[Civitello]

So, without reading, here are my uninformed thoughts on how I would do it:

You could probably figure out the distance by using a technique we use to figure out the distance to nearby stars, measuring the change in position in the sky relative to very far away stars. I think you'd only need to observe two stars to figure out the distance.

Could also use pulsar timing like gps signals to track the location of the Earth throughout its orbit.

Could also take measurements after launching a pair of space probes away from the earth.

[mannykannot]

Unfortunately, the parallax method depends on knowing the diameter of Earth's orbit, which is (except for a factor of two) the value we are seeking. There's also the issue that the change the Sun's position with respect to the stars over six months is about 180 degrees (with some fluctuation, perhaps, depending on where the earth is in relation to its orbit's major axis when the measurement begins), and will be regardless of the Sun's distance.

The distance of Venus was measured by the parallax method during a transit, with a baseline on the Earth's surface. This then yields all the other planets' distances from their orbital periods. This has me wondering why this had not been done for the Sun's distance, and perhaps the first reason to be considered is the difficulty of observing the Sun eclipsing distant stars.

Update: According to Wikipedia [1], Jeremiah Horrocks came up with reasonable figures for both the size of Venus and the distance of the Earth from the Sun from a single observation of a transit, but the article says he made use of a false premise, so does that just mean he was lucky?

[1] https://en.wikipedia.org/wiki/Transit_of_Venus#1639_%E2%80%9...

[ginko]

There was a pretty good CCC talk on this a couple years ago:

https://www.youtube.com/watch?v=HFWV6XAXyx0