Back in Classical Greece there was some debate as to what the cause of a lunar eclipse was. By this time it was generally accepted that it was due to the Earth coming between the Moon and the Sun and casting a shadow. But one point of evidence that was presented against this theory was that on occasion lunar eclipses were observed at sunset. You could clearly see both the Sun and the Moon, so the Earth did not appear to be between the two. This issue with the idea that lunar eclipses are due to the Earth's shadow wasn't really satisfactorily addressed until the 1700s or so when the refraction of light was systematically studied (though by the Hellenistic Era no one seriously doubted it).
This actually wasn't the only time when the refraction of the Earth's atmosphere produced surprising observations in the ancient world. One of the devices the Greeks used to determine the time of an equinox was what is called an equatorial ring. It's basically just a metal hoop oriented at an angle equal to 90 degrees minus the latitude. (Here's a diagram: https://en.wikipedia.org/wiki/Equatorial_ring#/media/File:Eq...) During an equinox the Sun would be right on the celestial equator, and the shadow cast by the upper half of the hoop would fall exactly on the bottom half.
But it was noticed that sometimes, the shadow would fall on the bottom half early in the morning, then cross to the other side, cross back, and then later cross over once again --- it seemed that there was three equinoxes! Ptolemy explained this away as being due to instabilities in the device's orientation --- somehow it was very slightly tilting and so it wasn't possible to measure the time of the equinox to better than half a day or so. But today we know that this was also due to the refraction of the atmosphere. Early in the morning, the Sun would be refracted to appear to be just above the celestial equator, but as it rose, the refraction would lessen and it would fall back to its original place. Then later in the day it would cross the celestial equator "for real" when the equinox actually occurred. So the device was much more accurate than ancient astronomers gave it credit for!
Besides the refraction, there's also a geometrical effect. An observer is not on the line of the Sun-Earth-Moon centers; he's offset from it by Earth's radius at Earth's surface, so he's at one point of a triangle and sees a Sun-Moon angle of slightly less than 180º.
The refraction is a larger effect, but even an airless planet could have an observer seeing the centers of both the Sun and Moon at eclipse time just above the horizon.
That is interesting… but to my intuition, it seems like that would have the opposite effect? You are offset in the “wrong” direction, ie the sun and the moon are further “down” and more obscured by the earth? I might be thinking all wrong about this, though.
I’d also question if this can have any meaningful effect on the sun, which is about 23500 Earth radii away. That’s a very, very slight perspective shift.
Imagine an ant standing on some random point on a soccer ball in the middle of a field. Now rotate the ball so where the ant is will be directly facing the side of the field, 90 degrees rotation of the ball from facing either goal. At this specific point the ant can see each goal at each end of the field even though the ball is directly between the middle of the two goals. Well, depending how tall the ant is given the goals are so close to the ball.
A huge distance is actually a helping factor in this case. A 1.75 meter person can see 4,700 away before the horizon curves out of view. That means (ignoring the bending of light by the atmosphere still) the viewing angle allows for 1 meter "down" every ~2,685.7 meters out. The radius of the Earth is ~6,371,000 meters so to be able to see the middle of an object from ~the radius of the earth "down" with that viewing angle would require the object to be a minimum of ~2,685.7 * 6,371,000 = 17,110,594,700 meters away. That's a minimum distance of ~0.11 AU so the person would only get a partial view of the moon but a full view of the sun because the moon -isn't- far enough away! Well technically the Earth could rotate slightly farther while having the middle of the sun still visible but I'm too lazy to calculate if it's actually enough, my hunch is no. If you wanted to see the middle of the moon and the middle of the sun (with no bending by the atmosphere) during an eclipse you'd have to be near the top of Everest while it happens to be exactly rotated between each.
So are you saying that the offset of 1 Earth/soccer ball radius is helping or hurting? It’s still seems to me like it’s just getting in the way. (Though I guess the ant wouldn’t see much of anything if it was down in the grass.)
I wonder if anyone back then, say an armchair astronomer, tried to argue that it was due to the atmosphere, and backed their argument up by comparing the atmosphere to how a pool of water bends light.
Interestingly enough, modern Greece - so presumably also ancient Greece but I'm not sure - are one of the very few places where the water can be so still and so clear as to appear absolutely transparent. I actually experienced this last October in Greece and I never imaged that seawater could be clearer than bottled spring water.
This actually wasn't the only time when the refraction of the Earth's atmosphere produced surprising observations in the ancient world. One of the devices the Greeks used to determine the time of an equinox was what is called an equatorial ring. It's basically just a metal hoop oriented at an angle equal to 90 degrees minus the latitude. (Here's a diagram: https://en.wikipedia.org/wiki/Equatorial_ring#/media/File:Eq...) During an equinox the Sun would be right on the celestial equator, and the shadow cast by the upper half of the hoop would fall exactly on the bottom half.
But it was noticed that sometimes, the shadow would fall on the bottom half early in the morning, then cross to the other side, cross back, and then later cross over once again --- it seemed that there was three equinoxes! Ptolemy explained this away as being due to instabilities in the device's orientation --- somehow it was very slightly tilting and so it wasn't possible to measure the time of the equinox to better than half a day or so. But today we know that this was also due to the refraction of the atmosphere. Early in the morning, the Sun would be refracted to appear to be just above the celestial equator, but as it rose, the refraction would lessen and it would fall back to its original place. Then later in the day it would cross the celestial equator "for real" when the equinox actually occurred. So the device was much more accurate than ancient astronomers gave it credit for!