First, we need to ask the question of how big is the universe, and that pertains to both spacial and temporal scale. And it involves concept of so called distance ladder, about which in a moment. And the basic unit of distance in the universe is the Hubble length, which is speed of light divided by the Hubble constant. Which is why it's so important to measure Hubble constant today. And the inverse of that gives rough temporal scale of the universe, commensurate with the age of the universe. Now, both of those are completely independent of the parameters that describe matter and energy, that is, the content of the universe, the defined curvature and all that stuff. And so, that's useful because we can separate the measurements of the two. All the distances includes to galaxies, quasars, everything else scale with this H naught. And that's why it was so important to find what it is. Now we can not measure directly, distances to very distant objects so instead of that, we deploy what we call distance ladder. The only real distances that we measure ever are trigonometric parallaxes for stars and as you may recall that's within a kiloparsec or so. It's going to get better with guidance. But everything then is based on that. We use parallaxes to calibrate distances to stellar indicators, and then we use those to calibrate distances to nearby galaxies, and then we use those to calibrate some other relations from more galaxies and of course the errors will add up, but we have no choice. And you want to push this until we can get through the regime when expansion velocity's the dominant velocity, which we call the Hubble flow. Turns out that we can independently estimate age of the universe, at least provide lower limit on it and that provides a kind of handle on what Hubble constant might be. So this is what I mean by the distance ladder. If you look at logarithmic distance scale, right, we can measure parallaxes to nearest stars. And then use methods associated with clusters of stars, like main sequence fitting and things like that to find distances to a whole bunch of clusters within our galaxy, that's now kiloparsecs. Then we can use those to calibrate distances to pulsating variable stars, which turn out to be very useful ways of measuring distances both within galaxies and also nearby galaxies. Then we use those to calibrate distances to galaxies now there are megaparsecs out to some tens of megaparsecs. And we use those to calibrate distances to indicators like super [INAUDIBLE] for hundreds of megaparsecs out. And there is some that can be used on a really large scale, but they're very model dependent. So, not any one of those spans the full range of distances that we need. They just don't exist. And so that's why we have to do this feedback ladder of calibrating one after the other after the other. As you can tell, this is going to be very tricky business because before you know it, your error bars will add up very fast. Amazingly enough, people who use to do this kind of thing never bothered adding up the errors properly. And in astronomy work I'm always joking how Hubble constant was always known to 10% or better, but it's value changed by an order of magnitude since Hubble first measured it. And that's because a lot of systematics were not taken into account. So parallax, as you know, and then the next basic step is we need to have calibrated HR diagram. Which is in itself a good example of what we call distance indicator relation because on the x axis is temperature, or spectral type which is independent of distance. On the y axis is luminosity, which is very much dependent on distance. And so once you calibrate this, you can slide any stellar group until it matches and then from absolute map an apparent figure of how far it is. Most importantly, we do this to calibrate pulsating variable stars that we use. And there are two kinds that are really very useful in particular. Cepheids, which are young, luminous giants that are instability strip in the H-R diagram. And since they're so luminous, absolute magnitude minus 4 to minus 7, we can see them far away, some tens of megaparsecs out, with Hubble Space Telescope. And so this gives us the principle bridge between measuring distances in our galaxy, and measuring distances to a whole bunch of other galaxies. And turns out that these stars obey a very good relationship between period, which is distance independent, and luminosity, which is various. This was first noted by Henrietta Leavitt who founded clouds, they're all in the same distance basically and it does this became one of the basic tools for observational cosmology. Now RR Lyrae stars are population II stars. So they're found in hail and globular clusters. They operate in similar principle but there's horizontal branch equivalent of the red giant branch cepheids. And so they're much dimmer and don't depend very much on, the period doesn't scale very well with luminosity. But nevertheless, they can be used. So this was the basic step that was used to finally achieve the modern value of Hubble constant, which up until the '90s was very much in dispute by sort of factors of two, which is kind of embarrassing. And took lot of observations with Hubble space telescope of nearby galaxies, 18 spirals. They had to find cepheids by taking a lot of pictures and looking for stars that change in brightness just like Hubble first noticed cepheid in M31. As you can tell, this is not going to be very easy. And moreover, the stars tend to be in regions of star formation because they're luminous young stars. So you have to account for extinction, things like that. So after many years of effort, they calibrated different things, supernova and what not and here is the Hubble diagram they got. And the slope of this is the Hubble constant, right? So velocity versus distance. So their value and they did very careful error analysis, was that Hubble constant is 72 kilometers per second per megaparsec, with random errors about 5% and prossible systematic errors about 10%. This is scaled very well to the present day, and they're minor, minor disagreements, if you will, with modern measurements from Plank satellite. But, 70 is as good a number to remember as any.
