Astronomers use many of the same units of measurement as other scientists. They often use meters for length, kilograms for mass, and seconds for time. However, the distances and sizes in the universe can be so big, that astronomers have invented more units to describe distance.

**Astronomical Units:**

Distances in the solar system are often measured in astronomical units (abbreviated AU). An astronomical unit is the average distance between the Earth and the Sun:

1 AU = 1.496 x 10^{8} km = 93 million miles

Jupiter is about 5.2 AU from the Sun and Pluto is about 39.5 AU from the Sun. The distance from the Sun to the center of the Milky Way is approximately 1.7 x 10^{9} AU.

**Light-Years:**

To measure the distances between stars, astronomers often use light-years (abbreviated ly). A light-year is the distance that light travels in a vacuum in one year:

1 ly = 9.5 x 10^{12} km = 63,240 AU

Proxima Centauri is the nearest star to Earth (other than the Sun) and is 4.2 light-years away. This means light from Proxima Centauri takes 4.2 years to travel to Earth.

**Parsecs:**

Many astronomers prefer to use parsecs (abbreviated pc) to measure distance to stars. This is because its definition is closely related to a method of measuring the distances between stars. A parsec is the distance at which 1 AU subtends an angle of 1 arcsec.

1 pc = 3.09 x 10^{13} km = 3.26 ly

For even greater distances, astronomers use kiloparsecs and megaparsecs (abbreviated kpc and Mpc).

1 kiloparsec = 1 kpc = 1000 pc = 10^{3} pc

1 megaparsec = 1 Mpc = 1,000,000 pc = 10^{6} pc

**Powers of Ten:**

The distances and sizes of of the objects astronomers study vary from very small, including atoms and atomic nuclei, to very large including galaxies, clusters of galaxies and the size of the universe. To describe such a huge range, astronomers need a way to avoid confusing terms like "a billion trillion" and "a millionth". Astronomers use a system called powers-of-ten notation, which consolidates all of the zeros that you would normally find attached to very large or small numbers such as 1,000,000,000,000 or 0.0000000001. All of the zeros are put in an exponent, which is written as a superscript, and indicates how many zeros you would need to write out the long form of the number. So for example:

10^{0} = 1

10^{1} = 10

10^{2} = 100

10^{3} = 1000

10^{4} = 10,000

and so on.

In powers-of-ten notation, numbers are written as a figure between one and ten multiplied by a power of ten. So for example, the distance to the Moon of 384,000 km can be re-written as 3.84 x 10^{5} km. Notice that 3.84 is between one and ten. The same number could accurately be rewritten as 38.4 x 10^{4} or 0.384 x 10^{6}, but the preferred form is to have the first number be between one and ten.

Very small numbers can also be written using powers-of-ten notation. The exponent is negative for numbers less than one and indicates dividing by that number of tens. So for example:

10^{0} = 1 |

10^{-1} = ^{1}/_{10} = 0.1 |

10^{-2} = ^{1}/_{10} × ^{1}/_{10} = 0.01 |

10^{-3} = ^{1}/_{10} × ^{1}/_{10} × ^{1}/_{10} = 0.001 |

10^{-4} = ^{1}/_{10} × ^{1}/_{10} × ^{1}/_{10} × ^{1}/_{10} = 0.0001 |

and so on. |

Once again, numbers are written as a figure between one and ten multiplied by a power of ten. So for example, a number like 0.00000375 would be expressed as 3.75 x 10^{-6}.

Some familiar numbers written as powers-of-ten: |

One hundred (100) |
10^{2} |

One thousand (1000) |
10^{3} |

One million (1,000,000) |
10^{6} |

One billion (1,000,000,000) |
10^{9} |

One trillion (1,000,000,000,000) |
10^{12} |

One one-hundredth (0.01) |
10^{-2} |

One one-thousandth (0.001) |
10^{-3} |

One one-millionth (0.000001) |
10^{-6} |

One one-billionth (0.000000001) |
10^{-9} |

One one-trillionth (0.000000000001) |
10^{-12} |

A few websites offer demonstrations of powers-of-ten and the scale of the universe.

### Some examples to try

1. Jupiter is about 5.2 AU away from the Sun. How far is this in km?

2. A star is 4.94 x 10^{13} km away from the Earth. How long will it take the light from this star to reach the Earth?

3. Another star is 3.5 kpc away from us. How far away is it in km and in ly?

4. Star A is 33 pc away, and Star B is 109 pc away. What is the difference in distance between the two stars in ly?

#### Answers

1. 7.78 x 10^{8} km

2. 5.2 years

3. 1.08 x 10^{17} km, 1.14 x 10^{4} ly (or 11,410 ly)

4. 247.76 ly