Skip to main content

About this free course

Author

Become an OU student

Share this free course

Astronomy with an online telescope
Astronomy with an online telescope

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

1.2 Exploring the magnitude scale

To explore the magnitude scale in more detail, let’s take a look at where some familiar objects appear on the scale.

In Figure 2, the magnitude scale has been extended to include objects far brighter than the stars – including Venus, the Moon and the Sun. Being extremely bright, these have very large negative magnitude numbers.

In order to cover such a wide range of brightness, the magnitude scale works on a logarithmic principle. This is a mathematical term meaning that each step along the scale multiplies the brightness by a certain amount, rather than simply adding a fixed amount. Specifically, a change of five magnitudes represents an increase or decrease of 100 times in the brightness – so that for example, a magnitude +1 star is one hundred times brighter than a magnitude +6 star.

Breaking this down into individual steps along the scale a change of one magnitude is equal to an increase or decrease of approximately 2.5 times in brightness.

[Many other scales work on this logarithmic principle in order to cover a wide range – the Richter scale for earthquakes and the decibel scale for intensity of sound are two other examples of logarithmic scales. In both cases, each step along the scale represents a multiplication in the value being measured.]

Activity 2 Caculating the difference in brightness of stars

Timing: Allow approximately 5 minutes

Two stars have magnitudes of +2.0 and +4.5 – a difference of 2.5 magnitudes.

How many times brighter is the magnitude +2.0 star than the magnitude +4.5 star ?

Answer

The stars differ in brightness by a factor of 10. To work this out, remember that a difference of 5 magnitudes multiplies the brightness by a factor of 100. Two steps of 2.5 makes a total change of 5 magnitudes, so each step of 2.5 magnitudes must multiply the brightness by 10. In this way, two steps of 2.5 gives a change of 10 × 10, which is 100.