When talking about Scale Models in astronomy, we're not talking about assembling small versions of spaceships or the solar system. We're putting together a mental model of scale so that we can compare things that are too big or too small for our minds to really grasp. Here is an interesting example regarding the number of stars in the universe:

Scientists estimate that there are 10²¹ stars in the universe. That's 1,000,000,000,000,000,000,000. Try to imagine how big that number is. Can you think of anything that truly relates what 10²¹ means? So can you really fathom how large this number is? Not really. Hence the scale model:

Know that there are 100,000 to 150,000 hairs on an average human head. Let's just say that there are 100,000 to account for bald people. There are roughly 6,374,589,428 people on the planet, and just to make things easier, we'll round that to a even 6 billion.

Now- Take all of the people and shave all of the hair from their heads. Collect all of the hair and chop each piece into - literally - a million pieces.

Do you now have more pieces of hair or more stars?

Look at the math:

10⁵ hairs * 6×10⁹ people × 10⁶ pieces = 6*10²⁰ pieces of hair.

There are about 4×10²⁰ more stars than hairs. Almost double. Cool, huh?

Try this one:

Atoms are pretty small, somewhere between .25 and 3 Angstroms(Å). A hydrogen atom is 25 picometers (pm), which is .25 Angstroms (100pm = 1Å).

How small is that exactly?

Well, 1000pm = 1 nanometer (nm).
1000nm = 1 micron.
10⁴ microns = 1 centimeter (cm).
So, 1 cm = 10¹⁰pm

Therefore, if you were to line up Hydrogen atoms end-to-end across the face of a quarter, which has a diameter of 2.495 centimeters (cm), you would need 2.495×10¹⁰ hydrogen atoms. That's 24 bilion: 24,950,000,000.

To figure out the space occupied by a quarter:
Quarter's radius in pm = 2.495cm × .5 × 10¹⁰ = 12475000000pm
Quarter's area = radius² × pi = 12475000000² * pi = 488912320210320066356pm²
Quarter's height in pm = 3mm × 10⁹ = 3000000000pm
Quarter's volume = area × height = 1466736960630960199068000000000pm³

That's roughly 1.4×10³⁰. Divide that by the size of a hydrogen atom (25³pm = 15625pm³) and you get about 10²⁶ hydrogen atoms.

The conclusion is that hydrogen atoms occupying the volume of a quarter are more numerous than all of the stars combined. One hundred thousand times more atoms than stars.

This type of relationship can be useful when thinking about radiation.

The use of scale models is not limited to astronomy, but you'll find that in astronomy we talk about things that are so large and so small so often that we tend to use a lot of scale models just so that we can understand these things a bit better.

If all the gold ever produced in the world, some 125,000 metric tons, were stacked on the site of New York's Empire State Building, the pile would stand a mere three and a half feet high. [[http://www.geoinvestor.com/archives/fpgarchives/march3000.htm]]