Download P7 Further Physics

22/05/2017
Further Physics
Studying the
Universe
M Barker
Shirebrook Academy
P7.1 Naked Eye Astronomy
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The Nine(?) planets of our Solar System
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Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Which planets can be seen
with the naked eye?
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The Earth orbits the sun…
…every year (365 1/4 days)
Ellipse
The Spin of the Earth
The Earth rotates on its axis every 24 hours…
What’s wrong with this picture?
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The Spin of the Earth
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Because of this spin the sun and
stars appear to “move” across
the sky in an east-west
direction…
The sun takes 24 hours, the stars take slightly less than this
and the moon takes longer!
Solar days vs Sidereal days
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Basically, a solar day is the normal 24 hours. However, the
Earth actually spins in 23 hours 56 minutes. This period of
time is called a “Sidereal day”. Here’s why:
After one day the Earth is in a different position and so the
sun and stars will “appear” in the same place after 23 hours 56
mins, not 24 hours.
The Earth and the Moon
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The moon appears to move east-west across the sky in 24
hours 49 minutes. This is because the moon moves around
during the course of 24 hours:
The moon is directly over
this point at the moment.
1) After 24 hours the Earth has rotated once but the moon
has “moved on”
2) Therefore the Earth needs to rotate for another 49
minutes for the moon to appear in the same place
Phases of the moon
Appearance:
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Appearance:
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Appearance:
Eclipses
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Solar eclipses occur when the moon is between the sun and the
Earth:
Total eclipse
Partial eclipse
Eclipses
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The moon takes a _____ to orbit the Earth. However, solar
eclipses do not occur every month because the moon’s orbit is
inclined at 5O to that of the ______. Eclipses only occur when
the moon passes through the _____ – the apparent path the
____ traces out across the _____.
Words – sky, sun, month, ecliptic, Earth
Eclipses
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Lunar eclipses occur when the Earth is between the sun and
the moon:
During a lunar eclipse the
moon might look like this:
Viewing stars
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The stars we see in the summer and in the winter should be
different:
Stars in the summer:
Stars in the winter:
Viewing Planets
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The position of Venus changes in a different way to the stars
behind it (“retrograde motion”). This was the first evidence
that planets orbit the sun:
Viewing stars
Positive angle
of declination
Negative angle
of declination
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P7.2 Light, Telescopes and Images
Refraction
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Refraction through a glass block
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Light slows down and bends
towards the normal due to
entering a more dense medium
Light slows down but is
not bent, due to entering
along the normal
Light speeds up and bends
away from the normal due to
entering a less dense medium
Lenses
Lenses use the idea of refraction:
When light enters a
MORE DENSE medium
it slows down…
A prism uses this idea
to split light. The
frequency of light does
not change, only the
speed and the
wavelength do:
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Converging and diverging lenses
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CONVERGING (Convex)
Thickest at the centre
DIVERGING (Concave)
Thinnest at the centre
Ray Diagrams for Lenses
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The rays of light are
refracted INWARDS and
meet at the focus, F.
F
F
The image formed is REAL –
in other words, it can be
seen on a screen
The rays of light are
refracted OUTWARDS.
A VIRTUAL image is formed
– in other words, the image
doesn’t actually exist
Ray diagrams
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To draw ray diagrams follow these three rules:
1) Draw a ray from the TOP of the object PARALLEL to the axis and
then going through F:
F
F
2) Draw a ray from the TOP of the object going
through the CENTRE of the lens (which will be
undeviated)
3) Draw a ray from the top of the object through F
to the left of the lens and parallel to the axis
This image is REAL,
INVERTED and
DIMINISHED
Ray diagrams 2
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If the object is below the axis follow this step:
4) Draw a ray from the bottom of the object parallel to the axis and
then up through the focal point:
F
F
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F
F
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F
F
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F
F
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F
F
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F
F
More about lenses
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Compare thin and thick lenses:
Lenses are measured in units called “dioptres”:
Power in dioptres =
1
focal length in m
…where converging lenses (for long sighted
people) have positive values and diverging lenses
(for short sighted people) have negative values.
Notice that these
glasses have got a large
curvature. How would
you make strong glasses
but also make them
thinner and with less
curvature?
Lenses in Telescopes
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Because stars are very far away, the rays of light from them
enter a telescope effectively parallel:
Objective lens
(convex)
Focal point
Eyepiece
lens
Notice that this telescope has two converging lenses. The
more powerful one is the eyepiece lens.
Using Concave Mirrors
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Notice that concave mirrors can be used to focus light:
Concave mirror
F
Mirrors in Telescopes
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Astronomical telescopes tend to use large concave mirrors as
well as a convex lens. This allows them to collect more light
and the bigger the telescope, the more light they collect:
Eyepiece lens to
produce a
magnified image
Objective lens
(convex)
Flat mirror
Concave
mirror to
collect light
from the
object
Magnification
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Basically, magnification means “how much bigger the object
looks”:
Magnification =
Focal length of objective lens
Focal length of eyepiece lens
Example questions:
1) What is the magnification of a telescope with an objective
lens focal length of 15m and a eyepiece focal length 3m?
2) A telescope has a 100x magnification. If the focal length
of the eyepiece is 50cm what is the focal length of the
objective lens?
Diffraction
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Diffraction is an effect seen when a wave travels around a corner or
through a narrow gap:
More diffraction if the size of the gap is similar to the wavelength
More diffraction if wavelength is increased (or frequency decreased)
Diffraction in Telescopes
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The hole at the end of a telescope is called an aperture. To
avoid problems caused by diffraction through this aperture,
the size of the hole must be much larger than the wavelength
of the radiation it is observing.
Spectra
Recall that spectra can be
produced by the refraction
of light through a prism:
A spectrum can also be produced
by the diffraction of light through
a diffraction grating (basically a
set of very small gaps):
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P7.3 Mapping the Universe
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Distances in space
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The Sun, our closest star, is 1.6x10-5 light years
away from us.
The next closest star, Proxima
Centauri (4.2 light years away)
The centre of our galaxy, the Milky Way, is
around 26,000 light years away.
The Andromeda Galaxy (our closest galaxy)
– approximately 2.5 million light years away
Parallax
Parallax uses the idea
that, as the Earth moves
around the sun, the
apparent position of
“nearby” stars changes in
relation to distant stars
behind it:
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Distant
stars
Nearby star
p
Stars that are further away
from the Earth will have a
smaller parallax angle.
1 A.U
Parallax
angle p
Using parallax
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Astronomers often use the “parsec” to describe galactic distances. A
parsec is roughly 3¼ light years.
Angles involved in parallax measurements are often very small and are
measured in seconds of an arc (arcseconds). A second of an arc is 1/60th
of a minute of an arc, which is 1/60th of a degree. In other words, one
arcsecond = 1/3600th of a degree. A parsec is defined as the distance to a
star with a parallax angle of one arcsecond.
The approximate distance to a star can be calculated using this formula:
Distance to star
(in parsecs, pc)
=
1
Parallax angle (arcseconds)
1) Proxima Centauri has a parallax angle of 0.77 arcseconds. How far
away is it in parsecs?
2) The nearest galaxy, Andromeda, is 0.77Mpc away. What would the
parallax angle be in arcseconds?
Luminosity
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“Luminosity” means “how bright the star is”. The
luminosity of a star depends on its size and
temperature.
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Measuring distance using brightness
The sun looks very
bright. But, to be fair,
it’s very close to us so it
should look bright!
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Measuring distance using brightness
When I look at these stars some appear brighter than
others. This because they are either brighter stars or
closer to me.
For example, the star Antares is 10,000 times brighter
than the sun but it is 500 light years away from me, so it
is only the 15th brightest star in the night sky.
There are also “Cepheid variable”
stars, which vary in brightness.
Astronomers use the frequency of
its “pulsing” to work out how bright
it is and how far away it is.
Cepheid Variable Stars
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A “Cepheid Variable” star is one whose magnitude varies over
time:
Apparent
magnitude
Time
The period is related to their luminosity.
You can measure the distance of these stars by:
1) Observe for a few weeks to find the period
2) Use various mathematical relationships to determine the distance
Measurements of the distances to Cepheid variable stars shows that
they are very far away and must be outside of our galaxy!
The Milky Way
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OUR SUN is one of
millions of stars that
orbit the centre of
the Milky Way
Scientists realised that the Milky Way contains millions of
stars only after the invention of telescopes. Telescopes also
helped scientists discover “fuzzy” objects and these were
originally called nebulae.
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The Curtis-Shapley debate, 1920
After observing nebulae I said
that the universe consisted of
many galaxies.
Heber Curtis,
1872 - 1942
I disagreed and said that the
universe contained only one big
galaxy – the Milky Way, and this
galaxy contained the nebulae.
Harlow Shapley,
1885-1972
I settled the debate by observing
Cepheid Variable stars and found
that they were much further away
than our own galaxy.
Edwin Hubble,
1889-1953
Hubble’s Law
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Recession velocity
Astronomers have observed Red Shift and
Cepheid variable stars in lots of galaxies and
deduced the fact that more distant galaxies are
moving faster than closer ones:
x
x
x
x
x
x
xx
x
x
xx
Distance to galaxy
Recession velocity
Hubble’s Law
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x
x x
x
x
x
x
xx
x
xx
Distance to galaxy
Using this evidence I concluded two things: that the universe
is expanding AND the recession velocity is proportional to the
galaxy’s distance from us, therefore:
V = Hd
…where H = Hubble’s Constant (2±1 x 10-18 s-1)
(or H can be measured in kms-1Mpc-1 and distance is in Mpc)
Questions on Hubble’s Law
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1) A galaxy is 5x1020km from Earth. If Hubble’s constant is
2x10-18s-1 calculate how fast that galaxy is moving.
2) Another galaxy is 10Mpc from Earth. Taking H to be
75kms-1Mpc-1 calculate its recessional velocity.
3) Another galaxy has a recessional velocity of 500km/s.
Calculate the distance to the galaxy in both megaparsecs
and kilometres (take H to be 2x10-18s-1).
The Big Bang Theory
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The motion of galaxies, as observed with telescopes, indicates
that galaxies are all moving away from each other. In other
words, the universe is expanding. What happened to start this
off around 14 billion years ago?
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P7.4 The Sun, the stars and their surroundings
Wavelength and Energy Output
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All stars give out lots of different wavelengths of radiation:
Luminosity
T=6000K
T=4500K
T=3000K
Wavelength
When wavelength goes up (and frequency goes down) what
happens to the star’s intensity and temperature?
Ionisation revised
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Radiation is dangerous because it “ionises” atoms – in other
words, it turns them into ions by “knocking off” electrons:
Spectra – introduction
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Spectra
Source of
light
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“Spectra”
Absorption Spectra
helium
Some wavelengths of light
are absorbed by the gas –
an “absorption spectrum”.
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Spectra
Continuous spectrum
Absorption spectrum
Emission spectrum
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Emission Spectra
Hydrogen
Helium
Sodium
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Spectra
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Consider a ball in a hole:
When the ball is
here it has its
lowest gravitational
potential energy.
5J
We can give it
potential energy by
lifting it up:
If it falls down again it
will lose this gpe:
5J
30J
20J
Spectra
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Absorption spectrum
When these wavelengths are absorbed
the energy is used to raise the electron
up to a higher energy level in the atom:
Emission spectrum
When the electron drops back down
again it gives out these wavelengths
depending on the energy level it falls
from
By looking at the spectra
from stars we can work out
what gases are inside it. This
is how we know the sun is
made of hydrogen.
An Example Question
Here are the emission lines for hydrogen and helium:
Hydrogen
Helium
Which gas is in this star?
Absorption spectrum
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Particle Motion in Gases
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Gas pressure is caused by particles hitting the side of a
container. Anything we do that increases those collisions will
increase the pressure:
Particle Motion in Gases
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Consider decreasing the volume:
The particles should collide with the sides of the container
_____ often, therefore the pressure is ________.
Particle Motion in Gases
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Now consider increasing the temperature as well:
The particles should collide with the sides of the container
_____ often, therefore the pressure is ________. This
could cause the container to ______.
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Pressure and Temperature in gases
P
T
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Pressure and Temperature in gases
P
“Absolute Zero”
-2730C
T
The Kelvin temperature scale starts at 0K (= -273OC). To convert degrees
centigrade into Kelvin simply add 273.
Absolute Temperature
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“Absolute Temperature” starts at 0K
and represents the temperature
at which particles have zero
kinetic energy. It goes up in the
same steps as OC. For example:
1) The freezing point of water is
273K
2) The boiling point of water is 373K
3) Room temperature is around 293K
Lord Kelvin, 1824-1907
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Volume and Temperature in Gases
V
For a constant mass of gas at fixed
pressure, the volume occupied by the
gas is proportional to its absolute
temperature.
Jacques Charles,
1746-1823
0K
T
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Volume and Temperature in Gases
Provided the pressure of a gas stays
the same we can use this
relationship to calculate the volume
of a gas:
V1 = V2T1
T2
Jacques Charles,
1746-1823
1) A gas changes in temperature from 200K to 300K. If its
original volume was 2m3 what is the new volume?
3m3
2) Another gas is halved in volume. What will happen to its
temperature?
It will
halve
3) A third gas is kept at constant pressure while being
compressed from 20 litres to 15 litres. If its new
temperature is 275K what was its original temperature?
367K
Boyle’s Law
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“For a fixed mass of gas at constant
temperature (“isothermal”), pressure is
proportional to 1/volume.”
Robert Boyle
1627-1691
Higher temperature?
Let’s draw this…
P
P
V
1/V
Pressure and Volume in gases
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This can be expressed using the equation:
Initial Pressure x Initial Volume = Final Press. x Final Vol.
PIVI = PFVF
1) A gas has a volume of 3m3 at a pressure of 20N/m2. What
will the pressure be if the volume is reduced to 1.5m3?
40N/m2
2) A gas increases in volume from 10m3 to 50m3. If the initial
pressure was 10,000N/m2 what is the new pressure?
20KN/m2
3) A gas decreases in pressure from 100,000 Pascals to
50,000 Pascals. The final volume was 3m3. What was the
initial volume?
4) The pressure of a gas changes from 100N/m2 to 20N/m2.
What is the ratio for volume change?
1.5m3
1:5
The Gas Equation
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A while ago we said that Pressure x Volume = Constant (Boyle’s
Law)…
…also, we just said pressure is proportional to temperature
(Pressure law)…
…and we said volume is proportional to temperature (Charles’
Law)…
Combining these three equations gives:
Pressure x volume = constant
temperature
P1V1 = P2V2
T1
T2
Some example questions
1) An ideal gas has a volume of 2m3 and a pressure of
101KPa (101,000 N/m2) at a temperature of 300K. The
gas is then increased in temperature to 400K but kept
at constant volume. Calculate the new pressure.
2) The same gas is then allowed to cool to 200K while
being kept at constant pressure. Calculate the new
volume.
3) Another gas at 300K and 101KPa is allowed to halve in
volume while being kept at the same pressure. What is
the new temperature?
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135KPa
1m3
150K
The Life Cycle of a Star
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Stage 1: Nebulae
A nebulae is a collection of dust, gas and rock.
Some examples of nebulae…
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Dark nebula
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Emission nebula
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Planetary nebula
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Reflection nebula
Stage 2: Protostar
Gravity will slowly pull these
particles together…
As they move inwards
their gravitational
potential energy is
converted into heat and
a PROTOSTAR is
formed. The
temperature increases
because the volume of
the gas decreases.
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Stage 3: Main Sequence
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In a main sequence star the
forces of attraction pulling
the particles inwards are
_________ by forces acting
outwards due to the huge
__________ inside the star.
Stars are basically ________ reactors that use _______
as a fuel. During its main sequence a star will release
energy by converting hydrogen and helium (light elements)
into _________ elements.
Our sun is an example of a main sequence star –
it’s in the middle of a 10 billion year life span
Words – heavier, balanced, hydrogen, nuclear, temperatures
Nuclear Fusion in stars
Proton
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Neutron
Nuclear fusion happens in stars but it’s not possible to use it
in power stations yet as it needs temperatures of around
10,000,000OC
Fusion Reactions
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When the temperature of the star increases nuclear fusion
reactions will start. Here’s the equation:
1
41p
4
He
2
+
0
2 1 β+ +
2ν + energy
1) What are β+ particles and why are they emitted?
2) Why is energy released in this reaction?
Energy-mass equivalence
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In every fusion (or fission) reaction a little
bit of mass is “lost”. This mass turns into
energy and you can use my famous equation
to work out how much:
E=mc2
Einstein (1879-1955)
…where E = the energy released, m = the mass converted into
energy and c = the speed of light.
The Structure of our Sun
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Photosphere – where energy
is released into space
The core – the hottest part
of the sun where nuclear
fusion takes place. The
hotter the star, the heavier
the elements it will make
The hotter a star is, the
higher peak wavelength it
emits (e.g. blue stars are
hotter than red stars).
The convective zone – where
energy is transported to the
surface by convection
currents.
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The Hertzsprung-Russell Diagram
L (relative
to our sun)
106
Supergiants
104
102
The sun
1
Main
sequence
10-2
10-4
40,000
20,000
10,000
5,000
2,500
T (K)
Stage 4: Red Giant
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Eventually the hydrogen and helium will run out and the star
will leave the main sequence. When this happens the star
will become colder and redder and start to swell…
If the star is relatively small
(like our sun) the star will
become a RED GIANT
If the star is big (at
least 4 times the size of
our sun) it will become a
RED SUPERGIANT
In red giants and supergiants, nuclei
such as oxygen and nitrogen are formed.
Stage 5: The Death
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What happens at this point depends on the size of the
star…
1) For SMALL stars the red giant will collapse under its
own gravity and form a very dense white dwarf, where
no fusion reactions will take place:
Red giant
White dwarf
Black dwarf
2) If the star was a RED
SUPERGIANT it will shrink and
then EXPLODE, releasing massive
amounts of energy, dust and gas.
Before
After
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This explosion is called
a SUPERNOVA.
Heavier nuclei such as
iron could be made in
the core prior to the
supernova.
The dust and gas on the outside
of the supernova are thrown
away by the explosion and the
remaining core turns into a
NEUTRON STAR.
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If the star is big
enough it could
become a BLACK
HOLE.
Life on Other Planets
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Research task
Is it likely that other planets in our solar system could have
life? Explain your answer.
Extend your inquiry to other solar systems – what criteria
must be met in order for a planet to potentially have life on it?
Searching for Aliens
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Humans have been searching for me for over 50
years. Do you think I exist?
Quite possibly, We know that hundreds of “nearby” stars
have planets around them and we also know that there are
billions of stars in the universe so surely one of these
planets has life…
P7.5 The Astronomy Community
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Observing the Universe
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Observing the Universe
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Consider different types of telescope:
Ground-based telescopes
Space-based telescopes
What are the advantages and disadvantages of each?
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Common sites for Ground-Based telescopes
Chile
Hawaii
What advantages do
these sites offer?
Canary Islands
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Using Computers with Telescopes
Telescopes like this one are often
controlled by computers.
What advantages does
this offer?
1) The telescope can be controlled
remotely
2) It can track objects continuously
3) It’s more precise
4) The computer can record and
process the data
Hawaii
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Benefits of observing above the atmosphere
Clearly, ground-based telescopes are a problem because of a
number of things:
• The amount of light absorbed by the atmosphere
• Bad weather
• Light is refracted, diffracted and scattered by the
atmosphere (causing stars to “twinkle”)
• Light pollution from nearby cities
The solution is to put telescopes in space or build them high up
on a mountain. Here are two examples of space-based
telescopes:
Hubble Space Telescope (HST)
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• Launched in 1990, due to finish operating in 2010
• Takes images in the visible light, ultra-violet and near infra
red regions
• Orbits the Earth every 97 minutes
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Infra Red Astronomical Satellite (IRAS)
• Surveys infra red patterns in space
• Launched in 1983 and operated for 11 months
• The number of known astronomical bodies was increased by
70% due to infra red observations
International Collaboration
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Here’s the International Space Station, a joint project by NASA, the
Russian Space Agency, the European Space Agency, the Japan Aerospace
Exploration Agency and the Canadian Space Agency:
What advantages does international
collaboration bring in terms of:
1) Cost?
2) Pooling of expertise?
Building Observatories
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What factors are involved in planning,
building and closing down a large
observatory?
• Cost
• Environmental impact
• Social impact
• Working conditions
Hawaii