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Mapping the Heavens
How Long is a Day?
22-May-17
WILF: Be able to draw diagrams to show the phases of the moon and be
able to explain what a sidereal day is.
Keywords:
Starter: True or false
Phases of the moon
1. The sun rises in the East
2. The sun comes up at the same
time each day
Sidereal day
Solar day
3. The moon only comes out at
night
7. The moon orbits the earth
once a day
4. The Earth goes around the
sun
8. The Earth is closer to the
sun in June than in
December
5. The moon goes around the sun
6. We always see the same side
of the moon
9. The moon rotates
10. There are no stars in the
daytime sky.
Complete the
diagram
Sidereal Days and Solar Days
Star is
seen at 23
hrs and 56
min
Midday – sun
is visible
Midday – sun
is visible
The average time it takes the sun to cross the
sky is 24 hrs. This is called a solar day.
The Earth rotates through 3600 once every
23hrs and 56 minutes. A star would appear in
the same position in the night sky therefore
23 hrs and 56 minutes later. This is called a
sidereal day.
Star is
seen at
midnight
23
hrs
56
18
12
hrs
later
6
hrs
later
24 hrs later
minutes later
Eclipses
Keywords:
Lunar eclipse
WILF: Be able to explain how seasons occur and why eclipses are
such rare events.
Solar eclipse
Shadow
Totality
Corona
Umbra
Penumbra
Starter: the sun appears to travel across the sky once every 24 hrs yet the
moon reappears every 24hrs and 49 minutes. Can you explain why this is so?
Eclipses
A solar eclipse happens when the Moon passes
between the Sun and the Earth. This casts a
shadow over the Earth.
The last solar eclipse over the UK was on 11th
August 1999. Solar eclipses do not occur very
often.
A lunar eclipse happens when the Earth passes
between the Sun and the Moon. This casts a
shadow over the Moon.
Lunar eclipses happen in most years.
What happens during a solar eclipse?
During
athe
solar
eclipse
Moon
moves
directly
Where
must
be forthe
athe
solar
eclipse
to
take
During
a Moon
solar
eclipse
Moon
blocks
the place?
the
Sun andpart
theofEarth.
Sun’sbetween
rays from
reaching
the Earth.
What happens during a lunar eclipse?
Where must the Moon be for a lunar eclipse to take place?
During
aa
lunar
eclipse
the
Moon
on thethe
opposite
During
lunar
eclipse
the
Earthisblocks
Sun’s side
light of
thereaching
Earth to the
from
the Sun.
Moon.
Why are solar eclipses so rare?
- Because the moons orbit is tilted relative to the plane of the
Earth’s orbit around the sun the chance of the Sun, Moon and
Earth all being perfectly in a line is very rare.
22-May-17
Retrograde Motion
WILF: be able to explain how the earth’s rotation causes the apparent motion
of the stars and planets.
Starter: Which constellations do you recognise?
Keywords:
Retrograde motion
Constellation
Polaris
21st
September
21st
December
21st June
21st March
Retrograde Motion:
To see retrograde motion for yourself:
Load Stellarium
Set the date to 23/11/2009
Set the time for 7pm
Search for Mars
Click on one of the nearby stars so the computer keeps that in the
centre of the screen.
Move time forward by 1 sidereal week at a time by pressing alt ]
Watch the retrograde motion of Mars
Can you make this happen with any other planets? Why is the effect
more pronounced with Mars?
Retrograde Motion:
The planets generally move in one direction across the “fixed” background of
stars. Sometimes they appear to slow down and even go in the reverse
direction. This is known as retrograde motion.
5
4
2
3
1
Where does Mars appear?
Background of fixed stars
Measuring the Distance to Stars
22-May-17
WILF: Be able to describe what parallax is and be able to use it to calculate
the distance to stars.
Keywords:
Parallax
Parallax angle
What is the parallax angle?
The parallax angle (θ)
is half of the stars
apparent angular
motion.
Original
telescope
direction
θ
2θ
1.5x1011m
Position of Earth
6 months later
3x1011m
Using trigonometry
distances to stars can
therefore be
calculated.
Examples using parallax
Worked example:
If the object in the diagram had a
parallax angle 50. How far away is
θ
it?
d
Sin θ = Opposite/hypotenuse
Sin5 = 2000/d
Therefore d = 2000/sin5
Therefore d = 22947m.
2000m
4000m
θ
d
Worked example:
If a star had a parallax angle 0.020.
How far away is it?
Sin θ = Opposite/hypotenuse
Sin0.02 = 1.5x1011/d
θ
Therefore d = 1.5x1011/sin0.02
d
Therefore d = 4.297 x 1014m.
How many light years is this?
Light travels at 3x108 m/s.
Therefore light travels
1.5x1011m
3x108x60x60x24x365
= 9.4608x1015 m/year
3x1011m
Therefore 4.297x1014/ 9.4608x1015
= 0.045 light years.
Using Really Small Angles to
Measure Distances to Stars
22-May-17
WILF: Be able to use the unit of parsec to calculate distances to stars.
Starter: What is the
parallax angle for the
object in the diagram
shown?
θ
Keywords:
Parsec
Minute
Second
Arc
d = 12000m
3000m
Smaller angles
In a circle there are 3600
We can split each degree of arc up into smaller
measurements:
60’ (minutes) of arc = 10
So 100 = 600’ of arc.
Or 0.10 = 6’ of arc.
Because stars are so far away – parallax angles are even
smaller than this. Therefore we need a small unit than the
minute of arc.
60’’ (seconds) of arc = 1’
So 0.5’ = 30’’ of arc.
So 1 second of arc (1’’) =
1
3600
of a degree
Parsec
An object whose parallax angle is 1 second
of arc is at a distance of 1 parsec.
So an object whose parallax angle is 4
seconds of arc is a distance of 0.25
parsec.
As the angle decreases the distance
increases.
θ = 1’’
d = 1 parsec
Distance in parsec =
1
Angle in seconds
1 parsec is about 3x1013km
The Brightest Star
22-May-17
WILF: be able to explain the difference between luminosity and observed
brightness and how the colour of a star is related to its temperature.
Starter: If you look up at the night sky. Is
there a way in which you can tell which stars
are closest to the Earth?
Keywords:
Luminosity
Observed brightness
Spectrum
Peak frequency
Definitions:
Luminosity – The amount of energy radiated into space every second by a
star.
Luminosity depends on:
• The stars temperature (a hot star radiates more energy/second from a
given area of its surface)
• The stars size (a bigger star has more surface that radiates energy)
• So a big hot star will be have a higher luminosity than a small cool star.
Observed Brightness – a measure of the light reaching telescope from a
star.
This will depend on:
• The distance the star is from the Earth
• The luminosity of a star.
• So just because a star appears bright does not mean it has to be close
to the Earth.
Black Body Radiation Applets – Explore how changing the
temperature of a star affects the electromagnetic radiation
emitted by it.
http://webphysics.davidson.edu/alumni/MiLee/java/bb_mjl.htm
http://www.astro.ubc.ca/~scharein/a311/Sim/bbody/BlackBody.html
Star Colours:
All hot objects emit a continuous range of electromagnetic radiation. The
surface temperature of a star will determine the wavelength of the
electromagnetic radiation we see emitted and hence the colour of the star.
Hotter
star
Intensity of
radiation at
each
frequency
Colder
star
wavelength
frequency
The graph shows that:
• a hotter star has a greater area under the graph so the luminosity is
greater.
• a hotter star produces a greater proportion of radiation at higher
frequencies (it peak frequency is greater).
22-May-17
Cepheid Variable Stars
WILF: Explain what a Cepheid variable star is and how they can be used to
measure distances to galaxies.
Keywords:
Cepheid Variable Star
Period
Leavitt
Globular Clusters
Shapley
Curtis
Hubble
Megaparsec
Use the text book pg 218/219 to help you answer the following:
What is a Cepheid Variable Star?
• A Cepheid variable star is a star whose observed brightness varies in a
regular pattern.
• What causes the variation in their luminosity?
• It is caused by the star expanding and contracting causing its temperature
and hence its luminosity to change.
• What is meant by the period of a Cepheid variable star?
• The time it takes for the star to go from its brightest back to its brightest
again.
• What is the relationship between their luminosity and their period?
• The more luminous the star the longer the period is.
• How can this be used to measure the distance to a Cepheid variable star?
• Measure the period of the star and calculate the luminosity based on this.
• Measure the observed brightness of the star
• From the luminosity and the observed brightness the distance to the star
can be calculated.
Read the text book pg 220/221.
Complete the following table. In each column outline what
theory each astronomer came up with.
Shapley
Curtis
Thought the Milky
Felt that the spiral
Way was at the
nebulae he had been
centre of the
studying were very
Universe. Said
distant from the
there were Globular Milky Way and were
Clusters (clusters
in fact galaxies just
of stars) orbiting
like our own Milky
around our Milky
Way.
Way galaxy.
Hubble
Used observations
of a Cepheid
variable star in a
spiral nebulae to
calculate its
distance. Found out
it was about 1
million light years
away – far further
away than the size
of the Milky Way
Hubble’s Constant
WILF: be able to calculate the Hubble constant and the distance to
distant galaxies given appropriate data.
Keywords:
Speed of recession
Hubble and the Big
Bang
Hubble Constant
Megaparsec
Distance
Mpc
km/s
S. Mag. Cloud
0.032
170
L. Mag. Cloud
0.034
290
NGC 5457
0.45
200
NGC 4736
0.5
290
NGC 5194
0.5
270
NGC 4449
0.63
200
NGC 4214
0.8
300
NGC 3627
0.9
650
NGC 4826
0.9
150
NGC 5236
0.9
500
NGC 1068
1
920
NGC 5055
1.1
450
NGC 7331
1.1
500
NGC 4258
1.4
500
NGC 4151
1.7
960
NGC 4382
2
500
NGC 4472
2
850
NGC 4486
2
800
NGC 4649
2
1090
The Hubble Constant
• Hubble managed to measure the
distance to different galaxies using
Cepheid variable stars.
• He also worked out the speed of
their recession from “red shift”
measurements (how fast they were
going away from us).
• Use his data in the table to plot a
graph on the axis below – what is the
general trend shown by your graph.
Speed of
recession (km/s)
Galaxy/object
Speed of
recession
Distance (Mpc)
Distance
Mpc
km/s
S. Mag. Cloud
0.032
170
L. Mag. Cloud
0.034
290
NGC 5457
0.45
200
NGC 4736
0.5
290
NGC 5194
0.5
270
NGC 4449
0.63
200
NGC 4214
0.8
300
NGC 3627
0.9
650
NGC 4826
0.9
150
NGC 5236
0.9
500
NGC 1068
1
920
NGC 5055
1.1
450
NGC 7331
1.1
500
NGC 4258
1.4
500
NGC 4151
1.7
960
NGC 4382
2
500
NGC 4472
2
850
NGC 4486
2
800
NGC 4649
2
1090
The Hubble constant
Use his data in the table to plot a
graph on the axis below – what is the
general trend shown by your graph.
Speed of
recession (km/s)
Galaxy/object
Speed of
recession
Distance (Mpc)
Plot a straight line of best fit on your
graph.
Work out the gradient of your line – this is
the Hubble constant.
The Hubble constant
Use his data in the table to plot a graph on the axis below – what is the
general trend shown by your graph.
Speed of
recession (km/s)
Plot a straight line of best fit on
your graph.
Work out the gradient of your line –
this is the Hubble constant.
Distance (Mpc)
From maths you should know that straight line graphs through the origin are
of the form y = mx.
Therefore:
Speed of recession = Hubble constant x distance
From this equation if we know the speed of recession of a galaxy we can
work out its distance.
Inside Stars and the
Lives of Stars
22-May-17
What is the Sun Made Of?
WILF: Explain how emission and absorption spectra allow us to know what
a star is made of.
Keywords:
Emission spectrum
Absorption spectrum
Energy levels
Photon
Electrons in atoms only
have certain values of
energy. We represent this
by drawing them in energy
shells.
All these other
possible energy
levels exist
even though
there are no
electrons in
them
1st2nd
energy
level
–
energy
level
lowest energy
Sometimes it is easier
to draw these energy
shells as a “ladder” of
energy levels.
Emission Spectra
When atoms get very hot
– electrons are excited
from their energy levels
to higher energy levels.
The electrons then fall
back down to their
original energy level and
emit a photon of light
that is equal in energy to
the gap in the energy
levels.
This will correspond to
a certain colour of light.
Emission Spectra
If excited to different
energy levels they will
emit different colours of
light corresponding to the
energy difference.
Absorption Spectra
Stars are blazing balls of gas where many kinds of
atoms emit light of all colours.
If you look at the spectrum you should therefore see all
colours of the spectrum present.
However as this light travels through the star’s outer
atmosphere photons of certain energies will be absorbed
by different atoms. These frequencies of light will
therefore not appear in the spectrum seen. This is known
as an absorption spectrum.
Absorption Spectra
Dark absorption lines appear in the spectrum when an atom
absorbs a certain frequency of light causing electrons to
jump out to higher energy levels. The frequencies of light
not absorbed will be seen.
Which of the mystery elements a, b, c or d are responsible for the
absorption spectrum shown.
a
b
c
d
Probing the Atom
22-May-17
WILF: Be able to explain the evidence that revealed the existence of the
nucleus in the atom.
Research the following:
What did John Dalton think an atom was?
What was the plum-pudding model of the atom?
What experiment did Geiger and Marsden carry out to show the plumpudding model was wrong?
How did their experiment show the existence of the nucleus in the
centre of the atom?
Good site with information and animation of alpha particle scattering:
http://www-outreach.phy.cam.ac.uk/camphy/nucleus/nucleus1_1.htm
The Strong Nuclear Force
The nucleus of an atom contains neutrons
and protons.
+
+
+
+
But the protons are all positively charged
so they should repel each other.
There is another force present called the
strong nuclear force.
It only acts over a very small range and is
able to balance out the repulsive
electrostatic force.
proton
neutron
22-May-17
Pressure and Volume
WILF: Be able to show and explain how the pressure
and volume of a gas are related.
Keywords:
Pressure
Kinetic theory
Volume
Now plot a graph of pressure
against 1/volume. What do you
notice?
Volume
Pressure
Plot your data on a graph to
show how pressure and volume
are related.
pressure
1/volume
Conclusion:
When the pressure is increased the volume ___________. The pressure
is __________ proportional to the volume.
Pressure is caused when the molecules of a gas collide with the container
walls. Each collision causes a tiny force. Together all the forces add up to
produce a gas pressure.
When the volume is decreased the pressure __________. This is
because……………………..
22-May-17
Pressure and Temperature
WILF: Be able to show and explain how the pressure
and temperature of a gas are related.
Keywords:
Kelvin
Temp/0C
Pressure/
kPa
10
9.8
20
10.1
30
10.5
40
10.8
50
11.2
60
11.5
70
11.9
80
12.2
90
12.6
100
12.9
Absolute zero
The relationship between temperature and pressure:
Plot the following data on a graph with the axis shown.
Extrapolate your graph back to the x axis. What is the
temperature where it crosses?
Temp/0C
Pressure/
kPa
10
9.8
20
10.1
30
10.5
40
10.8
50
11.2
60
11.5
70
11.9
80
12.2
90
12.6
100
12.9
Pressure (kPa)
13
-300
0
Temperature (0C)
100
Absolute Zero
The point where the line
crosses the x axis is known as
absolute zero. At this
temperature the molecules are
no longer moving and so there is
no gas pressure
-300
Pressure (kPa)
13
0
Temperature (0C)
The temperature of absolute zero is -2730C
100
The Kelvin Temperature Scale
The Celsius temperature scale was based on the freezing and boiling
points of water.
The Kelvin (K) scale starts at absolute zero.
O Kelvin (0 K) is absolute zero (-2730C).
Each graduation on the Kelvin scale is the same as on the Celsius scale
Temperature in 0C = temperature in K – 273.
373 K
273 K
0K
100 0C
0 0C
-2730C