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Comment by g4zj | Hacker News Reader

This is way outside my area of expertise (if I have one at all), but assuming we know the diameters of the sun, Earth, and our moon, as well as the distance between Earth and our moon, could we not determine the distance between Earth and the sun based on the scale of the shadow Earth projects onto the moon during a partial lunar eclipse?

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If you know the diameter of the sun you should be able to measure the distance by just measuring the size of the sun in the sky and using some simple geometry. I.e. if the sun takes up x degrees of space in the sky then tan(x) = (radius of sun / distance to sun).

But... how do you measure the diameter of the sun?

If you sent out probes to calculate the travel time of beams of light between two points, but at Lagrange points from one another, and then had them simultaneously slow their orbits to fall into the sun, and considered the "edge" of the sun the point at which it destroyed the probes...

How do you measure the diameter of the sun when your most advanced technology does not include a telescope. And even when it does, but just a telescope about 8x power (approx Gallileo’s first one)

That Copernicus got there at all is incredible

I feel like shadows are the "simple tech" path. It was known since ancient times you can get the circumference of the Earth (remarkably accurately) by doing some calculations based on the angles of shadows from the mid-day sun at two points sufficiently north/south from each other (a fantastic application of trig). Knowing the circumference of the Earth and these angles lets you know the diameter/radius as well which lets you create a "straight line" distance (i.e. not the over the surface distance) between those two points. Using those two points and known angles to construct a triangle with the Sun should let you see it is at least extraordinarily far away, even if your measurements are relatively innacurate.

By looking at it through a tinted glass, and noting down the apparent size of the core disk, then assume its a sphere, and calculate the diameter from that?

How to measure the distance? Easy, compare the apparent size to the actual size and calculate the distance from that. Then how do you measure the actual size? Easy, multiply the apparent size by the distance!

>How to measure the distance?

We already know the distance. About 8 light minutes away.

The question of the parent comment was "how do you measure the diameter of the sun?"

In the context of having just explained "this is how you get the distance from the diameter" in the broader context of "from first principles and simple technology"...

Why did those silly 18th century physicists even bother with those sextants and complicated mathematics when they just could have looked up the answer on Wikipedia?

Because they didn't have it. We have it. Imagine that!

The article has a whole section about how there's no way to know the distance to the sun in light-minutes to use as an input to figuring out how big it is

I didn't reply to the article though.

Done; the sun is a 7cm disk 10m above my head

Quickly disproven by seemingly parallel shadows "everywhere".

Oh, that makes a lot of sense. Thanks for explaining! My solution was far too complicated. :)

The problem is that the only way we have of knowing the Sun's diameter is to know its distance and then calculate its diameter from its apparent size.

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