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During a solar eclipse The Moon covers The Sun on some places on the Earth. Now the focal point is a bit above the Earth so the shadow area is about 160 miles. In history The Moon was a bit closer to the Earth but could there have been a time that the shadow area was just a dot. (probably for just some places as the Earth is not really perfect a sphere and the orbit of the Moon isn't also a perfect circle).

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    $\begingroup$ There are annular solar eclipses even today. So it is possible, it is probably a far rarer event than a total eclipse, but possible. But what would be interesting in it? It would only result, that only on a single point of the Earth do we have a total eclipse. $\endgroup$ – peterh says reinstate Monica Sep 15 at 16:42
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    $\begingroup$ Sun is not a point source. $\endgroup$ – Wayfaring Stranger Sep 15 at 22:31
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    $\begingroup$ @WayfaringStranger If the Sun and Moon were spherical, the umbra could still shrink to a point, ignorming diffraction. $\endgroup$ – uhoh Sep 16 at 8:53
  • $\begingroup$ @uhoh Yes, fundamental theorem of calculus and all, but it's not going to be in any spot we'll be able to see. Penumbra is a parallel sheath around umbra. That point might be at a different distance than umbra point. Too early on morning here to be certain. $\endgroup$ – Wayfaring Stranger Sep 16 at 16:05
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    $\begingroup$ @WayfaringStranger if the sun were a point source, there would never be a penumbra and there could never be a single dot umbra. I'm not sure why you felt the need to mention that the sun is not a point source. $\endgroup$ – Ingolifs Sep 17 at 0:16
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What you are calling a focal point is the end of the umbra, the point at which the umbra changes to the antumbra. In a total solar eclipse, that point is below rather than above the surface of the Earth. An annular eclipse occurs when that point is above the surface of the Earth. The Moon appears to be smaller than the Sun, leaving an unbroken ring of the Sun that appears to surround the Moon.

There are some solar eclipses that transition from annular to total, and from total to annular. A point on the surface of the Earth is exactly at the end of the umbra at those times of transition points in time. At this point in space and time the Moon will appear to be exactly the same size as and exactly in line with the Sun.

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    $\begingroup$ Tho' to be fair, diffraction effects (wavelength-related, not atmospheric) will never allow a mathematical "point" shadow. $\endgroup$ – Carl Witthoft Sep 16 at 18:24
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    $\begingroup$ It won't be a "point" shadow even without diffraction; there will be a single point of maximum darkness and it will gradually taper into lightness. $\endgroup$ – user253751 Sep 16 at 19:15
  • $\begingroup$ @immibis well, we'll always have a single point of darkness which gradually tapers into lightness, even in deep total eclipse — because of atmospheric scattering of light (at least it's a single point in ideally clear weather: clouds may introduce multiple minima). Reality is fuzzy... $\endgroup$ – Ruslan Sep 18 at 9:51
  • $\begingroup$ How big is this single point of darkness? Is this theoretically zero/invisible or a bit larger/a real dot? $\endgroup$ – Marijn Sep 19 at 18:26
  • $\begingroup$ @Marijn The question is asking about the possibility that it is an actual point of theoretically zero size. If it's bigger than zero size, then that's not the situation which the question is asking about. $\endgroup$ – user253751 Sep 22 at 9:32
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As the Moon's eccentric orbit around the Earth brings it nearer and farther, current solar eclipses can be total or annular. A few in between are hybrid eclipses: total along the midday part of the path, and annular near the sunrise or sunset end. This happens mostly due to the Earth's surface curvature and partly due to the Moon's orbital eccentricity.

Solar eclipses in the 21st century are about 34% partial, 32% annular, 30% total, and 3% hybrid. As millennia of tidal effects enlarge the Moon's orbit, there will be more annular eclipses and fewer total eclipses. Hybrid eclipses will happen sporadically as long as total eclipses are possible.

Hybrid eclipses occurred on 2005-04-08 and 2013-11-03 and will occur on 2023-04-20 and 2031-11-14. On Espenak's maps, the central path is blue where total and red where annular. At an annular/total transition point, the eclipse magnitude is 1.00, and an observer would see a "diamond ring" flip from one side to the other.

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    $\begingroup$ what about the rest 35%? What are those called? $\endgroup$ – Ev. Kounis Sep 16 at 13:11
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    $\begingroup$ @Ev.Kounis Partial. $\endgroup$ – Mike G Sep 16 at 16:18
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Is it possible that the shadow of the moon is a single dot during solar eclipse?

No, because the Moon is not round. Yes. I have to modify my answer after reading @IlmariKaronen's comment(s) below. Mathematically the umbra could collapse to a line segment, arc, or other short 1D shape, or to two or more points, but these are not likely for a randomly cratered Moon.

Images below are screenshots from the very cool NASA Goddard video Tracing the 2017 Solar Eclipse. They were used in The Moon's shadow could not possibly look like this — could it?.

enter image description here

enter image description here

In this answer I calculate the GIF shown below, which illustrates that the non-circularity remains and doesn't shrink. If the non-circularity of the Moon is say 10 km, then the umbra can't be smaller than roughly that size before you start getting light from the valleys reaching the center of the spot.

However, even if it were irregular the last bit of umbra would likely end up as a point, though it may not fall at the exact center of the Sun-Earth line.

(slow) GIF:

enter image description here

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    $\begingroup$ The moment when "you start getting light from the valleys reaching the center of the spot" is when the eclipse stops being total. Just before that moment, there will (almost surely) be exactly one spot on the surface of the Earth where the eclipse is still total, i.e. where all of the Sun's disk is still (just barely) eclipsed by the Moon. And this will happen regardless of the Moon's (and the Sun's!) shape and size, as long as they're such that both total and annular eclipses are possible. $\endgroup$ – Ilmari Karonen Sep 16 at 10:57
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    $\begingroup$ ... The only minor caveat is that, if the Moon's shape was sufficiently far from round, the umbra could in theory split into two or more parts before it disappears entirely. Generally those parts would still disappear at different times, so there would still be a moment when the umbra consists of a single point. But if the Moon's shape (and the Earth's surface topography) were very carefully tuned, you could in principle have the umbra instead shrink to two or more separate points that vanish (almost) simultaneously. But I don't believe such a coincidence is possible in practice. $\endgroup$ – Ilmari Karonen Sep 16 at 11:03
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    $\begingroup$ @IlmariKaronen hmm... okay, yep that's right! Mathematically, it could be a short line segment, or two or more identical points, but the chances of that happening from a randomly cratered moon are essentially zero. I'll make an edit, thanks for pointing that out! Ya, we posted at the same time ;-) $\endgroup$ – uhoh Sep 16 at 11:09

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