00:01
Here we're going to two stars which have the same apparent brightness b and are of the same size.
00:04
Star a has a wavelength of light that peaks around 750 nanometers, or star b peaks around 450 nanometers.
00:10
We want to find the relative distance to us.
00:13
In other words, we want to find the ratio between the distance to a and the distance to b.
00:18
So to do this, we can first find the temperatures of each of these stars using venus displacement law, and then using the stefan boltzmann law, find the flux emitted by each star.
00:30
And then, given that they are of the same size and same apparent brightness, we can relate them using the inverse square law, which will tell us that the proportion between the squares of their radii is equivalent to the inverse ratio between their luminosities, their absolute luminosities.
00:47
So we'll begin with venus displacement law.
00:50
If you want to rearrange this to find temperature, given that this concept, we'll just call it k.
00:56
So if lambda equals k over t, we can rearrange and find t equals k over lambda.
01:01
And that means that stefan boltzmann law, we can write the flux j star is sigma, stefan boltzman constant, times k over lambda to the fourth power.
01:11
We know that the luminosity of a star, and this is with the black body approximation, the luminosity is going to be the area of that star, the surface area, times j star times the flux...