You will recall that, value of Hubble's 
constant, was fairly unsettled all the 
way through 1980s. 
The reason for this, is that, these 
measurements are difficult. 
There are so many different relations, 
then one has to be calibrated against the 
other, and there are many opportunities 
for errors. 
And systematic errors in particular. 
And that resulted in the values of Hubble 
constants scattering by a factor of 2, 
which means that distances will be also 
uncertain by a factor 2 and things like 
luminosity by a factor of 4 and that, 
clearly, was not a satisfactory 
situation. 
So when the Hubble space telescope was 
launched, measuring Hubble constant was 
seen as one of it's key goals and it was 
a subject of a so called distance scale 
or Hubble Constant key project. 
This took ten years of very diligent 
measurements using Hubble space 
telescope. 
And even today Hubble space telescope 
continues to be used for this purpose, 
improving the results. 
The idea here was to observe Cepheids in 
a number of nearby spiral galaxies, and 
the reason why Hubble was needed is that 
these stars are faint, and they're in 
crowded fields, so the superb resolving 
power of HST was needed in order to 
actually measure their brightness and 
populate their light curves. 
Then, using the locally calibrated 
Cepheid relation, understand the distance 
to these galaxies and then use those to 
calibrate other things such as 
supernovae. 
A choice was made to use the distance to 
the Large Magellanic Cloud to establish 
The zero point to the Cepheid period 
luminosity relation. 
You recall that, that was the original 
discovered period luminosity relation by 
Henrietta Leavitt, and it still plays a 
role. 
And so any uncertainties in the distance 
to the Large Magellanic Cloud would then 
map directly into the inserted piece in 
the Hubble. 
Constant. 
Now not only did this team perform 
wonderful measurements, but they're also 
very careful about their analysis, and 
they tried to honestly account for every 
source of error they can think of. 
And the final result is shown here. 
Hubble constant turned out to be right in 
the middle of the disputed interval 
between 50 and 100 kilometers per second 
per megaparsec. 
It's 72 + or - 3 in just random errors, 
but also + or - 7 kilometers per second 
per megaparsec plus potential systematic 
errors and that's an honest result. 
In fact this is still perfectly 
consistent with all of the more modern 
measurements, Note, however, that there 
is still dependance, on the assumed to 
the [UNKNOWN] clouds. 
And that is osmething that people 
continue to improve. 
So here is a sample image of what they 
were looking at. 
The picture on the left, is 1 of the 
spiral galaxies used in their study, and 
superimposed on that, is an outline of 
the field of view of the camera, of a 
space telescope, that was used. 
This was the original White field 
Blanthery camera, and has the strange B2 
bumper shape. 
The picture on the right, shows a zoom 
in, on one of those images, with some of 
the candidates Cepheid's circled. 
As you can see, this would be a very hard 
thing to do from the ground. 
Some of these Cepheid's, occur in 
star-forming regions, so there may well 
be other bright stars that are blended 
with them and that has to be taken care 
of. 
And here are some light curves of 
cepheids discovered by the key project. 
These represent many measurements of 
different times that we folded together 
into the best fit period. 
And you can see that those really look 
like those of nearby cepheids. 
So here are some Hubble diagrams they 
obtain in the end. 
The bottom left one shows only that one. 
For galaxies, whose distance was derived 
from Cepheid's. 
The one on the right includes all 
possible calibration sources they could 
come up with. 
And here is a table that accounts for 
different sources of uncertainty in their 
measurement. 
I'm just showing for information only, 
and you can see how many things they can 
think of And here is their final error 
probability distribution around hubble 
constant This is actually a good 
scientific way of presenting result. 
It's not a number, it's a probability 
distribution for that number The peak 
value is the one that's quoted and the 
width of that distribution is indicative 
of that uncertainty. 
People continued, to try to determine 
Hubble constant, using any 1 of the 
number of methods and combinations of 
different indicators and callibrators, 
and here is again, a table of those. 
Not there for you to remember all of it, 
but just to see how, much the different 
measurements, scatter around each other. 
Most of them are certainly within the 
error bars of the value determined by 
Hubble key project. 
Now recall that the basis for the whole 
thing was distance to the Large 
Magellanic Cloud which is about 50 kpc 
from the Milky Way. 
So the uncertainty of this distance maps 
directly onto the uncertainty on Hubble 
Constant. 
And the distance to The Magellanic Cloud 
was measured many different ways by many 
different authors. 
That alone, has a spread of + or - 10%. 
There is maybe about, 10 different 
methods, by which this was attempted, and 
here is the table that shows some of the 
results. 
Again, not there for you to remember all 
of it, but just to see the, roughly, the 
spread of the numbers, and the accuracies 
that are involved. 
A more important Check, which is actually 
becoming a very powerful new method is, 
as follows: in the neclei, of many, large 
spiral galaxies, there is a massive black 
hole. 
Which, for all practical purposes, is 
like a point mass, just like, 
essentially, all of the mass in the solar 
system is in the sun. 
Now, if we have test particles moving 
around that black hole. 
From measuring their orbits, we can find 
out how far the galaxy is. 
The orbits can be well-assumed to be 
Keplerian. 
And the suitable test particles are 
so-called interstellar masers. 
These are interstellar clouds that have 
very sharp line due to the coherent 
emission, and as they're moving around, 
the center of this galaxy, they can be 
used to measure the central mass, But 
also they can be used to measure the 
semi-major axes of these orbits. 
This was the first case in which this was 
done, since then there have been more, 
and the distance to this particular 
galaxy was found to be consistent with 
that one determined by the Cepheids. 
Now wouldn't it be nice, if we can bypass 
all this messy distance scale ladder 
climbing from one to another and so on, 
and go directly into the tuple flow. 
Well, there're 2 methods by which death 
can be accomplished, that do not require 
any other calibration. 
They're both based on physical reasoning. 
The first one is gravitational lens time 
delay and the second one is so-called 
Senile of Gorbachev effect. 
Whereas these are based on physics, 
they're still very much model-dependent. 
Initially, at least, we are producing 
values that were somewhat lower than that 
when measured by the Hubble Key Project, 
but since then, they have converged a 
little more. 
Any of these small discrepancies can be 
understood in terms of systematic errors. 
So firstly, gravitational lens time 
delays. 
Assuming that we understand the geometry 
of the lensing, and I'll show this in a 
moment, we can in principal derive the 
distance between the lens and the lensed 
object using the measured time delay. 
Modeling the lens geometry is the key 
uncertainty here. 
Because masses responsible for 
gravitational lensing are not always 
perfectly straightly symmetric and there 
can be combination of many potential 
wells of say galaxies in a cluster or 
group. 
So here is how it works,.Here's a 
schematic diagram showing what 
gravitational source might be. 
There is a background source, say a 
quasar, There is a foreground which could 
be a galaxy or a cluster. 
It bends the lights rays coming from the 
original source and One usually sees 
mulitple images, on the sky. 
Each of these images correspond to 
particular path of light rays that came 
around the gravitational lens and there 
will generally difference in length. 
The difference in length would translate 
itself in to a difference in arrival 
times. 
So we are going to see in our ability in 
the place are we will first see it in one 
image And then some time later in the 
other. 
These time delays are typically in the 
range of weeks or months. 
The path difference between different 
rays, assuming that you know, know the 
geometry will scale directly with 
everything else, every other length in 
the system. 
And the ratio of this path difference to 
the, distance to the lens or the source. 
Is also something that the model will 
tell you. 
So by measuring the time delay, 
multiplying by the speed of light, we 
directly measure the difference in the 
path length. 
And if we knew the lens model, we can 
then use it to infer the distance to the 
lens, or the lensed object. 
Synyaev-Zeldovich Effect is something 
entirely different. 
Clusters of galaxies contain galaxies, 
dark matter. 
But also a lot of hot gas. 
Gas that was expelled from galaxies or 
accreted by the cluster. 
And since that gas is in a potential well 
of a cluster, the speed of individual 
particles. 
Protons. 
Electrons has to be such that the kinetic 
energy balances the potential energy. 
It turns out that [UNKNOWN] responds to 
temperatures of millions or tens of 
millions of degrees, which means that the 
gas will emit in the X-rays. 
Now we're looking at the cosmic microwave 
background [UNKNOWN] cluster Cluster. 
The photons of the micro background will 
come through, and some of them will 
scatter off these hot energetic 
electrons. 
In the cases of forward scattering this 
will generally result in an increased 
energy of the photon. 
The energy's been gained from the 
electrons in the cluster.Of course there 
is equal amounts going out from the other 
side. 
So essentially what you see on the micro 
background sky is there's going to be a 
bump that corresponds to this X-ray 
cloud. 
And the entire spectrum of the cosmic 
micro background will be shifted towards 
a somewhat higher energies. 
By measuring that shift We can find out, 
how long was the path? Because the longer 
the path along the line of sight, more 
chances the photons have to be scattered. 
Therefore, we can, derive from this 
measurement directly, physical we can 
measure the apparent size of the cluster 
on the sky. 
In an average, we expect the cluster will 
have the size in radial direction or 
orthogonal to it. 
So since we have observed apparant 
angular size of the cluster in the sky. 
And we know how much that is in physical 
units, the cluster's red shift. 
We can derive the angular diameter 
distance Now, any given cluster is not 
likely to be spherically symmetric, but 
the whole ensemble, on average, will 
probably work out. 
A beautiful thing about this method, is 
that it does not depend, on the distance 
to the cluster itself. 
The source that's observed, is cosmic 
microwave background. 
Cluster could be near by, or it could be 
very far away. 
So the method can work over a very broad 
range of redshift's. 
There are uncertainties in modelling the 
process because the gas could be clumpy, 
there are some density gradients, all of 
that has to be accounted for before we 
can derive the actual diameter of a 
cluster that photon goes through. 
Next we will talk about measurements of 
the age of the universe.