This is an introductory astronomy survey class that covers our understanding of the physical universe and its major constituents, including planetary systems, stars, galaxies, black holes, quasars, larger structures, and the universe as a whole.
Distances and Scales
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演变中的宇宙
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從本節課中
Week 1
Welcome to The Evolving Universe!
與講師見面
S. George DjorgovskiProfessor
Astronomy
All right, well, welcome again.
So today we will talk about three different things.
We'll talk about distance scales, in space, and how do we start measuring them.
And we'll talk about Kepler's Laws and where do they come from, and that will be
an interesting simple application of physics onto astronomical phenomena.
And then we'll talk about coordinate systems in the sky,
because that's sort of how we find our way around.
So let's begin with the distances and scales.
First, let me introduce some of the commonly used units, and
this is some of the very few numbers, that you will actually have to remember.
First, the distance.
The basic distance unit that we use, is the astronomical unit.
And it's the semi-major axis, so we can say radius, or
Earth's orbit around the sun.
And it's about 150 million kilometers.
So this is what's commonly used inside a Solar system.
Then of course, you know about light years.
Well, we never use light years.
That's just the popular astronomy unit, instead of that, we use Parsecs.
And Parsec is defining this weird fashion, that this is a distance
from which the radius of Earth's orbit, that is one astronomical unit.
Subtends an angle of 1 arc second, which is a teeny tiny angle.
And that turns out to be about 200,000 astronomical units.
Also, 3.26 light years, so we can always convert that.
So if I say, some galaxy is about 20 megaparsecs away,
how many millions of light years is this?
Anybody else?
20 million times 3.26 right, so they'll be about 17 million light years,
that means light took 17 million years to come from there to here, and
that means it started when dinosaurs were ruling the earth.
In this immediate neighborhood, if you will.
[COUGH] All right, one thing that you should remember is that Parsec's about 3
times to the 18th centimeters.
Astronomers used CGS units because they got used to them before,
as SI units became fashionable, but for sure we don't use imperial system.
So since you all know how to convert from centimeters to meters and
so on, I'll be usually using centimeters.
Now later in the class, we'll also be using units of mass and luminosity.
Mass is kind of fundamental parameter for many astronomical objects.
And we usually use solar mass as a unit.
And that turns out to be 2 times 10 to the 33 grams.
Also good number to remember.
Now all of these will of course be available to you on the website, so
you can always refer to them.
But if there aren't any, you should remember these.
And the sun shines and its volumetric luminosity, meaning if you add up over all
wavelengths, is about 4 times 10 to the 33 ergs per second.
Now, can somebody tell me how many gigawatts is this?
Whoever guesses, that gets a prize.
All right, how many ergs per second are in a watt?
One?
ten?
Million?
10 million?
Yes?
No?
Yes.
Now, for sure you need to convert that.
So, a joule is ten to the seven ergs and so,
four times ten to the 33 ergs per second,
would be four times ten to the 26.
Lots, and I asked for gigawatts.
So that would be few times ten to the 17 gigawatts.
A nuclear reactor produces about a gigawatt.
So sunshine's at the rate of about billion, billion nuclear reactors,
per second.
Okay, [INAUDIBLE] numbers to remember,
we'll work more with those on Friday during the sections.
So let's take a quick tour of the universe to put these scales into context.
One astronomical unit, obviously, is the distance between the Earth and
the Sun, and other planetary distances are kind of commensurate to it.
The outermost real planets, not dwarf planets,
are about fifty astronomical units from the sun.
And so that kind of defines the inner solar system.
But, much beyond that, there is first a thing called Kuiper Belt and
then a thing called Oort Cloud which is more spherical, and
that consists of little bits and pieces that they're left over from
making solar system, they're mostly chunks of dirty ice.
Sometimes, they get into the inner solar system, develop tails, and
we call them comets.
Well at Oort's cloud is inferred from dynamical arguments, and so
we're pretty sure it's there.
From the rate that comets are coming, and that's about 1,000 astronomical units out.
This is where we can think that sorta interstellar space begins.
Now, some people are thinking that the Sun
may have a companion dwarf star, which was even given the name Nemesis.
And the idea was, that every 70 million years, or sorry I forget,
23 million years, doesn't matter.
The orbit of Nemesis brings it close enough,
to give a tidal kick to a whole bunch of comets.
And then we have a shower of comets coming into the inner solar system,
when they hit planet Earth, they cause mass extinctions.
And so that's apparently what did dinosaurs in.
Now it's probably true, that it was an asteroid or
a comet impact that did dinosaurs in, but
the existence of Nemesis is pretty much excluded by now, from direct observations.
Okay, how far are the stars?
The picture here, is actually the closest start to us, it's called Proxima Centauri.
And it's a little dwarf companion of the much more famous and
brighter, Alpha Centauri.
And, anybody knows how far that is?
How far is the nearest star?
>> [INAUDIBLE] >> Yeah, that's right.
How many parsecs is this?
>> [INAUDIBLE] >> Yeah, okay.
One and a half, roughly speaking.
So that's the nearest start.
So nearest stars to the earth are from a few parsecs up on outwards.
And the most distant stars you can see with the naked eye,
those would be super giants, far away, are up to about kiloparsec.
Globular clusters,
which are very popular astronomical object, tend to be few kiloparsecs away.
Few to few tenths.
So, if the stars are of the order of parsecs to kiloparsecs away,
how many astronomical units is this?
Yeah, anybody?
Couple hundred thousand is one Parsec, that's right.
And so, multiply from there.
So, interstellar separations are vastly bigger
than the size of a solar system, and even more so
compared to the size of the stars, which is why stars almost never collide.
They do in some very special conditions, in some very dense stellar systems.
But by and large, if you mush two galaxies together,
they'll just pass through each other.
And that loss gap.
So, this is what our galaxy is roughly like,
a picture taken from Starship Enterprise.
Sorry, I forgot we cannot use that, so it's an artist conception.
And our solar system is about eight kilo parsecs away from the galactic center.
And that's pretty well established number by now,
we'll go over how that's measured later.
Our milky way galaxy extends to maybe 20 to 30
kilo parsecs in radius, now depends on what you call end.
They don't have real end, they kind of fuzz out, and
if you count all of the dark field or not.
But that's roughly the size of a good, big disk galaxy.
Few tens of kiloparsecs.
And, the nearest other galaxies to us are first,
there are dwarf galaxy satellites of the Milky Way.
The two famous ones discovered by Magellan
back in early sixteenth century are Magellanic Clouds.
And those are two dwarf galaxies that are about 50 kilo parsecs away, so
about the size of the Milky Way, away from us.
Other dwarf galaxies are roughly similar distances from us,
but the nearest big galaxy sort of commensurate with Milky Way is
the Andromeda, also known as Messier 31 and that is 700 kilo parsecs away.
How many light years is this now?
Yeah, I'm sure we can multiply small integers.
All right, so it's a little over 2 million light years away.
So light from Andromeda,
the one we just took in this picture, started two million years ago.
All right, and
then our immediate extra galactic neighborhood continues to the Virgo
cluster, which is center of a bigger structure called a local super cluster.
We'll go over that later.
And that is about 16 million parsecs away.
So 16 times 3.26, well, that's kind of pushing 60 million light years, so
yeah, some dinosaurs were probably still walking around when this light started.
Okay, so the extra-galactic world is tens of millions of parsecs away,
and parsecs is roughly the distances to nearest stars, and
those are about million times the size of the solar system.
Yes?
>> Speaking of distance as a size, approximately how big
are the constellation [INAUDIBLE] >> Okay,
the question is how big are the constellations.
Well, the question doesn't have a well defined answer,
because constellations are just projected images on the celestial sphere.
They're not physical groupings of stars.
And so stars that are parts of some constellation,
could be at vastly different distances from us, and in fact they are.
And then of course depends on where you choose.
So in Orion,
typically I think those stars would be few hundreds of parsecs away from us.
And the size of Orion, it's in tens of degrees,
so one gradient is fifty some degrees, so
those would be like small fraction of a radian, let's call it tenth of a radian.
And so then the distance to Orion would be ten times a couple hundred degrees.
A couple hundred parsecs.
That's about right.
Constellations are something that used to be popular,
they are just expression of Human need to see patterns in the sky,
patterns anywhere, stock market, sky, doesn't matter.
And they are arbitrary, they are just mnemonic device,
used to help people navigate and also set up the calendars.
They also produced very productive industry of astrology.
Which is making lot of money out of nothing.
And some death sentences like Facebook, right?
>> [LAUGH] >> But
constellations do not have physical meaning.
We still use them in some cases, because originally when
astronomers started charting the sky, they started giving names to stars and
other things according to in which constellation they happened to be, so
a star will be called Alpha Signi or something like that.
And a variable star might be called a [INAUDIBLE] and so on and so forth.
Okay, so let's step even further.
This is picture of one of the ultra deep fields done by the Hubble Space Telescope,
so called Goods field,
and every little bright dot you see there is a very distant galaxy.
Typical distance is a few giga parsecs from us.
So, furthest features of observable universe are of the order of
10 giga parsecs.
Well, it depends, what do you mean how far?
Because in expanding universe, that can have different meanings, and
we'll address those.
But anyway, think of 10 giga parsecs.
So this is 10 billion, times distance to the nearest stars.
Well, the universe is big.
I told you that.
So let's kinda roughly scan through this logarithmic scale, what's where.
Let's now talk about how do we actually measure that.
Well the first step in measuring how far stars and
other things are, is trigonometric parallax.
And that was figured out even by ancient Greeks.
Now parallaxes are too small, and they couldn't possibly measure them so
they knew that stars are far away, so did Galileo.
And, the idea here is that if there is a star,
like the one hanging above the solar system, and then you look at it
six months apart, the angle of that line of sight will change a little bit.
And here it's grossly exaggerated.
Right?
The stars are much, much, much further out.
So that typical parallaxes will be tiny fractions of an arc second.
All right.
Because if that star was one parsec away,
what would be the size of this parallactic angle?
What was the definition of a parsec?
>> One arc second?
>> Yeah, Ella.
That would be one arc second.
But this closer than Proximus Centauri,
so stellar parallaxes will be all smaller than an arc second.
This is a very hard angle to measure.
Because even in best telescopes,
atmospheric blur makes stellar ranges couple arc seconds in size.
And so you have to center that, and then compare with many others, and so on.
But, this is the only real way of measuring
interstellar distances and beyond.
Everything else gets calibrated on the basis of the stars to which we do measure
through [INAUDIBLE] parallaxes, because this is pretty simple geometry.
Everything else is some indirect manner, and as we go along,
I'll point out some of the ways this is done.
Today, state of the art is about one milliarcsecond.
So we can, in principle, measure distances out to a kiloparsec or thereabouts.
Okay, well, the history of this was astronomers keep trying to do this,
because up until well, 19th century,
we actually didn't know how far the stars are.
We just knew they're far away.
And the first one to succeed was Bessel, a mathematician, astronomer, physicist.
And he measured parallax to the historical 61 Cygni.
Constellation as one.
And he got it within a few percent, right.
So it's about three parsecs away, so pretty close.
But even since then, things got better and better, and
from the ground based measurements, using optical interferometers,
and things like that, we can do a milliarcsecond but only over small scales.
In order to do better than that, you have to be free of Earth's atmosphere.
And this is why now the frontier of astrometry, which is part of astronomy
that deals with measurements of stellar positions and such, is moved to space.
The first space mission that made a real difference here is called Hipparcos.
It was launched by the European Space Agency.
And it scanned the sky for a few years, and
measured parallaxes to about 100,000 stars with the milliarc second precision.
And that was completely revolutionary at the time, so
that let us recalibrate all manner of astrophysical distance scales.
Now, just launched, is a better version of it, called GAIA.
And the GAIA will scan the sky for several years, and
will measure parallaxes of billion stars going up to maybe 10 kiloparsecs.
And that gets to be vastly more interesting, because you can see even
faster galactic center, you can see to globular clusters with that.
And it will certainly improve our understanding of the galaxy and
stellar astrophysics as well.
So anyway, the current state of the art is a few hundred parsecs,
maybe 1,000 in best cases, but that's sort of immediate neighborhood, because
we remember, Earth is eight kilo parsecs away from the center of the Milky Way.
So we're just measuring distances within our immediate galactic neighborhood,
never mind the extra galactic world.
