There are two basic things you'll need to understand before you begin with astronomy: Math and Measurement. Before you run away afraid, let me explain what I mean.

In a real explanation of astronomy there would probably be more math than you would care to hear. This book offers a summary of concepts so that you can have a basic grasp of what is going on and how you can find out more. As such, any complex math that appears here should either be very well explained or just taken for granted.

Nonetheless, it's helpful to review a few fundamental precepts of math, just so that you can more easily follow along if it's been a while since your last math class. Don't worry, I'm going to do all of the heavy lifting when the math gets weighty.

Exponents

When you use an exponent with a number, you are saying that you want to multiply that number by itself a certain number of times.

For example, the expression 10² has a base of 10 and an exponent of 2. We read it as "ten to the second power" or "ten squared". This expression has a value of 100 because 10×10=100. This is not the same as 2×10. It is 10 times itself 2 times.

Antoher example: 10⁶ = 1,000,000. One million. This is 10×10×10×10×10×10. Note that the exponent of 10 - in this case it's 6 - is equal to the number of zeros after the 1 in 1,000,000. Easy, huh?

Generally speaking, there aren't a lot of crazy exponents in astronomy. Sometimes you use exponents to figure out the volume or area of a thing and the base changes. An exponent is used in the Inverse Square Law, which is important for determining the strength of light at a distance. You aren't going to be tested on these things, but I thought that it might be nice to understand them a little before we proceed.

Measurement

Here's where you grumpy old fogies always get caught up, and it's the easiest thing to learn: The metric system.

If you were in school when they taught the imperial system (that's the one with feet and inches) exclusively, you might not know the metric system too well. If you know the metric system, it's possible that your parents never heard of it or know what it's all about.

The idea behind the metric system is to have a universal standard to which we tie our measurement. This is what makes the metric system so easy.

Measure What?

Astronomy works on many different scales, particularly distances, sizes, weights, and temperatures. It's often handy to know how much of something you have, how big (or small) something is, and how hot it is. Having a coordinated way to communicate these values allows one astronomer to share data with another astronomer with accuracy.

Mass

In order to measure a thing, it must have mass. The term "mass" refers to amount of matter, or generic stuff, of which the universe is made. Matter can be solid or gas, but it is stuff. Specifically, a vacuum is an absence of matter.

Here is the tricky part: Mass is not weight. What's the difference?

If you have an object with a mass of 10 kilograms, it will be 10 kilograms no matter where you are. Obviously, if mass is a measurement of the amount of stuff that you have, then you wouldn't change the amount of stuff that you have by moving it to some other place. So in space, where things are "weightless", things still have mass. And on other planets, where things are heavier and lighter dependent on the pull of gravity, the mass of an object would remain the same.

Volume

Matter tends to take up a certain amount of space. This is recorded with a measurement of volume. Note that volume is the space that matter occupies, and mass is the amount of stuff that the matter consists of. You can see the difference by comparing equal volumes of water and air. Even thogh the volumes are equal, the air has less mass than the water does.

Temperature values record the average temperature of

Temperature

Can you remember the boiling temperature of water? It's 212°F. (That's "F" for Fahrenheit, invented by Gabriel Daniel Fahrenheit in the early 1700s.) How do you remember this number? It's completely arbitrary. [1]

But in Celcius, the de-facto scientific measuring standard (as are most other metric measurements), the boiling point of water is an easy to remember 100°C.

Look at the freezing point of water. In Fahrenheit, it's 32°F. In Celcius, it's 0°C. Are you starting to get the picture here?

Relating Volume, Mass, and Length

Let me now ask a crazy question. If you have 2 Liters(L) of water (just like they put in a bottle of soda), how much does the water weigh?

If you use the imperial system, it's going to take a while to figure this one out. Assume that you know that 2 L of water equals 0.528 Gallons. How much does a gallon of water weigh?

Without looking for a conversion chart, it's easy for me to tell you that 2L of water weighs exactly 2 kilograms (kg). The conversion is set up so that this is true. Isn't that easy?

You probably won't be too surprised if I tell you that 2L of water will fit into a box with sides having a length and width of 0.2 meters (m). That's the conversion:

1 liter of water = 1 kilogram of water = 0.1 cubic meter of water

Compare that to the imperial system:

1 liquid gallon of water = 8.344 pounds of water = 15 cubic inches of water

You can see one of the reasons why scientists prefer the metric system.

Conversion within metrics

Ok, I'm going to consider you convinced that the metric system is good. But if you've heard people talking about the metric system, you're probably wondering what a centimeter is or maybe what "ml" stands for and how big it is.

The metric system was designed to work on the base of tens. There are a series of word prefixes that denote different powers of ten that when combined with an appropriate suffix denote a size of measure.

Consider a meter. A meter is roughly equivalent to a yard. Two meters is taller than a six-foot-tall person by 5 inches. But say that you wanted to measure that person more exactly.

In the imperial system, you would use inches. In metrics, you need centimeters.

Just like there are 12 inches in a foot, there are 100 centimeters in a meter. The prefix "centi-" means "1/100th", therefore, "centimeter" means "1/100th of a meter". Easy, right?

What if we wanted to measure the thickness of a quarter? This is too small to measure with centimeters, and is very difficult to measure with inches.

If you did use inches, you would use fractions of inches. I don't know about you, but fractions are a math nightmare. Any effort you can make to remove fractions from math that you do is an effort well spent. Instead, let's try using decimals.

A quarter is 0.2 centimeters (cm) thick. That means that it's 2/10th of an inch thick. If we wanted to know how many millimeters that was, we could convert it easily.

The prefix "milli-" means "1/1000th", so a "millimeter" is "1/1000th of a meter". Note that this is 1/10th of a centimeter. So 1cm = 10 millimeters (mm), and our quarter is 2mm thick.

Here are a list of prefixes and what they mean:

• milli- (m) = 1/1000th
• centi- (c)= 1/100th
• deci- (d)= 1/10th
• kilo- (k)= 1000 times

If you combine a prefix with "meter" then you get a unit of length, if you combine a prefix with "liter" then you get a unit of volume, and if you combine a prefix with "gram" then you get a unit of mass (weight).

1m = 100cm. 3L = 30dL. 5kg=5000mg. The conversions are very easy when you know the prefixes.

To relate this a little to exponent math, take a look at these conversions:

• 1km = 10³m
• 4g = 4×10³mg
• 3L = 3×10²cL