Science starts with measuring something. You need to quantify so you can study the phenomenon.

The simplest astronomical measurement is angle between two objects. This does not involve the distance to the objects. Such an angle between two things is said to be "on the sky." Sixteenth century observers could make angle measurements with simple non-telescopic devices. They had no telescopes because the telescope wasn't invented till the early seventeenth century.

When something is so far away as to be inacessible, distance measurment gets difficult. The technique used involves triangles. These simple figures are very useful. The triangles used in astronomical distance measurement are called "skinny" triangles, which means that the base is very small and the triangle is VERY long.

The length of the baseline, or base of the skinny triangle, determines the maximum distance you can practically measure. This is why your 3-dimensional vision does not work at large distances - everything seems to be equally far away. If your eyes were 10 feet apart, you'd look very strange, but your stereo vision would work a lot farther than it now does, like 48 times farther. (This is figured with 2.5 inches as the distance between your eyes.)

How to find distance to **very** distant objects? Use triangulation.
Measure the shift (parallax) of object against distant background.

Parallax of stars is measured in seconds of arc. Those angles are REALLY small.
A star so far away that it has a parallax of 1 second of arc turns out to
be 3.26 light-years away. That distance is known as 1 parsec (parallax second).
It's a made-up word. Note that we are talking about an isosceles triangle
with a base of 186,000,000 miles (or 2 AU; see below) and a vertex angle
of 2 seconds of arc. This is a REALLY skinny triangle. It turns out to
be 3.26 light-years (LY) high. The Light Year (LY) is the distance that
light travels in one year.], which is 5.87 trillion (10^{12}) miles.
You can use 6 trillion miles as an easy-to-remember number. By the way,
in light-time, the AU is about 8.5 light-minutes.

This system (the parsec) is based on the diameter of Earth's orbit, because that is the longest baseline we can get. By the way, the average Earth-Sun distance is known as the Astronomical Unit, or AU. It's another way of referring to the radius of Earth's orbit. The orbit diameter is therefore 2 AU.

The distance of an object and its parallax angle are related in a very simple way.

distance = 1 / parallax

So - a star that has a parallax of 0.1 second of arc is 10 parsecs (32.6 LY) away.

Simple.

Note: There are no stars as close as 1 parsec; all are farther than that.

This brings up a practical problem: angles of 1 second or smaller could not be measured till the nineteenth century. Small telescopes cannot measure the shift; it is below the detection limit for them.

The detection limit is the smallest value of something that a particular instrument can measure. If you need to measure smaller values, you need a better instrument.

Since you likely don't have any idea of what 1 second of arc means, let's use something you can see. Next time the Moon is full, look at it. While you do so, remember that the full Moon is about 1/2 degree in angular width. We divide the degree into 60 minutes of arc, and each minute is further divided into 60 seconds, making one degree equal to 3600 seconds of arc. One second of arc is therefore about 1/1800 of the width of the full Moon. That's far too small to detect without precision instruments.

The measurement of stellar parallax was so difficult that it was not done until 1838, when Friedrich Bessel successfully measured the parallax of the nearby star 61 Cygni. To do it he used a precision telescope made by Joseph von Fraunhofer, a premier telescope maker in Germany. Wilhelm Struve also used a Fraunhofer telescope to measure the parallax of Vega.

The scientific method is a vaguely defined method for finding out things about
the universe. Its purpose is to weed out mistakes and avoid fooling yourself.
A scientific **hypothesis** is used to make a testable **prediction**
which is then tested by means of some **observation or experiment**. If the
prediction holds up, then you have support for the hypothesis. If the
prediction does not hold up, you have disproved the hypothesis.

As the hypothesis stands up under more and more tests it can reach the status
of a **theory**, which means that is well-accepted and its predictions
are correct. Note: the word theory is usually misused in the press. There,
something may be described as "only a theory" instead of the more correct
"only a hypothesis." Scientifically, "theory" implies an accepted model.
Important to note: you can never PROVE that the hypothesis/model is correct.
You can omly increase your confidence in it with repeated attempts to disprove
it that fail. As far as proof goes, there is only area where you REALLY
prove something, and that field is mathematics.

Also note the description of Occam's Razor on page 20. It means that, if you
must choose between several explanations for something, choose the simplest one.
It is a **heuristic** and is not guaranteed; heuristics can fail.
Lots of things about the Universe are not simple.
But - old Occam will improve your chances of getting to the right choice.

Notice that the use of Occam's Razor would make the choice between the geocentric model and the Copernican model quite easy.