11/15/99Norm Herr (sample file) The Inverse Square Law and the distance to stars. As a result of this law we can determine how far away a light source is if we know its intrinsic luminosity – or the rate at which it radiates energy per second – and measure its brightness when its energy reaches us..This is the basis for the second method for measuring the distances to distant stars and galaxies. For example, if we observe two stars, each of the same luminosity, but one 100 times brighter than the other, then the brighter object must be 10 times closer.

11/15/99Norm Herr (sample file) Luminosity of an object and its brightness We can relate the luminosity of an object to its brightness as follows: Consider a star which radiates its light equally in all directions. The brightness of any object is really a measure of its flux, or the amount of energy from the object incident per unit area (I.e. per square metre), per second. This brightness depends on the distance of the object from us, d. Lets assume that the object radiates its energy at a rate of L (I.e. L joules per second). Then, at a distance d, this energy must be radiated into an area of 4  d 2 Therefore, we can relate the intrinsic luminosity, L, to a stars brightness (or flux), and distance (d), via Flux = L /4  d 2

11/15/99Norm Herr (sample file) So, if we measure the brightness of the star, and know its luminosity, we can easily calculate its distance. The only problem is - how do we know the luminosity of the star ? Luckily, there is at least one class of star for which the intrinsic luminosity can be calculated: the so-called CEPHEID VARIABLES. These are stars that pulsate, and their period of pulsation depends on their luminosity. So if we measure this period, we know the luminosity of the star. Combining this with a measure of their brightness (flux), we can then estimate their distance from us. Using these stars, it has been possible to measure the size of our Galaxy, and the distance to other galaxies too. In fact, this is one of the fundamental methods astronomers have of investigating the size of the Universe around us.