So, using closely looking at the stars 
and making some measurements and thinking 
about it, we can actually measure the 
mass of stars. 
And we can ask, 
we're almost ready to start modelling. 
We need to know where do the masses of 
stars along the main sequence line up 
with their masses. 
And so, we can add masses into our plot 
for the main sequence. 
And here's what we learn, masses don't 
vary very much. 
way down here, down where the red dwarves 
reside, masses of stars, we discover, are 
as small as a tenth of a solar mass, but 
not much smaller than that. 
And the biggest, most luminous, hottest, 
main sequence stars top out at 50 solar 
masses. 
We rarely find anything even up there. 
And so, by measuring a few stars along 
the main sequence, we can figure out the 
mass of a point along the main sequence. 
The main story is that the 
heaviest amounts stars are the hottest 
and the most luminous. 
And now, we can fit it into the model. 
Because when you're going model of star, 
basically, if you say a star is a ball of 
hydrogen, I don't need to tell a good 
model or the luminosity of the radius. I 
would tell them take a bottle of 
hydrogen, 
held up on in hydrostatic equilibrium 
against its gravitational attraction by 
hydrogen fusion, and then run your 
equation. Now, in practice, that's a 
little bit difficult. 
But in principle, nature knows how to do 
that. 
So, if you give nature a ball of hydrogen 
of a given mass, it'll produce a star, 
and that star will lie somewhere along 
the main sequence. And 
we can now attempt to study modeling. 
We'll discuss the results of that in our 
next clip. 
But first, let's note that there's a very 
reasonable approximation you can do 
better but the luminosity along the main 
sequence scales with mass. 
As I said, the heavier stars are more 
luminous and it scales like the three, 
third, three and a half, or fourth power 
of mass. 
It's not exactly fixed relation you can 
improve this, and go into the details, 
but this is good enough. 
What this means is that a ma, a star that 
is twice as massive as the sun has a 
luminosity between eight and sixteen 
times the luminosity of the sun. It's way 
more luminous, this is how change from a 
tenth of a solar mass, to ten solar 
masses, gives us this five orders of 
magnitude or seven orders magnitude 
change in luminosity. 
Now, this sort of makes and are models 
bear this out. A heavier star has more 
pressure from the outer layers crushing 
down on its core, the pressure in the 
center is higher, densities in the center 
are higher. 
We said that fusion proceeds best at high 
temperatures and densities, and that 
means the rate of fusion in a big star 
will be higher. 
That's the way that mass is going to 
determine the rate of fusion. 
And so, it makes sense that bigger stars 
will be more luminous. 
But note, 
that if say, the core of a star like the 
sun, we estimated how long the sun would 
last by saying, if it converted all of 
it's hydrogen to helium, it would last 
100 billion years. 
But, the sun will actually stop 
converting hydrogen to helium when it has 
converted a tenth of it's hydrogen 
because that's the amount that will be 
available in the core. 
If all stars had a bout a tenth of their 
hydrogen available in the core, what this 
would tell us is that big stars run out 
of hydrogen much faster than slow stars, 
and indeed, appended to this table of the 
main sequence is a list of main sequence 
lifetimes adjusted. Remember, right over 
here, the sun has a main sequence 
lifetime of about ten billion years and 
stars with te, luminosity ten times that 
of the sun, it turns out only last a 
billion years. And up here, the really 
bright type O and B stars might last only 
ten or a few million years, and the 
lightest red dwarfs last hundreds of 
billions of years. 
What that tells us is that if we see a 
type O main sequence star, since they 
only live, two, three, five, ten million 
years, 
that star is brand new. 
When the sun was formed five billion 
years ago, that star was nowhere near to 
existing. 
So, when we see, say in Orions belt type 
O stars, we know that very recently stars 
have been forming there. 
And we'll see what modeling tells us and 
conclude the week and the last clip of 
the week now.