Powers of Ten and Units

Astronomers have to deal with very large distances and masses. It is inconvenient to express these numbers as, for instance, one million million million million million (which is about half the mass of the Sun in kilogrammes!). Instead, we use powers of ten . This is easier to demonstrate than explain. Very simply, the number above could be written as a 1 followed by 30 zeros. The shorthand for this is to say ten to the power of thirty . This is written as 10¹⁹. Some more examples are given below.

An extension to this is if we have a number like three million million (a three followed by twelve zeros), this can be written as 3x10¹², which is pronounced three times ten to the power of twelve

Another way we deal with big numbers is to change the units we use. You would not give the distance between Stoke and Stafford in inches you would use miles! Astronomers use light years for distances, which is the distance travelled by a ray of light in one year. One light year is roughly equal to 10¹⁶ metres, so it saves us a lot of zeros! The distance to the nearest star is 4 light years.

For weights (more properly called masses), astronomers use the mass of the Sun as a unit. This is actually a 2 followed by 30 zeros in kilogrammes, or in our new notation, 2x10³⁰ kilogrammes. So, the mass of the Sun is one solar mass. A star that is ten times as heavy as the Sun is ten solar masses. A similar system is used for brightness or luminosity . The Sun has a luminosity of 1 solar luminosity. This is equal to about 4x10²⁶ Watts in metric units. Our Galaxy emits as much light as ten thousand million Suns, so it has a brightness of 10¹⁰ solar luminosities. Some more examples of these quantities in the Universe are shown in this diagram, which shows mass, distance and luminosity for a variety of objects.