I stand corrected. Always a risk when you come to a thread late.
yeah, I do it all the time. Sometimes I remember the thread search tool.
Despite his guess-work, and being lucky Venus is just a hair smaller than earth, Venus at the time, IIRC, was really the only planet to make out its phases. Mars and Jupiter, if not full, are rarely observed anything less than gibbous.
And Mercury was less than ideal for spying phases when you already have a Venus at your disposal.
But, yeh, point noted.
Wait a minute.
Before we start arguing from the shape of the lunar eclipse shadow, we must establish the shape of the lunar surface itself, n’est-ce pas? I see no explicit mentioning of it upthreads, but I take it we are all agreed upon that it must be a sphere? There is no alternative explanation for the lunar phases, right?
(Well, I suppose it could be a half-sphere. But in this particular context it doesn’t matter.)
I believe that was one of the strongest/earliest arguments that the earth is probably a sphere too. But yes, anyone with a round stone and a candle in darkness would’ve noted the unmistakable correlation of the way the moon is lit by the sun.
So, squattin’ 'neath the camp-fire, the great sceptical chieftain grudgingly admits that the moon is most likely a ball, reflecting the light of the sun.
That is certainly something to stand on!
Now this next step may not be evident, and would perhaps take rather more than a stone and a candle, besides the mind of an Archimedes; but could one,( besides the general analogy in terms of shape), use the ashen glow as a corroborative, although not conclusive, evidence to show that something akin to the moon’s phases is happening with respect to the Earth?
Maybe I’m mathematically illiterate, but it seems a lot of the measurement experiments (and stuff like ships disappearing over the horizon) only disprove a naive perfectly flat Earth. But they’d be fooled if the flat Earth was misshapen and lumpy and we lived on a curved portion of it.
IIRC, and obviously YMMV, the shadow question was answered by the best fit for the shadow shape was a sphere casting a shadow on another sphere. I wasn’t there, tho, so I can’t say for sure.
Not if measured on the sea, or at least at opposite shores of a lake, since it has been understood since antiquity that water is level, no mater the topology beneath.
The problem is that accurate clocks (or the technology to actually build one even if you don’t have to figure out how to do so from scratch) didn’t come along until the sphericity of the earth had already been nailed down by other methods.
This is true. You can be as abstract and imaginative as you like in fitting a model to data (A seismologist buddy of mine once pointed out that you could make seismo data fit an earth model in which the core was made of butterscotch, if you were so inclined).
But look at how round the moon and the sun are. (and how round earth looks from space. Kepler took years to accept an elliptical orbit for Mars because he was carrying over the ancient idea that an imperfect earth (with mountains and valleys and disease and sin) was in contrast to the perfect heavens, with spherical planets and circular orbits.
So, for the people we’re talking about, the circular shadow of the earth means either (a) a spherical earth, or (b) a flat circular earth. And the horizon effect means a curved earth, which means a spherical earth.
A flat circular Earth will not cast a circular shadow at all angles. It will generally be an ellipse. The ancients used this very point in arguing a sphere as opposed to a disk.
As to “local topography” messing up things, a lot of things counter it. A lot.
E.g., the length of day and the changes of length of day cannot be explained by anything on a local scale. The ancients knew that in the far north the Sun never rose above the horizon. And then understood this was because the Earth was round. A flat Earth has the same length of day everywhere. In fact, a late/early sunrise due to having a mountain range nearby is an inverse explanation. E.g., someone in Denver on a flat Earth would have an earlier, not later, sunset than someone in Kansas City.
But I think the OP boils down to how do we prove the Earth is not flat given methods at the time they thought it was and so there is a certain assumption that it is local not global data that we can use.
We have already dispensed with earlier sunrise at elevation and different angle of the sun at different latitudes. Those can easily be explained using a flat Earth model and anyone still claiming those work should reread my earlier posts.
We have the ship at sea method but how would that work if you are not by the sea?
We have measuring the angle of the Sun at various latitudes (at least three) but we have to account for how far the ancient could reasonably travel, the accuracy of the equipment and understanding trig.
The Bedford Level looked interesting but again, do the local conditions have a flat canal/stream? Also interesting was how due to atmospheric refraction it was used to prove the Earth was flat.
I have checked all your posts in this thread and not a single one actually “dispensed with” any such thing. Yes, elevation will change the time of sunrise, a very little bit. In order to explain the vast differences in time of day the elevation has to be really, really big, i.e, on the scale of the curvature of the Earth! I.e., your alleged elevation argument is in fact a curvature argument.
And how does elevation (on the scale of mountains, not Earth’s curvature) change why the Sun never rises on the solstice in far northern climes?
The incredible absurdity of this argument is explaining why the elevation is mainly a north-south effect. Someone on a mountain top and someone down at the base will experience fairly similar length of days. But someone on a mountain top a thousand miles north will experience a much shorter day in the winter than someone at sea level in the south. Something is uniformly bent, it’s the Earth. Get used to it.
The argument that was dispensed with was: an earlier sunrise/later sunset can ONLY occur on a curved Earth.
And I don’t know how you think elevation creates a “vast difference” in time of day. Assuming a radius of 8000 mi., at 10’ the angle of depression to the horizon is 0.0394 degrees. At a 1000’ the angle of depression is 0.39425. The Sun travels approximately 0.0042 degrees every second yielding a sunrise just under 1 min 15 seconds earlier or a total of 2.5 minutes more daylight for that 1000’ elevation. Did the OP allow us to take two precise watches back in time?
Now what I will admit is that those angles and elevations give a distance to the edge of the Earth 10 times larger at 1000’ than 10’ - but that “proving” the Earth is curved means having a device capable of precision of at least hundredth of a degree and keeping with the OP, did such a device exist back when the Earth was believed flat and would that civilization understand the trig involved.
So your point is that in the modern world with modern equipment and modern mathematics we can with local measurements prove the Earth is curved? Well OK but I don’t see how that answers the OP.
I really don’t know what’s going on with Saint Cad.
Apparently logic isn’t going to work here.
Look, precision is not needed to tell that the length of day at two places at the same latitude but different elevations are fairly similar. While length of day at places at different latitudes can vary greatly. You don’t need a stopwatch to notice that the sun barely goes down in summer and barely comes up in winter in northern Europe. Meanwhile the difference between day and night is modest in southern Egypt regardless of time of year.
“Precise watches” my foot.
If SC can’t understand something so simple and straightforward, then I give up.
The radius of the earth is ~4,000 miles, not 8,000.
Umm why don’t you understand I didn’t discuss daylight at different latitudes but SAME latitude DIFFERENT elevation and that more daylight at elevation at the same latitude can occur on the flat Earth.
I also pointed out that while the curvature of the Earth is provable using measurements at different latitudes, would the distance needed to travel vs. the precision of instruments be ruled out by the ground rules in the OP.