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.|
For very small numbers, such as the mass of the proton,
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 1.9890033 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.
4.3 x 106 x 2 x 102 = 8.6 x 108
4.3 x 106 x 2 x 10-2 = 8.6 x 104
4.2 x 106 ¸ 2 x 102 = 2.1 x 104
4.2 x 106 ¸ 2 x 10-2 = 2.1 x 108
42 x 106 = 4.2 x 107
4200 x 106 = 4.2 x 109
42 x 10-6 = 4.2 x 10-5
0.42 x 106 = 4.2 x 105
0.000043 x 106 = 4.3 x 101
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.
4.2 x 106 + 6.4 x 105 = 4.2 x 106 + 0.64 x 106 = 4.84 x 106
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 1011 + 9.4 x 1010 = 9.2 x 1011 + 0.94 x 1011 = 10.14 x 1011 = 1.014 x 1012
4.2 x 106 - 6.4 x 105 = 4.2 x 106 - 0.64 x 106 = 3.56 x 106
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 1011 - 9.4 x 1010 = 1.2 x 1011 + 0.94 x 1011 = 0.26 x 1011 = 2.6 x 1010