Since Astronomy is one of the oldest sciences, it has developed many traditions over the years. While an astronomer would not hesitate for an instant to apply cutting-edge technology at the telescope or computer, the language and units of measurement in the field change much more slowly. So, as you set out to investigate the Universe with us, let us introduce you to a few words, units and short-hand that you'll encounter here.

As we have seen in class, the important numbers in Astronomy span
almost 40 orders of magnitude in size. Consider
the mass of the Sun:

It's cumbersome, to say the least, having to write out all of those zeros. Even kilograms (eliminate 3 zeros) or metric tons (eliminate 6 zeros) don't help much. Furthermore, we really don't know the Sun's mass beyond the accuracy of the fourth digit. All those zeros are just place-keepers, carrying no useful information. For this reason, scientists use a short-hand called Scientific Notation to express very large or very small numbers. |

The number above the ten, called the

For very small numbers, such as the mass of the proton,

we use negative powers of 10. The mass of the proton becomes

For negative exponents, the powers of 10 are after the decimal point; 10

In both of the examples above, the **coefficient** (the part before
the times sign), contains 4 digits. This means that there are
4 ** significant figures** in the number. If, for example, we knew the Sun's
mass to 6 significant figures, we would say that its mass is
1.98900^{33} grams.

There are several good web pages about Scientific Notation. If you would like to read a bit more, try out the University of Maryland's Astronomy Programs site, with a Scientific Notation Exercise and an Astronomical Distance Calculator.

A centimeter is pretty small - not a very practical unit for the
enormous distances in the Universe. If
Astronomer A had to use centimeters to tell Astronomer B the distance to the
Sun, it would look like this:

There are three special units of distance used by astronomers. These
are the *astronomical unit (AU)*, the
*light-year* and the *
parsec*. The astronomical unit is the average distance of the Earth
from the Sun shown above.

A *light-year (ly)* sounds like a measure
of time, but it is a length - the distance light travels in one year.(We
can use a light-year as a unit of measure because ALL light travels at the
same speed; it is a fundamental constant of the Universe. More about this
later...) So, in one year, light travels:

The name *parsec* comes from the technique of measuring distance called
parallax, and will be introduced later.

- A number written in
**scientific notation**consists of a**coefficient**(the part before the times sign) and an**exponent**(the power of 10 by which the coefficient is multiplied. For example, in`4.3 x 10`(which equals 4,300,000; four million three hundred thousand), 4.3 is the coefficient and 6 is the exponent. Sometimes the "times" symbol "^{6}`x"`is replaced by a dot, for example`4.3∙10`.^{6} - When you
*multiply*two numbers, you*multiply*the coefficients and*add*the exponents. For example,

4.3 x 10^{6} x 2 x 10^{2} = 8.6 x 10^{8}

4.3 x 10^{6} x 2 x 10^{-2} = 8.6 x 10^{4}

- When you
*divide*two numbers, you*divide*the coefficients and*subtract*the exponents. For example,

4.2 x 10^{6} ¸ 2 x 10^{2} = 2.1 x 10^{4}

4.2 x 10^{6} ¸ 2 x 10^{-2} = 2.1 x 10^{8}

- When you move the decimal place in the coefficient one position to the
*left*(i.e. you divide the coefficient by 10), you*add one*to the exponent. For example,

42 x 10^{6} = 4.2 x 10^{7}

4200 x 10^{6} = 4.2 x 10^{9}

42 x 10^{-6} = 4.2 x 10^{-5}

- When you move the decimal place in the coefficient one position to the
*right*(i.e. you multiply the coefficient by 10), you*subtract one*from the exponent. For example,

0.42 x 10^{6} = 4.2 x 10^{5}

0.000043 x 10^{6} = 4.3 x 10^{1}

0.42 x 10^{-6} = 4.2 x 10^{-7}

You should always adjust the decimal place in the coefficient so that the coefficient is always greater than one but less than ten. Mathematically it doesn't make any difference, but that is the standard practice, and it does make a number easier to read.

- When you
*add*two numbers, you need to*make their exponents equal*. Take the number with the smaller exponent and move the decimal point to the left until its exponent matches the larger. Then*add*the coefficients and*keep*the (matching) exponent. For example,

4.2 x 10^{6} + 6.4 x 10^{5 }= 4.2 x 10^{6} + 0.64 x 10^{6 }= 4.84 x 10^{6}

4.2 x 10^{-6} + 6.4 x 10^{-5 }= 0.42 x 10^{-5} + 6.4 x 10^{-5 }= 6.82 x 10^{-5}

9.2 x 10^{11} + 9.4 x 10^{10 }= 9.2 x 10^{11} + 0.94 x 10^{11 }= 10.14 x 10^{11} = 1.014 x 10^{12}

- When you
*subtract*two numbers, you again need to*make their exponents equal*. Take the number with the smaller exponent and move the decimal point to the left until its exponent matches the larger. Then*subtract*the coefficients and*keep*the (matching) exponent. Note that you might have to adjust the exponent when you are done to get into "standard form." For example,

4.2 x 10^{6} - 6.4 x 10^{5 }= 4.2 x 10^{6} - 0.64 x 10^{6 }= 3.56 x 10^{6}

4.2 x 10^{-6} - 6.4 x 10^{-5 }= 0.42 x 10^{-5} - 6.4 x 10^{-5 }= -6.38 x 10^{-5}

1.2 x 10^{11} - 9.4 x 10^{10 }= 1.2 x 10^{11} + 0.94 x 10^{11 }= 0.26 x 10^{11} = 2.6 x 10^{10}

- WARNING TO PEOPLE WHO USE CALCULATORS: Many calculators handle
**scientific notation**. The exponent is usually displayed all the way on the right, with a space between it and the coefficient. To enter a number in**scientific notation**, you enter the coefficient, press the`EXP`key (one some calculators it is labeled`EE`) and enter the exponent. For example,`4. 05`means 4 x 10^{5 }. To enter the number 10^{3}, you have to enter`1. EXP 03`. DO NOT enter`10. EXP 03`, since that equals 10 x 10^{3 }or 1 x 10^{4}. This is a common mistake. See your calculator instruction booklet for more help.