question: How in a solar eclipse, from earth, moon´s diameter looks same as sun´s diameter?
comment: Literally an amazing coincidence. The sun is 400x farther away from us than the moon, and the sun is roughly 400x the circumference of the moon, making it a perfect match. It won't stay that way, however... As we will inevitably move farther away from the sun at some point.
passages: The Sun's distance from Earth is about 400 times the Moon's distance, and the Sun's diameter is about 400 times the Moon's diameter. Because these ratios are approximately the same, the Sun and the Moon as seen from Earth appear to be approximately the same size: about 0.5 degree of arc in angular measure.
   This measure should not be confused with the covered fraction of the apparent "area" (disk) of the eclipsed body, whereas the magnitude of an eclipse is strictly a ratio of diameters. Neither should it be confused with the astronomical magnitude scale of apparent brightness.
  
  Section::::Effect of the magnitude on a solar eclipse.
  
  The apparent sizes of the Moon and Sun are both approximately 0.5°, or 30', but both vary because the distance between Earth and Moon varies. (The distance between Earth and Sun also varies, but the effect is slight in comparison.)
   Some eclipses are longer when the Earth is slightly closer to the Moon. During such on eclipses, the Moon is seen on Earth with its apparent diameter larger than the Sun's. Meanwhile, some eclipses are shorter when the Earth is slightly further away from the Moon. On Earth, the Moon is seen with its apparent diameter smaller than the Sun's.
  
  Unlike the Earth, where its eclipses start and end at a different place, all of the Moon's solar eclipses begin in the westernmost parts of the near side and end in the easternmost parts of the near side.
   A hybrid eclipse occurs when the magnitude of an eclipse changes during the event from less to greater than one, so the eclipse appears to be total at locations nearer the midpoint, and annular at other locations nearer the beginning and end, since the sides of the Earth are slightly further away from the Moon. These eclipses are extremely narrow in their path width and extremely short in their duration at any point, at most just a few seconds at any location within just a few kilometres of the centerline of the path. Like a focal point, the width and duration of totality and annularity are near zero at the points where the changes between the two occur.
   As noted above, the Moon's orbit is also elliptical. The Moon's distance from the Earth can vary by about 6% from its average value. Therefore, the Moon's apparent size varies with its distance from the Earth, and it is this effect that leads to the difference between total and annular eclipses. The distance of the Earth from the Sun also varies during the year, but this is a smaller effect. On average, the Moon appears to be slightly smaller than the Sun as seen from the Earth, so the majority (about 60%) of central eclipses are annular. It is only when the Moon is closer to the Earth than average (near its perigee) that a total eclipse occurs.
   To put this in perspective, the full Moon as viewed from Earth is about °, or 30′ (or 1800″). The Moon's motion across the sky can be measured in angular size: approximately 15° every hour, or 15″ per second. A one-mile-long line painted on the face of the Moon would appear from Earth to be about 1″ in length.
   Eclipses only occur when the Sun, Earth, and Moon are all in a straight line (termed "syzygy"). Solar eclipses occur at new moon, when the Moon is between the Sun and Earth. In contrast, lunar eclipses occur at full moon, when Earth is between the Sun and Moon. The apparent size of the Moon is roughly the same as that of the Sun, with both being viewed at close to one-half a degree wide. The Sun is much larger than the Moon but it is the vastly greater distance that gives it the same apparent size as the much closer and much smaller Moon from the perspective of Earth. The variations in apparent size, due to the non-circular orbits, are nearly the same as well, though occurring in different cycles. This makes possible both total (with the Moon appearing larger than the Sun) and annular (with the Moon appearing smaller than the Sun) solar eclipses. In a total eclipse, the Moon completely covers the disc of the Sun and the solar corona becomes visible to the naked eye. Because the distance between the Moon and Earth is very slowly increasing over time, the angular diameter of the Moon is decreasing. Also, as it evolves toward becoming a red giant, the size of the Sun, and its apparent diameter in the sky, are slowly increasing. The combination of these two changes means that hundreds of millions of years ago, the Moon would always completely cover the Sun on solar eclipses, and no annular eclipses were possible. Likewise, hundreds of millions of years in the future, the Moon will no longer cover the Sun completely, and total solar eclipses will not occur.
   Section::::Predictions.:Duration.
  
  The following factors determine the duration of a total solar eclipse (in order of decreasing importance):
  
  BULLET::::1. The Moon being almost exactly at perigee (making its angular diameter as large as possible).
  
  BULLET::::2. The Earth being very near aphelion (furthest away from the Sun in its elliptical orbit, making its angular diameter nearly as small as possible).
  
  BULLET::::3. The midpoint of the eclipse being very close to the Earth's equator, where the rotational velocity is greatest.
   For a total solar eclipse to happen, the ratio of the apparent diameters of the Moon and of the Sun must be 1.0 or more, and the three celestial bodies (Sun, Earth and Moon) must be aligned centrally enough. When that is the case, the Moon's disk covers the Sun's disk in the sky completely. The path of totality (i.e. of the travelling shadow of the Moon cutting off all direct sunlight from reaching the Earth's surface) is a relatively narrow strip, at most a few hundreds of kilometers across.
   The Moon's orbit around the Earth is slightly elliptical, as is the Earth's orbit around the Sun. The apparent sizes of the Sun and Moon therefore vary. The magnitude of an eclipse is the ratio of the apparent size of the Moon to the apparent size of the Sun during an eclipse. An eclipse that occurs when the Moon is near its closest distance to Earth ("i.e.," near its perigee) can be a total eclipse because the Moon will appear to be large enough to completely cover the Sun's bright disk or photosphere; a total eclipse has a magnitude greater than or equal to 1.000. Conversely, an eclipse that occurs when the Moon is near its farthest distance from Earth ("i.e.," near its apogee) can only be an annular eclipse because the Moon will appear to be slightly smaller than the Sun; the magnitude of an annular eclipse is less than 1. Slightly more solar eclipses are annular than total because, on average, the Moon lies too far from Earth to cover the Sun completely.
   From this distance, the Sun's angular diameter is reduced to one and a quarter arcminutes across. Here are the angular diameters of the moons that are large enough to fully eclipse the Sun: Naiad, 7–13'; Thalassa, 8–14'; Despina, 14–22'; Galatea, 13–18'; Larissa, 10–14'; Proteus, 13–16'; Triton, 26–28'.
   In the 2nd century CE, Ptolemy estimated the mean distance of the Sun as times Earth's radius. To determine this value, Ptolemy started by measuring the Moon's parallax, finding what amounted to a horizontal lunar parallax of 1° 26′, which was much too large. He then derived a maximum lunar distance of Earth radii. Because of cancelling errors in his parallax figure, his theory of the Moon's orbit, and other factors, this figure was approximately correct. He then measured the apparent sizes of the Sun and the Moon and concluded that the apparent diameter of the Sun was equal to the apparent diameter of the Moon at the Moon's greatest distance, and from records of lunar eclipses, he estimated this apparent diameter, as well as the apparent diameter of the shadow cone of Earth traversed by the Moon during a lunar eclipse. Given these data, the distance of the Sun from Earth can be trigonometrically computed to be Earth radii. This gives a ratio of solar to lunar distance of approximately 19, matching Aristarchus's figure. Although Ptolemy's procedure is theoretically workable, it is very sensitive to small changes in the data, so much so that changing a measurement by a few percent can make the solar distance infinite.
   BULLET::::- The full moon covers only about 0.2 deg of the sky when viewed from the surface of the Earth. The Moon is only a half degree across (i.e. a circular diameter of roughly 0.5 deg), so the moon's disk covers a circular area of:  × (), or 0.2 square degrees.
  
  BULLET::::- Viewed from Earth, the Sun is roughly half a degree across (the same as the full moon) and covers only 0.2 deg as well.
  
  BULLET::::- It would take times the full moon (or the Sun) to cover the entire celestial sphere.
   Determination of the value of L for an eclipse is best done near mid-totality with the naked eye. The scale is subjective, and different observers may determine different values. In addition, different parts of the Moon may have different L values, depending on their distance from the center of the Earth's umbra.
  
  Section::::Factors affecting the value of L.
   The Moon's average orbital distance is , or 1.28 light-seconds. This is about thirty times the diameter of Earth. The Moon's apparent size in the sky is almost the same as that of the Sun, since the star is about 400 times the lunar distance and diameter. Therefore, the Moon covers the Sun nearly precisely during a total solar eclipse. This matching of apparent visual size will not continue in the far future because the Moon's distance from Earth is gradually increasing.
   Hipparchus measured the apparent diameters of the Sun and Moon with his "diopter". Like others before and after him, he found that the Moon's size varies as it moves on its (eccentric) orbit, but he found no perceptible variation in the apparent diameter of the Sun. He found that at the "mean" distance of the Moon, the Sun and Moon had the same apparent diameter; at that distance, the Moon's diameter fits 650 times into the circle, i.e., the mean apparent diameters are = 0°33′14″.
   A total solar eclipse occurred at the Moon’s ascending node on Wednesday, April 17, 1912. It is a hybrid event, starting and ending as an annular eclipse, with only a small portion of totality. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partly obscuring the image of the Sun for a viewer on Earth. A total solar eclipse occurs when the Moon's apparent diameter is larger than the Sun's, blocking all direct sunlight, turning day into darkness. Totality occurs in a narrow path across Earth's surface, with the partial solar eclipse visible over a surrounding region thousands of kilometres wide.
   The relative distance of the Moon from Earth at the time of an eclipse can affect the eclipse's duration. In particular, when the Moon is near apogee, the farthest point from Earth in its orbit, its orbital speed is the slowest. The diameter of Earth's umbra does not decrease appreciably within the changes in the Moon's orbital distance. Thus, the concurrence of a totally eclipsed Moon near apogee will lengthen the duration of totality.
   A similar procedure was later used by Hipparchus, who estimated the mean distance to the moon as 67 Earth radii, and Ptolemy, who took 59 Earth radii for this value.
  
  Section::::Illustrations.
  
  Some interactive illustrations of the propositions in "On Sizes" can be found here:
  
  BULLET::::- Hypothesis 4 states that when the Moon appears to us halved, its distance from the Sun is then less than a quadrant by one-thirtieth of a quadrant [that is, it is less than 90° by 1/30th of 90° or 3°, and is therefore equal to 87°] (Heath 1913:353).
   The effect on a lunar eclipse is quite similar, with a few differences. First, the eclipsed body is the Moon and the eclipsing 'body' is the Earth's shadow. Second, since the Earth's shadow at the Moon's distance always is considerably larger than the Moon, a lunar eclipse can never be annular but is always partial or total. Third, the Earth's shadow has two components: the dark umbra and the much brighter penumbra. A lunar eclipse will have two geometric magnitudes: the umbral magnitude and the penumbral magnitude. If the three bodies are not aligned enough, the Moon does not reach into the Earth's umbra - it may still pass through the Earth's penumbra though, and such an eclipse is called a penumbral eclipse.
   Section::::Possible explanations.:Relative size hypothesis.
  
  Historically, the best-known alternative to the "apparent distance" theory has been a "relative size" theory. This states that the perceived size of an object depends not only on its retinal size, but also on the size of objects in its immediate visual environment. In the case of the Moon illusion, objects in the vicinity of the horizon Moon (that is, objects on or near the horizon) exhibit a fine detail that makes the Moon appear larger, while the zenith Moon is surrounded by large expanses of empty sky that make it appear smaller.
   BULLET::::- Proposition 17a in al-Tusi's medieval Arabic version of the book "On Sizes" states that the ratio of the distance of the vertex of the shadow cone from the center of the Moon (when the Moon is on the axis [that is, at the middle of an eclipse] of the cone containing the Earth and the Sun) to the distance of the center of the Moon from the center of the Earth is greater than the ratio 71 to 37 and less than the ratio 3 to one (Berggren & Sidoli 2007:218). In other words, that the tip of the Earth's shadow cone is between 108/37 and 4 times farther away than the Moon.
   Total eclipses are rare because the timing of the new moon within the eclipse season needs to be more exact for an alignment between the observer (on Earth) and the centers of the Sun and Moon. In addition, the elliptical orbit of the Moon often takes it far enough away from Earth that its apparent size is not large enough to block the Sun entirely. Total solar eclipses are rare at any particular location because totality exists only along a narrow path on the Earth's surface traced by the Moon's full shadow or umbra.
   At this distance, the sun covers only about 3 arcminutes in the sky of Saturn. In comparison, the seven major moons of Saturn have angular diameters of 5–10' (Mimas), 5–9' (Enceladus), 10–15' (Tethys), 10–12' (Dione), 8–11' (Rhea), 14–15' (Titan), and 1–2' (Iapetus). Iapetus is Saturn's third largest moon, but is too far away to completely eclipse the sun. Janus, a very close moon to Saturn, has an angular diameter of about 7', meaning that it can fully cover the sun.
   An inex also is close to an integer number of days (10,571.95) so solar eclipses on average take place at about the same geographical longitude at successive events, although variations of the moon's revolutionary speed at different points of the eclipse mask this relation. In addition sequential events occur at opposite geographical latitudes because the eclipses occur at opposite nodes. This is in contrast to the better known saros, which has a period of about days, so successive solar eclipses tend to take place about 120° in longitude apart on the globe (although at the same node and hence at about the same geographical latitude).
  