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.