How do solar and lunar eclipses happen?

Conditions for the occurrence of solar eclipse There are certain conditions for the occurrence of solar eclipse and lunar eclipse. Knowing these conditions, people can calculate and predict the occurrence of solar eclipse. It is an important part of ancient astronomy in China and occupies an important position in the history of world astronomy. The movement of the moon to catch up with the sun to the east occurs in the process of its respective movement to the west on Sunday, and the specific situation varies with latitude, season and northern and southern hemispheres. -The equator of the celestial sphere inclines to the south and the north pole of the celestial sphere tilts upward, indicating that it is in the northern hemisphere; —— The intersection angle between the celestial equator and the horizon map is the local residual latitude, so the latitude is 45° N；; ; —— The sun's Sunday circle (declination) is south of the celestial equator, so it is winter in the northern hemisphere; -The sun and the moon are setting towards the western horizon; It can be seen that the time is approaching evening. Simply put, the condition of solar eclipse is that the earth is located in the back direction of the moon (that is, the direction of the shadow of the moon), so it is located on the extension line connecting the sun and the moon. The condition of an eclipse is that the moon is located in the back direction of the earth (that is, the direction of the shadow), so it is located on the extension line connecting the sun and the earth. For the convenience of explanation, this general condition can be divided into two specific conditions:-First month condition: solar eclipse must occur in the new moon, and lunar eclipse must occur in the line of sight. In the new moon, only on the date of the new moon can the earth be located in the direction of the moon shadow; On the date of the moon, the moon may be in the direction of the shadow. In this way, solar and lunar eclipses are associated with the moon. According to this principle, the calendar was tested by solar eclipse in ancient China. If the solar eclipse does not occur on the first day of the first year, then the calculation of the lunar calendar will definitely become a problem. -Intersection conditions: the solar eclipse occurs in the new moon, and the eclipse is in sight; However, not every new moon will have an eclipse, and not every moon will have an eclipse. Experience tells us that solar and lunar eclipses will not occur in most areas of Wang Shuo. This is because there is an intersection angle of 5 9' between the ecliptic and the ecliptic (called the intersection angle of yellow and white), and the apparent diameter of the moon and sun gear is only about 0.5. It can be seen that the conditions of an eclipse are only necessary conditions, not sufficient conditions. The new moon (conjunction of the sun and the moon) and hope (collision of the sun and the moon) only indicate that the eclipses of the sun and the moon are the same or different180; However, if they really overlap on the celestial sphere, then their yellow latitudes should be equal (or close). This requires the moon and the sun to be at or near the intersection of yellow and white at the same time. If the sun and the moon meet or collide and are not near the intersection of yellow and white, then at the new moon, the shadow cone of the moon passes through the north and south of the earth and does not touch the ground; The apparent moon also passes through the north and south of the earth's shadow cone and does not enter the umbra of the earth. Generally speaking, the condition of solar eclipse is that the sun and the moon meet at or near the intersection of yellow and white; The condition of solar eclipse is that the sun and the moon collide (see) into yellow and white. In the food season, food restriction and solar eclipse occur, which requires the sun and the moon to meet (or collide) at or near the intersection of yellow and white. This "neighborhood" has a certain limit, that is, the food limit. As far as solar eclipse is concerned, at this limit, the moon wheel on the white road and the sun wheel on the ecliptic are close to each other, and the angular distance between their centers is the sum of their apparent radii, that is, about 32'. At this time, the ecliptic arc length from the center of sun gear to the intersection of yellow and white is called the eclipse limit. As we know, the sun runs along the ecliptic, and its position is represented by the ecliptic; The solar eclipse limit is expressed by the difference of the yellow meridian between the center of sun gear and the intersection of yellow and white, which is directly related to the length of time the sun has experienced. If the sun collides with the moon instead of the sun meets the moon, and the sun gear is replaced by the cross section of the umbra, then such a limit is the eclipse limit. When the sun is tangent to the moon, the arc length of the ecliptic from the intersection of yellow and white to the center of sun gear is the difference between the center of sun gear and the adjacent intersection of yellow and white at this moment. The size of the food limit depends on the size of the intersection of yellow and white, the distance between the moon and the earth, and the distance between the sun and the earth. These factors are changing: the intersection angle of yellow and white varies from 4 59 ′-518 ′; The distance between the moon and the earth varies between 363,300 km (perigee) and 405,500 km (apogee). The distance between the sun and the earth varies between 147 100 000km (perihelion) and 152 100 000km (apohelion). Therefore, the size of the solar eclipse limit and the solar eclipse limit are also changing. We can't explain their specific size here, but only their general changing rules:-The greater the intersection angle between yellow and white, the smaller the food limit and food limit; The greater the distance between the moon and the earth, the smaller the apparent radius of the moon wheel, and the smaller the eclipse limit and eclipse limit; —— The greater the distance between the sun and the earth, the smaller the apparent radius of sun gear and the smaller the solar eclipse limit; However, the apparent radius of the shadow part increases, so the eclipse limit also increases. Therefore, when the intersection angle of yellow and white, the distance between the moon and the earth and the distance between the sun and the earth are the largest, the solar eclipse limit is the smallest; On the contrary, when all three are the smallest, the solar eclipse limit is the largest. The situation of eclipse limit is different: when the yellow and white intersect, the distance between the moon and the earth is the largest, the distance between the sun and the earth is the smallest, and the eclipse limit is the smallest; On the contrary, when the intersection angle between yellow and white is the smallest and the distance between the moon and the earth is the largest, the eclipse limit is the largest. The difference between the intersection of the yellow meridian and the yellow meridian in the center of sun gear is less than the minimum eclipse time, and a solar eclipse is bound to occur. Daily (monthly) eclipse may occur if it is greater than the minimum food intake limit but less than the maximum food intake limit; If it is greater than the maximum food limit, there will be no food. The size of the eclipse limit (including partial eclipse and central eclipse) and the eclipse limit (including penumbral eclipse, partial eclipse and total eclipse) are compared as follows: As can be seen from the above table, the eclipse limit is slightly larger than the eclipse limit. However, if the penumbral eclipse is excluded, the eclipse limit is much greater than the eclipse limit. In order to calculate the size of the food limit, besides the apparent radius of the sun and the moon and the intersection angle of the sun and the moon, the geodetic adjustment of the sun and the moon should also be considered. S, e, m and M' represent the centers of the sun, the earth and the moon, respectively. As far as the eclipse is concerned, when the moon begins to contact sun gear (the first loss), the opening angle of the center of the sun and the center of the moon to the center of the earth is the yellow latitude of the moon at that time. SEM=∠SEA+∠AEB+∠BEM. Where ∠SEA and ∠BEM are the apparent radii of the sun and the moon, respectively, which are expressed by S⊙ and S-moon; ∠ AEB = ∠ CBE-∠ CAE, which are the earth adjustment of the moon and the sun, respectively. If expressed by π moon and π ⊙, there is ∠ SEM = S ⊙+S moon-π ⊙+π moon. For an eclipse, at the initial loss, the moon, where ∠ m ′ ed is the apparent radius s of the moon; And det = CDE-etd. ∠CDE is the earth adjustment of the moon π moon; And ∠ ETD = ∠ AES-∠ CAE, which are solar apparent radius S⊙ and solar-terrestrial adjustment π ⊙ respectively. Then it is: ∠ tem ′ = smoon+π moon-s ⊙+π ⊙ We know that the sun and the moon have similar apparent diameters, with the former averaging15 ′ 59 ″ .6 and the latter averaging15 ′ 32 ″. However, their geodetic adjustment is quite different: the average geodetic adjustment of the sun is only 8. "8, and the average adjustment of the moon is 57' 2". Therefore, ∠SEM >∠TEM'. The greater the latitude of yellow latitude, the farther away from the intersection of yellow and white, and the solar eclipse limit is greater than the lunar eclipse limit. The food season is a period when solar and lunar eclipses may occur, which is related to food restriction. Because the occurrence of solar and lunar eclipses must meet two conditions at the same time, not all new moons and eclipses can occur. Therefore, solar and lunar eclipses can only occur at certain times of the year. As we know, the conditions of solar eclipse and lunar eclipse are that the sun and the moon must be at the same yellow-white intersection (eclipse), or separated by two yellow-white intersections (eclipse) or close to two yellow-white intersections. Comparatively speaking, the moon passes through the intersection of yellow and white frequently (twice a month), 24.5 times a year; And the sun comes to the intersection once every six months. Therefore, whether there was a solar eclipse or a lunar eclipse at that time mainly depended on whether the sun was located at or near the intersection of yellow and white. The time when the sun exceeds the food limit is called food season. Generally speaking, there are two food seasons in a year, about half a year apart.

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