudes.
Over the course of the year, the duration of day and night changes in them. In summer the day lasts longer than the night, in winter vice versa. It receives varying amounts of radiation from the sun throughout the year, by far the greater amount in the summer half of the year. There is a distinct seasonal natural variation, and the seasons are clearly marked. In temperate zones, the sun never tops at the zenith. The sun’s altitude decreases from the tropics toward the poles. As latitude increases, the sun’s raysfall at a lower angle, weaker, thus heating up the Earth’s surface.
