The mods have changed the title, which absolutely is fair enough, and this one is more descriptive. So "thank you" to the mods for doing that.
In the interests of full disclosure, this specific post is how to calculate your latitude from watching a shadow on a wall. To calculate the size of the Earth you need to combine that with the earlier posts:
Incidentally and on an vaguely related note, Pytheas (that I mentioned here: https://news.ycombinator.com/item?id=18801645 ) also was the first recorded to measure latitude using a gnomon.
Slightly related, but in the Hanuman Chalisa by Hindu poet-saint, Tulsidas, who was born in 1497, mentioned that the distance from the earth to the sun is approximately 108 times the width of the sun.
yuga sahasra yojana para bhānū
līlyo tāhi madhura phala jānū
yuga-sahasra-yojana = 12000 x 1000 yojanas.
Yojana is a Vedic measure of distance and approximately equals to 8 miles (according to the 14th century scholar Parameshvara, the originator of drgganita system). And 1 mile = 1.60934 kilometers.
According to the calculation presented in Hanuman Chalisa
Distance between Sun and Earth = 12000 x 1000 yojanas = 96 million miles = 153.6 million kms, which is much closer to the calculation of modern science.
The Sun's angular size is about 0.5 degrees. If A is the angular size of the Sun then the distance to the Sun is 1/sin(A).
Using the rough figure of 1/2 a degree, that makes the Sun about 114.6 times as far as its width. You can measure it more accurately and get a better figure.
You don't need modern trigonometry to do this - part of the point of the linked post is how to do these calculations without knowing about modern trigonometry, just using distances and ratios.
For the lazy, when an angle is small you can just approximate sin(theta) with theta. Theta of course has to be in radians. So 0.5 degrees is .0087267 radians. sin(0.5 degrees) is .0087265.
Putting it all together, 1 / (0.5 * Pi / 180) = 114.6.
That would be child's play compared to the claim that they were doing plastic surgery and full head transplants even earlier. The claim was made , among others, by the current prime minister of India -- I kid ... not.
I agree that what Eratosthenes did was brilliant, but it relies on being able to travel and measure large distances. The whole point of these techniques is that they can be used simply on the beach front without having to travel.
Seriously, if you can get to a beach, you can do this.
Yes it cannot be considered the same method, but my guess is that who is interested in this more advanced method absolutely need to know the Eratosthenes method. I absolutely need to use the method in this post with my children, one of the most powerful showcase of science I can think of.
Interestingly, a misinterpretation of his measuring units misled columbus to think that earth was way smaller than what it actually was(which is why nobody gave him proper funds, the 3 ships were a pity compared on portuguese expeditions to india) and discover with a fluke a new continent for european powers
Also, I believe if we're being pedantic, this causes issues:
> However, because the Moon (and to a lesser extent the other planets) cause the motion of the Earth to vary from a perfect ellipse, the equinox is now officially defined by the Sun's more regular ecliptic longitude rather than by its declination. The instants of the equinoxes are currently defined to be when the longitude of the Sun is 0° and 180°.[4] There are tiny (up to 1¼ arcsecond) variations in the Sun's latitude (discussed below), which means the Sun's center is rarely precisely over the equator under the official definition. The two understandings of the equinox can lead to discrepancies of up to 69 seconds.
Yes indeed - "Equinox" us being used here as a shorthand for "the date that makes this work, which is roughly Equinox, but might be a little different".
The differences are small, there are larger error margins elsewhere in the calculations as given. It's an interesting exercise to start to chase these down and make this as precise as possible, but that wasn't the purpose of the post.
It's not a trick, you can do it, but the geometry and the calculations are more complicated. At Equinox we don't have to know or worry about the axial tilt. Away from Equinox we do have to both know it and use it.
It's not hard, but there's a lot more too it, so it starts to lose its elegance and simplicity.
In the interests of full disclosure, this specific post is how to calculate your latitude from watching a shadow on a wall. To calculate the size of the Earth you need to combine that with the earlier posts:
https://www.solipsys.co.uk/new/TheRadiusOfTheEarth.html?sa03...
https://www.solipsys.co.uk/new/RadiusOfTheEarthPartTwo.html?...
However, the title is a good 'un, and again, my thanks to the mods.