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.