What is the half day arc length and how to calculate the daytime arc length

When studying the length of day and night, half of the length of the day arc is often calculated by the half-day arc formula, and then the length of day and night is calculated. The meridian of the diurnal arc must be 12 noon when it is equivalent. Night arcs are also applicable.

cost=-tanδ·cot A formula used in astronomy to find the length of the day and night arcs. where t is the semi-diurnal arc (the semi-diurnal arc is half of the diurnal arc, i.e., the solar hour angle at sunset), and δ is the solar declination, which is the local geographic latitude. The north latitude is positive and the southern latitude is negative.

This formula is calculated by solving spherical triangles. Under the condition of ignoring the apparent radius of the sun and the refraction of light by the atmosphere, the half-day arc can be found as long as the solar declination and the local geographical latitude are known. Here's how:

Make a spherical triangle ZPS (z is the zenith, p is the celestial north pole, and s is the position of the sun's center point on the horizon at local sunset). It is not difficult to see that the spherical angle zps is equal to the half-day arc. The zp side of a spherical triangle (the length expressed in radians) is the co-angle of the local latitude; The ps edge is the co-angle of the sun's declination; The zs edge is equal to 2 (the arc length from the zenith to the horizon circle is determined to be 2).

According to the cosine law, the relationship between t and the geographical latitude and the declination of the sun can be obtained by solving this spherical triangle, and finally the above formula can be derived.

It is the length of the half-axis arc, which can be found on the Internet.

The knowledge that must be possessed to calculate the length of day and night is:

Familiarize yourself with the basic properties of warp and weft threads. On the same parallel, the length of day and night is equal everywhere, and the place of sunrise and sunset is the same; On the same meridian line, the local time is the same everywhere, and the longitude is 1 hour apart every 15° time, that is, the longitude is every 1°, and the local time is 4 minutes apart.

It can correctly identify the morning line and the evening line. The morning and dusk line is composed of two parts, the morning line and the dusk line, which follows the direction of the earth's rotation and enters the night hemisphere from the day hemisphere, which is called the dusk line; On the contrary, the one that enters the day hemisphere from the night hemisphere is called the morning line. The dot on the morning line coincides with sunrise, and the dot on the dusk line coincides with sunset.

Understand the distribution of the length of day and night. The day is longer than the night in the hemisphere, and the day length increases from low latitudes to high latitudes, while the days in the other hemisphere are shorter than nights, and the day length decreases from low latitudes to high latitudes.

There are several special cases to keep in mind. The equinox is equinox, and the annual diurnal equinox is equinoxized on the equator, with a day length of 24 hours and a polar night length of 24 hours in the polar circle.

The methods and techniques for calculating the length of day and night are:

Calculated using the difference in longitude between two adjacent meridians. On the light map, generally only a few meridians are given evenly, and the longitude difference between two adjacent meridians can be obtained by dividing 360° by the number of meridian intervals in the figure; Then according to the interval of the meridian crossed by the daytime arc, the longitude spanned by the daytime arc is calculated, and the longitude is multiplied by 1 15 to be the day length of the place.

It is calculated using the ratio of the day arc to the night arc. The ratio of the day arc to the night arc can be calculated from the longitude spanned by the day arc and the night arc, if it is found: day arc arc arc = a, then day length = 24 (1 + 1 a).

Calculate the slag when using the place of sunrise and sunset. When calculating places, the influence of the topography of the earth's surface, the elliptical shape of the earth and the scattering of the atmosphere on the pre-day sail is generally not considered, so the time interval from sunrise to noon and from noon to sunset is the same, if the place of sunrise or sunset is assumed to be a, then the day length of the place = 2 |12-a|.

Calculated using symmetrical latitude. Two parallels with the same latitude in different hemispheres complement each other in terms of day and night. That is, the length of the day (night length) of a certain latitude is equal to the length of the night (day length) of another latitude with the same number of latitudes

The Earth does not emit light or is transparent, so at any given moment, one half of the Earth faces the Sun, called the day hemisphere, and the other half faces away from the Sun, called the Night Hemisphere.

The dividing line between the day and night hemispheres is called the morning and dusk line. The morning and dusk lines are divided into two parts: the morning line and the dusk line. Sunrise is everywhere on the morning line, and sunset is everywhere on the dusk line. The morning line and the dusk line are combined into a morning and dusk circle.

On the solar chart, if you follow the direction of the Earth's rotation, if you enter the day hemisphere from the night hemisphere, Ze crosses the morning line, and if you enter the night hemisphere from the day hemisphere, you cross the dusk line.

The morning and dusk line divides the passing weft coil into two parts, the part in the day hemisphere becomes the day arc, and the part in the night hemisphere becomes the night arc. The long arc of the day is the length of the day, and the length of the arc of the night is the length of the night.

The day-night arc is the dividing line between the day and night hemispheres, and the area on the day arc changes from night to day, and the area on the night arc changes from day to night.

The section located on the day hemisphere is called the day arc. The section located on the night hemisphere (and vice versa) is called the night arc.

What are the arcs of day and night?

Since the Earth is an opaque, non-luminous sphere, the Sun can only illuminate half of the Earth at any one moment. The half of the Earth illuminated by the Sun is called the day hemisphere, and the half of the Earth that is not illuminated by the Sun is called the Night Hemisphere. The boundary between the day hemisphere and the night hemisphere is the morning and dusk line.

The morning and dusk line divides the parallel line through which it passes into two segments, and the section located on the day hemisphere is called the day arc. The section located on the night hemisphere is called the night arc.

For example, the day arc and night arc of place B are required.

First of all, the position of place B can be transferred to the same latitude, and the red pen in the figure (a little next to b) and then select the intersection point of the day arc, the night arc and the latitude where B is located.

Calculate the AC longitude difference of 135-45=90

The inferior arc ac is in the night hemisphere, so the night arc is 90 degrees, and the day arc is 360-90=270 degrees.

Day (night) length = day (night) radian 15

The length of the night is 90 15 = 6

Therefore, the night is 6 hours long.

Morning and dusk lines. The latitude on the earth is divided into two parts: the day arc and the night arc, and the length of the day and night arcs determines the length of the day and the length of the night, and the arc length of 15° is 1 hour. On the light map, the meridians divide the parallels into segments, and the longitude difference between adjacent meridians is generally 30° or 45°, which shows that the time difference between each longitude segment is 2 or 3 hours.

The length of day or night can be determined by reading the degrees of longitude.

The higher the latitude, the longer the days and the shorter the nights; The hemisphere (north or south) to which the point of direct fire moves, the day becomes longer and the night becomes shorter.

The morning and dusk lines coincide with the meridian planes, and the global day and night are equally divided; The intersection angle between the morning and dusk lines and the meridian plane is the largest (23°26'), and the difference between day and night is the largest.

The length of day and night is determined by looking at the corresponding lengths of the day and night arcs in the same latitude coil:

When the sunrise is known to be a: day length = 2 (12-a), night length = 2a, a + b = 24 hours.

When the sunset is known to be b: day length = 2 (a 12), night length = 48 2a

Day length = sunset Sunrise, night length = 24 day length.

Different regions with the same latitude have the same length of day and night.

When the sum of the day lengths of two parallels with the same north-south relative and equal latitude values is 24 hours, and when the sum of the night lengths is 24 hours, the relative values of day and night are equal (the night length of a certain latitude in the southern hemisphere is equal to the same latitude value in the northern hemisphere.

The length of the day).

The sum of the day and night arcs at the same latitude is equal to 360°The day arc divided by 15° cryptogenous hours is equal to the day length, the night arc divided by 15° hours and so on are balanced by the night length, and the day length plus the night length and the width of the stove are equal to 24 hours. 360° divided by 15° hours equals 24 hours.

The diurnal arc on the Tropic of Cancer in the figure above is the arc ABC, and the longitude spanned by the arc ABC is the longitude of the diurnal arc. Divide this longitude by 15 to get the length of day.

The longitude occupied by the day hemisphere on a certain latitude, that is, the longitude range of the day hemisphere is the longitude span of the day arc, for example, the longitude span of the day arc on the equator is 180 degrees, and the corresponding day length is 180 15 = 12 hours.

The daytime arc represents the length of daylight in a region at the same latitude, and the longer the daylight arc means the longer the daylight hours in that place.

<> each latitude coil is divided into two ends of the day arc and the night arc by the morning and dusk lines, and the equator is always equally divided by the morning and dusk circles, so the day and night arcs on the equator are of equal length, and the length of the day and night arcs in the northern and southern hemispheres is controlled by which hemisphere the sun directly hits: when the sun directly hits the northern hemisphere (as shown in the figure), the day and night in the northern hemisphere are shorter, so the day arc is longer than the night arc; The north and south balls have short days and long nights, and the night arc is longer than the day arc. The opposite is true when the sun is shining directly on the Southern Hemisphere.

Every year, only on the day of the spring and autumn equinoxes, the morning and dusk lines coincide with the warp coils and bisect the weft coils.