Flux and the Inverse Square Law

Flux is the amount of power going through a unit area. This diminishes with the square of the distance.
This is simply a geometric effect expressed as:



fluxCredit: Cosmoswhere F is the flux, L is the Luminosity and r is the distance to the star. This is called the Inverse Square Law because flux decreases with the square of the distance.



Stars appear in the sky to have a particular brightness but the actual energy output of a star may be vastly different to what we see.



torches1Two torches at same distance


As a practical example, if someone takes two torches, one bright and the other one not so bright and walks to a distance of say 50 m, then we will see the bright torch still brighter than the less bright one, but both are less bright than at a closer distance.


torches2Brightest torch (left) now further away


If you now leave the less bright one at that distance and walk further say to 100 m with the bright one, that bright one may now look fainter than the one that was left at a distance of 50 m.

If we don’t know the distance to the torch (or a star), the brightness we see (we call that apparent or relative brightness) may give a wrong indication of the actual brightness.





The brightness of the torch or of a star diminishes with distance according to how the flux diminishes with the Inverse Square Law.


This means that if the distance increases by a factor of two, the brightness diminishes by a factor of two-squared or four. If the distance is tripled, the brightness decreases with a factor of three-squared or nine, etc.





 So how can we find the distance to a star with the brightness that we observe?

The method of finding distance we are going to discuss is based on assumptions about the luminosity of the star.
Suppose we know the luminosity (L in the image), then with the Flux (brightness that we observe) we are able to calculate the distance with the Inverse Square Law.


In astronomy it is common to express brightness not in Flux but in Magnitude. So let us discuss that first.