So first step, in trying to figure out 
more about how stars work, is going to be 
to figure out how far they are. 
Because, how we interpret what we see, 
which is a point of light, 
depends greatly on how far we think that 
point of light is. 
That will tell us how to read and 
interpret the information we see. 
So how do you measure the distances to 
stars. 
Well, you use a method that has an old 
and ancient and storied pedigree and was 
well known to the ancients. 
It was called Parallax and you probably 
used this to solve some high school 
algebra problems. 
So, the picture here is of someone stuck 
on a road here trying to estimate the 
distance to the boat out in the lake, and 
what this person notices is that as they 
move along the road, 
and you can see on the right what they 
see, 
The position of the boat, though the boat 
is not moving, it appears to move 
relative to the more distant shore, 
opposite shore of the lake. 
And so when I stand here for example, the 
boat line appears to me to be lined up 
with this tree at the top of the hill and 
when I move over here the boat appears to 
line up with that mountain. 
The boat didn't move but by drawing the 
lines. 
from me to the boat, whose angle changes? 
I see the boat obscuring different parts 
of the different scenes and by doing some 
calculations I can figure out the 
distance to the boat from trigonometry. 
So, we could try to do this, if we had a 
star that is playing the role of the 
boat. 
And who would play the role of the 
opposite shore? 
Well, the boat point is that, some very 
small number of stars are near to us. 
Why is that, or is the number of stars 
near to us small? 
Only because most of the universe is far 
from us. 
And so, most of the stars we see are very 
far, some of them are nearer. 
The ones that are nearer can play the 
role of the boat. 
The part, ones that are farther, much 
farther, will play the role of the 
opposite shore, and as I move my 
observation point the stars that are 
nearer will move relative to the more 
distant stars. 
Well that's very nice. 
That's in fact the way that I measure 
distances, you know, as I walk around and 
try not to hit walls I compare what my 
right eye sees to what my left eye sees 
and this difference in perspective, in, 
in the angle, this parallax, as it's 
called, tells me how far things are. 
The problem is that stars are very far 
away. 
the views seen by my two eyes are 
completely identical. 
The lines from my eyes to the star are 
parallel. 
And I can't distinguish the distance to a 
star with my eyes, what I need are eyes 
spaced farther apart, 
or two observatories very far apart. 
Stars are so far apart that no matter 
where you put two observatories on Earth, 
measuring the difference in the way the, 
sky appears from two points on Earth. 
you will not obtain accurate parallax 
measurements. 
I need observatories that are even 
farther away than the size of the Earth. 
The easy way to do this, and the best, 
reliable way to do this is simply to stay 
in the same observatory, and allow the 
Earth's motion around the Sun to carry 
us. 
Because, remember, that over the course 
of a year, the Earth's motion carries us 
300,000 mile kilometers from where we are 
now to where we will be in six months, 
around the Earth's orbit. 
There's the way to get distant 
observatories. 
And so using this method, we apply this 
in, as follows. 
We have here, the Earth moving around the 
Sun, we have a star that is nearby 
playing the role of the boat. 
We have distant stars, way farther away, 
playing the role of the fixed stars. 
And we observe that relative to the 
distant stars, as the earth moves in a 
circle, this star move, appears to move 
in a circle in the sky relative to the 
fixed stars. 
And the geometry of the situation allows 
us, if we can measure this angle P. 
So, the angle P is this angle P. 
It's the radius of the, of apparent 
circle in the sky. 
Not the diameter the radius. 
Of the apparent angular circle in the sky 
that the star appears to move in relative 
to the distant stars. 
And if I measure this angle, and if I 
imagine that the distance to the star 
from the Earth or the Sun, stars are so 
far away that the difference is 
irrelevant, is d, then, since I know that 
this side of this triangle is just one 
astronomical unit. 
It's the radius of the Earth's orbit. 
I could use my small angle formula. 
My small angle formula tells me that one 
AU divided by D. 
Is the angle P, divided by 206, 265 
arcseconds. 
I'm interested in finding these, so I'll 
invert both sides and write this as D, 
divided by one astronomical unit, is 206, 
265 arcseconds, divided by P. 
most stars will be many astronomical 
units away, 
so their paralex angle will be much 
smaller than an arcsecond, and you need 
precise measurement to obtain parallax 
angles. 
But in principle it's doable. 
Let's rewrite that cleanly. 
The distance of in astronomical units to 
a store is 206265 arc seconds divided by 
it's parallax angle which remember is the 
radius of the circle that appears to 
inscribe in the sky. 
this definition is very useful, it 
inspires in fact the invention of a new 
distance unit, a parsec. 
And one parsec is defined to be 
approximately, I'll define it exactly in 
a minute, 206,265 astronomical units. 
The reason that we use this definition is 
that then, if I divide both sides by this 
crazy number, I find that the distance to 
a star in parsecs is exactly one arc 
second divided by its parallax angle. 
And this is, in fact, the precise 
definition of a parsec. 
A parsec is that distance at which a star 
sub, has a parallax angle of one arc 
second. 
A star at a distance of ten parsecs has a 
parallax angle of one tenth of an arc 
second. 
The farther the star, the smaller the 
parallax angle, as we expected. 
So here's that expression written 
cleanly. 
And this is what a parsec means. 
And it, 
we'll often use parsecs to measure 
distances. 
And this is great. 
I can define the geometry. 
Can I actually measure it? 
the definitions in the geometry were 
known to the ancients. 
The first successful measurement of a 
parallax angle to star was by Bessel in 
1838. 
And this is an important thing because 
once you the measure a distance to a star 
and you realize there are other stars 
that are farther, 
this is the end of the celestial sphere. 
We now are beginning to build an actual 
3-dimentional universe. 
Building a 3-dimentional universe, 
understanding the distances to things, is 
going to be a light motif. 
Something we'll come back to again and 
again in this class because interpreting 
what we see depends on critically on how 
far we think it is. 
In particular, as an example to 
understand what a parsec really is, well 
I told you what a parsec is it's the 
distance at which the parallax angle is 
one arcsecond. Well how many meters is a 
parsec? 
Well to know that I have to know the 
parsec is 206,265 astronomical units, 
what's an astronomical unit? 
Well. 
Astronomical unit is the radius of 
Earth's orbit, or now it's defined some 
other way. 
More importantly, how do I measure the 
radius of Earth's orbit, which is what I 
really need. 
Well, to measure the radius of Earth's 
orbit, 
initially you make whatever measurements 
you can that, that, the way Kepler did. 
Our best measurement today involves 
measuring the distance from Earth to 
Mercury in a given moment by bouncing 
radar waves from a, 
an antenna on Earth off of Mercury, and 
measuring the time of flight. 
Multiply by the speed of light. 
Divide by two. 
You have a distance to Mercury, or to 
Venus at a particular instant. 
And since we know the relative distances 
in the solar system very well from 
Keppler's laws. 
This tells us how much an astronomical 
unit is in meters. 
Use that to defi-, determine parsecs. 
We'll later use parsecs to define other, 
distance measurements. 
We're building the first steps in what it 
called the cosmic distance ladder. 
The point I want to emphasize is that 
every time somebody improves the 
precision of a measurement low on the 
rung, 
that improves the precision of everything 
above, that depends on it. So for 
example, parallax angle, as a measure of 
distance, depends on how well you know an 
astronomical unit. 
Obviously measuring distances to stars is 
important, it is so important, that in 
1989, the Hipparcos mission was launched, 
with the express purpose. 
It actually spent about a decade in space 
with the express mission, of measuring 
the parallax angles to as many stars as 
it could, of course, to the stars near 
us. 
And if a host produced initially a 
catalog of 120,000 stars, 
that catalog's been expanded. 
We now got 2,500,000 stars to which we 
have reasonably reliable distance 
measurements. 
So this is great. 
We now have a whole ball around Earth. 
More distant things perhaps not but a 
whole ball around Earth where we can 
build a three dimensional atlas, that's 
what Hipparcos catalog is. 
It's a three dimensional atlas of at 
least our local neighborhood, the, 
data is so important that a Gaia mission 
is planned to launch in 2013 with the 
express purpose of vastly extending the 
Hipparcos catalog. 
Hipparcos produced many useful scientific 
observations, also the following 
beautiful image. 
these are two images of Sirius, 
and it's stellar neighbors taken in two 
seasons. 
And if you look at them carefully, you 
will see that Sirius is farther to the 
left in the image on the right and 
farther to the right relative to the 
nearby stars in the image on the left. 
In fact, this is one of those serial box 
images. 
If you relax your eyes, it's best to 
print this and look at it from just the 
right distance. 
the images of the stars will merge and 
you will see, be seeing a three 
dimensional picture of the region of the 
sky near Sirius using the your brain's 
interpretation of 
the images in your two eyes, and this is 
just simply produced by the images that 
Hipparcos took at two different times of 
year.