I still don't quite understand the whole process but I'll talk about what I do! But if you don't want to listen to me talk, you can go ahead and read my reference. And before we measure the radius of the Sun, we need to measure the distance to the Sun. Or atleast that's how it was done in the olden days.

So, to start, Halley envisioned a way to estimate the distance to the Sun, using the transit of Venus across the Sun. Depending on what latitude one observes from, the time taken by Venus to cross the Sun is different. If one records the time taken and has an estimate of the drift velocity of Venus, in radians per sec, one can estimate the distance between the two paths Venus takes across the Sun's surface. How to estimate the drift velocity of Venus you ask? Well, we know that it takes the Earth 365 days to complete 360 degrees and that it takes Venus 242 days to do the same. We can therefore estimate the relative velocity with which Venus drifts away or comes towards us. And using this, one can estimate the distance between Earth and Venus (this is where I am stuck!).

Coming to the distance between the Sun and the Earth, it can be written as the sum of the distance between Sun and Venus and Venus and Earth. The distance between Sun and Venus was estimated to be 0.72 times that of the distance between the Sun and the Earth. How you ask? Kepler's third law of course, which relates the time taken for a celestial body to complete one full revolution to it's distance from the center of revolution. We know the time it takes for the Earth to go around the Sun and astronomers were also able to measure how long it takes Venus to go around the Sun (one more thing I need to look up!). Using this, they were able to relate the distance between the Sun and the Earth and the Earth and Venus. Okay, I need to be more quantitative than qualitative. Sigh...

But well, you understand how I can estimate the radius of the Sun once we have an estimate of the distance to the Sun, because we know that the angular size of the Sun is approximately half a degree.

On a serious note, this is getting interesting. I need to make proper notes of this, after I make sense of it. While I was searching for how astronomers estimated the distance to the Sun, I came across similar estimates and methods used for the rest of the planets. It's all geometry, trigonometry and sheer brilliance! I never realized that the lower rungs of the cosmic distance ladder were this interesting. Actually, I thought the lowest rung was stellar parallax, but then even to reach that step, we need the value of One Astronomical Unit i.e the distance between the Sun and the Earth!

Apart from the link I provided at the beginning of this post, there were a few other articles I found online that were of (a bit of) help. Some of them are 1, 2, 3, 4, 5, 6.

So, to start, Halley envisioned a way to estimate the distance to the Sun, using the transit of Venus across the Sun. Depending on what latitude one observes from, the time taken by Venus to cross the Sun is different. If one records the time taken and has an estimate of the drift velocity of Venus, in radians per sec, one can estimate the distance between the two paths Venus takes across the Sun's surface. How to estimate the drift velocity of Venus you ask? Well, we know that it takes the Earth 365 days to complete 360 degrees and that it takes Venus 242 days to do the same. We can therefore estimate the relative velocity with which Venus drifts away or comes towards us. And using this, one can estimate the distance between Earth and Venus (this is where I am stuck!).

Coming to the distance between the Sun and the Earth, it can be written as the sum of the distance between Sun and Venus and Venus and Earth. The distance between Sun and Venus was estimated to be 0.72 times that of the distance between the Sun and the Earth. How you ask? Kepler's third law of course, which relates the time taken for a celestial body to complete one full revolution to it's distance from the center of revolution. We know the time it takes for the Earth to go around the Sun and astronomers were also able to measure how long it takes Venus to go around the Sun (one more thing I need to look up!). Using this, they were able to relate the distance between the Sun and the Earth and the Earth and Venus. Okay, I need to be more quantitative than qualitative. Sigh...

But well, you understand how I can estimate the radius of the Sun once we have an estimate of the distance to the Sun, because we know that the angular size of the Sun is approximately half a degree.

On a serious note, this is getting interesting. I need to make proper notes of this, after I make sense of it. While I was searching for how astronomers estimated the distance to the Sun, I came across similar estimates and methods used for the rest of the planets. It's all geometry, trigonometry and sheer brilliance! I never realized that the lower rungs of the cosmic distance ladder were this interesting. Actually, I thought the lowest rung was stellar parallax, but then even to reach that step, we need the value of One Astronomical Unit i.e the distance between the Sun and the Earth!

Apart from the link I provided at the beginning of this post, there were a few other articles I found online that were of (a bit of) help. Some of them are 1, 2, 3, 4, 5, 6.