Activity 1:

The Sun: Source of Heat & Light

Module 19: The SunSwinburne Online Education Exploring the Solar System

© Swinburne University of Technology

Summary:

In this Activity, we will investigate

(a) why the Sun is so important to astronomers ...

(b) the temperature at the surface of the Sun ...

(c) the brightness of the Sun …

and …

This will include a discussion of the inverse square law, and the definitions of luminosity and flux.

You will also be introduced to some of the units and conventions used in astronomy:

• scientific notation• the Kelvin temperature scale• the astronomical unit• the lightyear• the parsec

(d) a few basic definitions and ideas

And now, let’s have a look at the Sun … carefully, because looking directly at the Sun can permanently damage your eyesight.

Don’t look at the Sun itself ...

… only at a filtered, low-intensity image

(a) Why the Sun Matters

The Sun is important to everything, living or non-living, in the Solar System because:

• it provides the planets with the heat and light necessary for life and many other developments

• it is the gravitational centre around which the planetary system moves

“Sunrise, sunset …”

Since the earliest times, humans have realised the importance of the Sun, venerating it as a deity or the chariot of a deity, and sharing myths about why and how the Sun continues to rise and set and what would happen if it didn’t.

A Model StarCompared to most stars, the Sun is not significant by any means.

The Sun’s place in the Milky Way Galaxy

The Sun’s place in the Solar System

However it provides a useful model for us to study when we seek information about stars in general.

(note: this is not actually the Milky Way, but a similar spiral galaxy called NGC2997)

In particular, • The Sun is much, much closer to us than any other star, and therefore is a great deal easier to study in detail. The next nearest star is about 250,000 times as far!

Earth to Sun: about

15 millionths of a light year

Earth to nearest star (Proxima Centauri):

4.2 light years

Earth to Aldebaran:

60 light years

Earth to nearby galaxies:

about 3 million light years

“What’s a lightyear?”

Also,

• The Sun has been studied by astronomers for thousands of years, and therefore data are available for the Sun which are not available for other stars.

Physical properties of the Sun

There are two very obvious things humans notice about the Sun:

• it is a source of heat, and

• it is a source of light.

So the Sun’s temperature and brightness make a pretty good place to start.

0 5000 10000 15000 20000 25000 30000

Sirius B

Sirius A

The Sun

Betelgeuse

Boiling iron

Venus

Earth

Mars

Jupiter

Pluto

Interstellar space

Temperature (K)

The surface temperature of the Sun is about 5780 Kelvin.

(b) Surface Temperature “What’s Kelvin?”

33

130130

3000030000

4040

250250

300300

700700

30003000

35003500

57805780

1000010000

When you turn on a heater, the element will glow red until it warms up. Then the colour will become closer to yellow, or to white.

How the Sun’s Temperature is measured

high energy & temperature

low energy & temperature

The same thing happens with iron as it heats up. It glows orange at first, then becomes more yellow or white in colour as it warms up. Scientists say that it emits like a “black body”. To a good approximation, stars also emit like a “black body”.

We tend to associate blue with cold and red with heat, but that’s only because of what our blood vessels do when the day is cold or hot.

The truth for the rest of the Universe is that

cooler stars are reddish;

hot stars are bluish.

high energy & temperature

low energy & temperature

You have to forget all about that, in astronomy...

(c) Luminosity

The luminosity of a source of light is a measure of the power it can provide: that is, how much energy it puts out per second.

Luminosity will vary from star to star ...

and will also vary during the life cycle of a star.

25 W

25 W = 25 joules per second

Time

Luminosity

The luminosity of the Sun at present

is 3.863 x 1026 Watts

0.1 1 10 100 1000 10000

Sun = 1

Procyon A

Arcturus

Antares

Betelgeuse

luminosity

“What does 1026 mean?”

equivalent to about 4,000,000,000,000,000,000,000,000light globes.

This can be compared with the approximate luminosity of other nearby stars:

FluxFlux is the power passing through a unit area, so the units of flux are watts m -2

(watts per square metre), or joules s-1 m-2 (joules per second per square metre).

The power of the Sun (luminosity) is measured in

watts:

Power = 3.8 x 1026 W

The power of the Sun (luminosity) is measured in

watts:

Power = 3.8 x 1026 W

Close to the Sun, the power passing through a square metre

is high (for instance, on the surface of Mercury)

Close to the Sun, the power passing through a square metre

is high (for instance, on the surface of Mercury)

Further from the Sun, the power per square metre is lower (for instance, on the

surface of Neptune)

Further from the Sun, the power per square metre is lower (for instance, on the

surface of Neptune)

1 square metre 1 square metre

The flux of energy at the surface of the Earth depends on

• the distance between the Earth and the Sun,

according to the inverse square law

What’s the inverse

square law?

How bright?How bright? How far?How far?

• the luminosity of the Sun

Luminosity = 3.8 x 1026 WLuminosity = 3.8 x 1026 W Distance = 1.5 x 108 kmDistance = 1.5 x 108 km

If you alter the setting on a heater in your home, you will quickly feel the effect on your own temperature. Similarly, the surface temperature of the Earth will vary during the Sun’s history, as the luminosity of the Sun varies.

Changes in luminosity

Changes in distance:

You get colder as you move further from the heater. In the same way, the surface temperature of planets further from the Sun is almost always lower than that of planets closer to the Sun, largely because of the decreased energy flux.

* Remember that AU stands for Astronomical Units, and 1 AU is the average distance between the Earth and the Sun. Not to Scale!

Earth

Jupiter

Mercury

0

100

200

300

400

500

600

700

800

0.1 1 10 100

Distance from Sun (AU)

Average surface

temperature(K)

Pluto

Venus is hotter than you’d expect, as it is covered in thick

cloud that keeps in the heat

Venus is hotter than you’d expect, as it is covered in thick

cloud that keeps in the heat

Just for interest:

Here is a graph showing the distance of the planets from the Sun (in AU) plotted against their average surface temperature (in degrees K).

Other than that, the further out a planet is, the cooler it is

Other than that, the further out a planet is, the cooler it is

This Activity focussed mainly on the temperature and brightness of the Sun.

In the next Activity we will investigate more of the Sun’s properties: its mass and density, and what it is made of; and we’ll take a first look at how it produces energy.

Image Credits

AAO: Clusters and nebulae © David Malin (reproduced with permission)

http://www.aao.gov.au/local/www/dfm/dark_frames.html

AAO: Sprial galaxy NGC2997 © David Malin (used with permission)http://www.aao.gov.au/images/general/galaxy_frames.html Stonehenge (reproduced with permission)

http://antwrp.gsfc.nasa.gov/apod/ap971217.html

NASA:

Solar flare

http://antwrp.gsfc.nasa.gov/apod/ap970918.html

Skylab

http://nssdc.gsfc.nasa.gov/photo_gallery/photogallery-spacecraft.html

Hubble Deep field

http://antwrp.gsfc.nasa.gov/apod/image/hst_deep_big.gif

Now return to the Module home page, and read more about the Sun in the Textbook Readings.

Hit the Esc key (escape) to return to the Module 19 Home Page

The Kelvin temperature scale 1

The Kelvin temperature scale is the same as the Celsius scale, except that the definition of zero is different.

The Celsius scale specifies 0 degrees as the temperature at which water freezes.

On the other hand, the Kelvin scale specifies 0 degrees as the temperature of an object in which the kinetic energy of the particles making up the object is at a minimum. This is called absolute zero (0 K).

The Kelvin temperature scale 2

Therefore, 273.15 degrees Kelvin is the freezing point of water and 373.15 degrees Kelvin is the boiling point of water.

Melting point of ice

Boiling point of water

Kelvin 0 100 200 300 400 500 600

Celsius -273 -173 -73 27 127 227 327

The Celsius scale is 273.15 degrees “out of sync”:

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Scientific notation 1

In order to save writing heaps of zeroes, scientists and engineers use a system of notation where very large numbers are written with the number of factors of ten as an exponent.

For instance: 5 000 is written 5 x 103

6 000 000 000 is written 6 x 109

42 700 is written 4.27 x 104

Note that in scientific notation the aim is to present the number as a number between 1 and 10 multiplied by a power of ten: 4.27 x 104

On the other hand, engineering notation always presents the power of ten as a multiple of 3, e.g. 42.7 x 103

Scientific notation 2

Note that in scientific notation the aim is to present the number as a number between 1 and 10 multiplied by a power of ten: 6.0001 x 10-5

On the other hand, engineering notation presents the power of ten as a multiple of 3, e.g. 60.001 x 10-6

For instance: 0.007 is written 7 x 10-3

0.00000010436 is written 1.0346 x 10-7

0.000060001 is written 6.0001 x 10-5

Also, in order to save writing heaps of decimal places, scientists and engineers use a system of notation where very small numbers are written with the number of factors of ten as an exponent.

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Inverse square law 1

If something is being emitted with equal intensity in all directions from a point source, it will obey the

“Inverse Square Law”.

Closer in, the intensity of light is high as the light is only spread over a small area

Further out, the intensity of light is low as the light is spread over a larger area

Point source of light

Inverse square law 2

Imagine that a star is emitting light equally in all directions.

At planet Alpha, the light is observed as being fairly intense, as it is being shared over a small area:

• small radius, therefore• small area, therefore• high light intensity.

At planet Beta, the light is being shared over a larger area and so the intensity of the light is far less:

• large radius, therefore• large area, therefore• low light intensity.

Star

Inverse square law 3

Mathematically,

Note that the flux is proportional to the inverse square of distance, which is where the law gets its name from!

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Because astronomical distances and sizes tend to be so large, our usual (Earthly) units of length (m, km and so on) are clumsy. Instead you will frequently find astronomical measurements made in one of these units:

• AU• pc• ly

Units in Astronomy 1

AU = astronomical unit = average distance between Sun and Earth = 1.496 x 1011 m

1 AU

Another astronomical unit of measure is the parsec, which uses angle to measure the distance to other stars, galaxies and so on.

Units in Astronomy 2

pc = parsec = distance d at which 1 AU perpendicular to the observer’s line of sight subtends an angle of 1 second of arc = 3.086 x 1016 m

d (in parsec)d (in parsec)

Angle(in seconds

of arc)

Angle(in seconds

of arc)1 AU1 AU

Even though the unit arose from measuring angles, it is a measure of distance and not angle

• AU (based on distance)

• pc

… and is seen here a year later

… and is seen here a year later

A third astronomical unit of measure - the lightyear - came from the knowledge that light takes a finite length of time to travel through space.

The lightyear is the distance that light will travel in a year, and 3.26 lightyears = 1 pc.

• AU (based on distance) • pc (based on angle)

• ly

Units in Astronomy 3

ly = lightyear = distance that light travels in one year = 9.461 x 1015 m

1 ly (distance)1 ly (distance)

An event happens here ...

An event happens here ...

Let’s imagine that three stars A, B and C are all “born” at about the same time. Because the stars are at different distances from Earth, and light coming from them travels at a finite speed, light which arrives at our eyes simultaneously must have been emitted from each star at a different time.

C

B A

The lightyear is a particularly useful unit because it reminds us that what we see actually happened a while back, when the light left the star (or planet) that we are looking at.

Look-back time 1

Light received from star C was emitted long ago. It will give us pictures of C close to when it was first formed.

Look-back time 2

Light from star B was emitted more recently, and so the pictures we receive of B will be of the star in “middle age”.

C

B A

Light received from star A was emitted very recently. We will see the star just about as it looks today.

In this way, we can construct a series of images and ideas about the life cycle of stars, using their distances to “travel in time” and see similar stars at different stages of their development.

Pictures from C, then B, then A, will show us how that kind of star changes with time.

looks young

looks middle-aged looks old

Look-back time 3For example ...

Distance = 10 ly

We see this star as it was 10 years ago

Distance = 100 ly

We see this star as it was 100 years ago

Distance = 1000 ly

We see this star as it was 1000 years ago

... when we examine these three stars, we are looking not just out into space but back in time: hence the term “look-back time”.

In practice, “look-back time” is most useful when studying distant galaxies.

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