Are we alone? This course introduces core concepts in astronomy, biology, and planetary science that enable the student to speculate scientifically about this profound question and invent their own solar systems.

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From the course by Princeton University

Imagining Other Earths

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Are we alone? This course introduces core concepts in astronomy, biology, and planetary science that enable the student to speculate scientifically about this profound question and invent their own solar systems.

From the lesson

Properties of Stars

Stars are remarkably simple objects: their mass and age determine the basic properties. This lecture discusses how we determine the distance and luminosity of stars and how this relates to the Star’s size and temperature.

- David SpergelCharles Young Professor of Astronomy on the Class of 1897 Foundation and Chair

Department of Astrophysics

Welcome back.

Today we're going to step away from planets for

a little bit, and talk about properties of stars.

Because if we want to understand planets, we're going to

need to understand more about the properties of their host stars.

So we're going to begin by talking about how we'd measure distance to stars.

How we infer their luminosity.

Their intrinsic brightness.

Define magnitude.

The magnitude scale.

This is a language, that astronomers use.

And I think it's important that you know it.

So that you can understand what people are talking about when we

talk about sixth magnitude stars, or tenth magnitude stars and so on.

And then we'll go over the properties of light.

We'll step back for a little bit, I'll talk about

the physics of light, and then use what we've learned

or reviewed to see how we can determine stars' temperatures

and then classify stars and talk about their overall properties.

In the next lecture we'll take these observations of stars, combine them

with some of the physics we talked about earlier on in the course.

When we talked about atmospheres of planets, and see

how we can use that to construct the history

of a star and look at how the star evolves over timeand space.

So let me begin by how we measure distance.

We talked about transits.

We described how you could use transits to determine the astronomical unit.

The distance between the sun and the earth.

So we now have this ruler.

1 AU in hand.

With that ruler, we can now measure the distance to the nearest stars.

And the way we do that, is an effect that,

I think that I'd like you all to try at home.

Hold up your finger like this, close first your left eye.

Then your right eye.

Left eye, right eye.

You'll notice your finger moves relative to the screen.

That effect is the parallax effect.

The same thing happens with the Earth, as the Earth

goes from one side of the Sun to the other.

The position of a nearby star moves relative to the very distant stars.

This motion is quite small.

Typically about one arcsecond for the nearest stars,

and one arcsecond is one 60th of an arcminute.

One 360th of a degree.

It was a tremendous challenge for early astronomers

to make that measurement, and it was a big

step forward when Bessel made the first measurement

of stellar parallax, back in the 19th century.

If you have a star that has a parallax of

one arcsecond, that puts it as a distance of one

parsec, which is three times ten to the 13 kilometers or equivalently,

200,000 astronomical units or about four light years.

We're about to take a big step forward in our ability to measure distances to stars.

The European Space Agency has just launched

in December, a mission called Gaia.

And Gaia, here's an artist conception of Gaia.

And here it is being constructed.

It's going to be able to make much more accurate measurements of parallax.

It will be able to make very accurate determinations of stars' positions and

let us take a big step forward in our ability to measure positions.

Hipparchus, a early astronomer, note the date.

Made some of the first attempts to measure parallax.

And he was only able to measure with

an accuracy of about a thousand arcseconds

using the technology he had available at the time.

When Hipparchus made those measurements then,

he noticed that the stars didn't move.

That the stars' positions in the sky did not vary through out the year.

He took that, as he understood as a fact, Hipparchus understood this picture here.

Hipparchus said well, the stars aren't moving relative to each other.

That must mean that the Earth doesn't move around the Sun.

And Hipparchus, though he did very important

observation for his time, drew the wrong conclusion.

He concluded that the Earth was the center of the solar system and it didn't move.

And just missed the idea that the stars in the sky were

so far away, that with his technology he couldn't measure their motions.

And then over time, positional improved.

Tycho Brahe took a big step forward in around 1600.

Measured the positions of about a thousand

stars with accuracies with about ten arcseconds.

But it took to the 1800s when Bessel was able to make the first measurement

of motions of stars and over the

last two hundred years, there's been increasing improvement.

Notice that on this plot, each tick is a factor ten improvement in sensitivity.

So we've improved over the last 200 years from Bessel's first measurement.

To the Hipparchus satellite which has made accurate

measurements of the positions of about 120,000 stars.

With uncertainties of what we call a milliarcsecond,

so one thousandth of an arc second.

With that kind of accuracy, you can measure the distance to the nearest stars

who are a parsec away with the uncertainty of only a tenth of a percent.

And can get 10% measurements out to about a hundred parsecs.

So it could measure a lot of the nearby volume.

But Gaia is going to make a huge step forward.

It's going to be a hundred-fold improvement in accuracy

over Hipparchus and will survey a billion stars.

It will get the positions, and distances to a

significant fraction, of all the stars in our galaxy.

So we will soon have very accurate distances.

This will actually be a very important test of stellar evolution theory.

And that will inform a lot of what we infer about the properties of planets.

Because, when we talk about a planet around a distant star.

One of the most important things that we want

to know is, what is the distance to the star.

And that always tends to, often comes back

to astrometry, making these accurate measurements of distance.

So, Gaia's about to take a big step forward.

Once we know the distance to a star, we can infer its luminosity.

Luminosity is the total energy emitted per second, doesn't depend on distance.

It's an intrinsic property of a star.

Think about it like a light bulb.

You have a 100 watt light bulb.

That will emit 100 watts, that's a measurement of energy.

And that's a light bulbs luminosity.

A light bulb that's far away seems dim

to us but its intrinsic luminosity is the same.

What does vary with distance is flux.

That distant light bulb is dim.

That means the flux that reaches us is small.

We could quantify flux and its

relationship between luminosity and distance as follows.

That the flux we measure from a light bulb depends

on its luminosity, 100 watts, divided by 4 pi D squared.

Let's say the light bulb's a kilometer away.

Well, it's pretty faint.

And the flux we see from a light bulb a kilometer away is quite small.

We can use this same equation to describe the flux we see from a distant star.

L is the luminosity of the star, D is the distance, F's the flux we measure.

Fact we usually turn this formula around.

because what we observe is the flux, that's what we

see reaching our telescope, that's what we measure with our cameras.

We use our astrometric observations to determine the distance.

And given the flux and the distance, we infer the luminosity.

Now when astronomers talk about the flux from a star, we often use, what I think

of as actually kind of a strange unit

but we need to learn it, called apparent magnitude.

It's a logarithmic scale that we use in

astronomy, and it's in many ways quite ancient.

It's based on a visual ranking of the brightest stars.

It starts with the star Vega, one of the brightest stars in the

night sky, and we define Vega as being a zeroth magnitude star.

Spica, is what we call a first magnitude star

And Spica is 2.5 times dimmer, than Vega.

A second magnitude star, would be 2.5 times dimmer, than Spica.

Or equivalently 2.5 times squared, dimmer than Vega.

We just keep going down.

A third magnitude star is 2.5 times dimmer than a second magnitude star.

2.5 times squared, or 6.25.

Times dimmer than a first magnitude star.

And about 50 times dimmer than a zeroth magnitude star.

So the further you go down in magnitude, the dimmer it gets.

And it's a funny scale that way, in that a

sixth magnitude star is dimmer than a zeroth magnitude star.

The dimmest naked eye stars you see at most sights is about six magnitude.

Sirius is the brightest star in the night sky.

It's actually magnitude minus 1.4.

It's about 2.5 to the 1.4 power or about 3.6 times brighter than Vega.

Well, at apparent magnitude measures flux,

absolute magnitude is a measurement of luminosity.

Absolute magnitude is the logarithm of luminosity.

In fact, it has this funny minus 2.5 factor.

So absolute magnitude is minus 2.5 times log

base 10 of the luminosity of the star divided by the star's

luminosity, plus a constant, which is 4.83 and that's

set because the Sun, in these units, have absolute magnitude of 4.83.

It's funny units, I didn't invent them.

I would have just worked in luminosities.

But this is the convention in the field.

And it's historic, it goes back over time and we're kind of stuck with it.

Since we're stuck with it, you want to be able to look things up

and I want to be able to describe them to you in these units.

We've gotta live with this.

Alright, so the Sun has an absolute magnitude of 4.83.

Go up by factor one.

A star with an absolute magnitude of 3.83 would be 2.5 times brighter than the Sun.

And a star with the absolute magnitude of

2.83 would be 2.5 times brighter than that.

So you can see the magnitude scale is useful for computing

relative brightnesses and we just need to keep track of this factor.

We can also use this scale to convert from apparent

magnitude, what we see, how much flux reaches our telescope.

And, absolute magnitude, once we know the distance.

And, this equation here, is just equivalent to what we wrote down earlier,

when we wrote, related flux equal to

luminosity divided by 4 pi distance squared.

This is just writing that same relationship in a different form.

The intrinsic luminosity or the absolute magnitude can be related

to the apparent magnitude, what hits our telescope, and the distance,

If you observe a star and it's very far away,

well, its intrinsic brightness must be quite large.

Its absolute magnitude must be large.

And we can just plug into this equation to find

out what the absolute magnitude is if we know the distance.

Sirius, Sirius, one of the brightest star in the night sky.

Has an apparent magnitude of minus 1.46.

It's pretty close, say a distance of 2.6 parsecs.

We plug those numbers in its absolute magnitude is about a factor of 1.4.

Now what I'd like you to do next is to go, apply these concepts of magnitude.

Absolute magnitude and apparent magnitude.

Work through some numbers on these questions just to make sure you understand

these, so that we can make use of them as we go on.

So why don't you take out a calculator, sit down, plug the numbers into the equations

we just wrote down and work out these apparent and absolute magnitudes.

See you in a moment.

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