When looking at stars that are relatively 
close to Earth, there is another 
phenomenon that we are going to see. 
and that is that, 
the old statement that stars are fixed on 
the celestial sphere is not precisely 
true if you look close enough. 
Of course, stars in general in the sky 
are in orbit. 
They're moving in all kinds of 
directions. 
They're very far so their motions are 
typically minimal when you convert them 
to angular. 
measures but nearby stars are, if 
measured precisely enough, are observed 
to move relative to the distant stars. 
This is called proper motion. 
It is the term for the motion of the 
stars. 
And this is a motion over and above the 
annual oscillation that nearby stars 
perform due to parallax. 
But even if you subtract parallax, you 
observe that relative to the background 
stars there's an on going continual 
motion. 
This is due to the actual motion of the 
stars. 
So we can measure the motion of the star. 
it's characterized by the Greek letter 
mu, and mu is typically expressed in 
arc seconds per year, because those are 
the, useful units, for the 
the typical orders of magnitude of proper 
motion, and. 
When we're looking at an object, notice 
that an object can't be in motion and 
have zero proper motion if it's moving 
right at us or away from us. 
And so when. 
looking at an object, we define a plane 
called the transverse plane. 
The transverse plane in this image, is 
this direction and the direction 
perpendicular to it, coming out of the 
page towards us. 
And, a radial direction so there's a 
plane here, and then there's a radial 
direction, which is the direction along 
the line. 
From us, to the star. 
And, we think separately of radial 
motion, that's motion towards us or away 
from us which does not change the star's 
position angular in angular terms in the 
sky. 
And, transverse motion, which is motion 
along the sky, relative to the other 
stars. 
And, proper motion captures any motion in 
the transverse direction. 
And, we can convert, if we know the 
distance to the star, we can convert the 
angular motion, of course, to measure of 
its actual velocity, its actual 
transverse velocity which is label by VT. 
And 
basicaly the idea is imagine waiting a 
year, 
the star's positioned in the sky will 
have changed by an angle mu. 
If we know it's distance, which I call, 
capital D on like this diagram that the 
small angle formula, tells me that the 
little distance D that it travels. 
In the course of a year is D * mu and 
this is its motion in web units. 
Well if I write mu divided by 206, 265 
arc seconds. 
Then, this is a number D will be in 
whatever units you measure capital D 
distance to the star. 
If you write it this way. 
but since this is in arc seconds per 
year, I will get an answer for the 
velocity when I 
this, this number, is the distance the 
star travels in a year. 
that'll give me say, parsecs per year, as 
the units in which I measure the 
velocity. 
Typically, we measure velocity in a more 
convenient units of kilometers per 
second. 
And so, in kilometers per second, one 
finds that V In kilometer per second, 
is basically given by mu divided by one 
arc second times D in parsec times a 
collection of 
convertion factors converting parsecs to 
kilometers and years to seconds. 
And the net result is that the conversion 
factor you can do the algebra is 4.74. 
So that's the meaning of this rather 
dimensionally confusing expression that 
we have here. 
this is only a measure of stars' 
transverse velocity. 
A star can also have an a radial 
velocity. 
We can measure its radial velocity up by 
measuring the Dopler shift. 
If you find some spectral line, we find 
its shift. 
if you're careful you will notice that I 
have changed the sign here of the radial 
velocity relative to our convention, the 
previous convention that I used when I 
explained the Doppler shift, is the one 
common among when studying sound. 
This convention is the astronomical 
convention. 
A positive radial velocity here means 
that lambda is bigger than lambda zero. 
That's a redshift. 
A positive radial velocity represents a 
star moving away from us and that's the 
convention we will follow from now on. 
So that if I'm looking at a star, and 
it's over here then the radial velocity 
is a measure that I get from the Doppler 
shift measures this component of its 
motion, the tangential velocity measures 
this component of its motion, and this 
represents a star that is doing both 
motions at the same time in other words, 
moving in some diagonal direction. 
And that way, I can get a complete 
picture of the motion of the star. 
And just to give you an illustration of 
the dramatic effects over the long term 
of proper motion, most stars move 
relatively slowly, but if you give them 
enough time, things get interesting. 
This is an animation of the constellation 
that we now call the Big Dipper. 
this is not the way the Big Dipper looks. 
This is as it would have looked from 
earth in 100,000 BC were you to look at, 
at it and time runs rather quickly here, 
but you see the stars moving. 
we are approaching the present. 
Here we have the Big Dipper. 
The stars of the Big Dipper are a 
constellation. 
They are not a cluster. 
They are not near each other in the sky, 
in any sense. 
And over time their peculiar motions as 
it's called will completely change the 
appearance of a constellation. 
It will not stay the way it is. 
Stars do move, if you give them time.