Reddit reviews Chasing Venus: The Race to Measure the Heavens

First came the size of the Earth. That was done around 240 BC by Eratosthenes.

Then a whole lotta nothing happened till Kepler who figured out some rough orbits for planets that was proportional, but didn't have exact figures. But he did have the P^2 = a^3 thing going which was cool since it meant if we could get the orbital distance from the Sun for one planet, we could standardize the formula and make it work for all planets.

Then Newton came along and tweaked Kelper's 3rd law by noting it wasn't quite that simple because masses of the objects mattered. But barely since the Sun is so much more massive.

Then in the late 1700's, Venus was set to transit the Sun a few times. By observing the transit from different points on Earth, astronomers were able to use parallax to determine the exact distance to Venus and the Sun. By 1771, French astronomer Jérôme Lalande had come up with the distance to the Sun being off by only 2%. (Good book on the topic)

Once we knew the Earth-Sun distance, we could again use parallax to get distances to nearby stars by observing them when Earth was in different parts of its orbit for a long baseline. The hardest part was knowing which stars to choose as a target since many stars don't show much as they're far away. At the time, many astronomers thought all stars were the same intrinsic brightness and therefore, brighter ones must be closer. Turns out not so much. Ultimately, the first successful attempt was in 1838 for 61 Cygni. Several others followed soon afterwards. (Another book on that topic)

This is a long answer, but you need to know a bit of the history of astronomy to understand how astronomers figured out how to calculate the distances to stars. Astronomy is the oldest science there is. It goes back to the most ancient civilizations, the Messpotamians were looking up at the sky and studying it. Even they noticed that the stars were not all there was. The stars themselves, sure, lots and lots of dots. But there are also 5 planets, the sun and the moon and all of those things move across the sky as time passes. The stars all moved together, but the planets were different. They didn't follow the same path across the sky as the stars did.

Ancient thinkers like Aristarchus and Eratosthenes calculated surprisingly accurately the circumference of the earth and the scale between the earth, the moon and the sun. The used measurements from lunar and solar eclipses, geometry, etc to make really, really good estimates for the time.

In the 1400's or so, attempts to understand what we saw in the sky were made by people like Johannes Kepler. He saw the sky as layers of geometric shapes or crystal like... things, that rotated around the earth. A model he build looked like this with earth in the center, the sun above it, the moon above that, mars above that and so on until you got to the stars which was the biggest enclosure. He tried for many years to figure out why mars retrograded, that it appeared to stop, move backwards, stop, then move forwards again over time in the sky. He eventually figured out that it was because the planets didn't move in perfect circles like people thought, but that they moved in elipses or ovals

Nicolaus Copernicus was one of the first to propose that the earth revolved around the sun, and not the other way around, using what Kepler figured out which was that the planets do not move in circles, but elipses (ovals).

Galileo Galelie with an understanding of Keplers and Copernicus' work was the first person to point a telescope (invented a few years earlier by someone else) at Jupiter in the sky. He discovered that Jupiter had 4 moons that orbited around it and he could observe and measure it. This was further proof that the earth went around the sun and not the other way around.

There are also sometimes rare events, which give us invaluable information used to calculate astronomical distances. One such event being a transit. That's when one of the planets close to the sun, Mercury or Venus, passes in front of the sun from earths point of view. Here it is in 2012 Astronomers could use this information to calculate the distances to the planets, and determine the size of the solar system. In 1761 and 1769 Hundreds of scientists from all across the world planned for the transit. Some traveled half way across the world, not an easy feat in the 1700's to get the data. Then they all collaborated it (which took years) and this gave us a much better understanding of the size of the solar system and the distances involved.

In the late 1700's William Herschel and Charles Messier were cataloguing stars and nebula. It turns out that what looks like just dots with the naked eye have a lot of differences when viewed through a telescope. Some are brighter, some dimmer, some are bigger, some are smaller and even some of different colors. Many stars will also fluctuate in how bright or dim they are over time, like a very slow pulse. It also turned out there were objects that weren't stars in the sky. But they were too dim to see with the naked eye and only visible in a telescope. Messier cataloged over 100 galaxies and nebula and produced a guide still used today. The telescope also enabled astronomers to figure out that there weren't about 5000 or so stars that we could see with the naked eye, as everyone in history before then thought, but that there were millions upon millions (and as telescopes got better, billions upon billions) of other stars, too dim to see with the naked eye. All this can be measured, recorded, compared and calculated. The invention of the telescope gave astronomers lots and lots (and lots and lots) of data to work with.

Here's where we get to the specific of your question.

In the late 1800's Henrietta Leavitt employed as a "computer" (someone who just "computes", or records, analyses and does the math of data collected about stars) discovered the relation between the luminosity and the period of Cepheid variable stars. She figured out how to determine the distance to astronomical objects. First calculating the Large & Small Magellanic Cloud, two small galaxies outside that were thought to be just clouds of dust.

Edwin Hubble, namesake of the Hubble Telescope used Leavitt's data and method to figure out that the universe was expanding, by measuring the redshift of galaxies outside our own. This was the biggest step towards the big bang model of the universe.

These are only really the top names and discoveries. Many scientists during all that, and up until now have worked together to figure out how to determine the size of a star, what the stars are made of, how they work and what they actually are, and how to figure out how far apart all those little dots are.

But what we know about the universe today is everything learned in many fields across lots and lots of time. If you're really interested in a great "history of science, what we know and how we know it" I'd recommend A Short History Of Nearly Everthing by Bill Bryson. It does a great job of explaining all this and more in easy to understand laymen terms.

Here are some books about astronomy. (Not how-to on astronomy)

Coming of Age In The Milky Way

Chasing Venus

The Hole In The Universe

Atom

Miss Leavitts Stars

Pale Blue Dot Sequel to the original book, Cosmos.

Death By Black Hole