Download Chapter 12 Our Place in the Universe

Chapter 12 Our Place in the Universe
Curriculum Time Study Pack
Student Name:______________________________________________
The astronomy and cosmology section of the specification is very interesting, but
quite short. Here it is in full:
Candidates should demonstrate evidence of:
1. knowledge and understanding of phenomena, concepts and relationships by describing:
(i) the use of radar-type measurements to determine distances within the solar system; how distance is measured
and defined in units of time, assuming the relativistic principle of the invariance of the speed of light;
(ii) effect of relativistic time dilation using the relativistic factor ; γ=1/(1−v2/c2)1/2
(iii) the measurement of relative velocities by radar observation;
(simple arguments using two successive pulses are sufficient);
(iv) evidence of a ‘hot big bang’ origin of the universe from:
• cosmological red-shifts (Hubble’s law);
• cosmological microwave background;
2. scientific communication and comprehension of the language and representations of physics, by sketching and
interpreting:
(i) logarithmic scales of magnitudes of quantities: distance, size, mass, energy, power, brightness;
3. quantitative and mathematical skills, knowledge and understanding by making calculations and estimates
involving:
(i) distances and ages of astronomical objects;
(ii) distances and relative velocities from radar-type measurements.
This pack is designed to help you cover this material through independent study.
You may well want to look at aspects more deeply. If so, look at the A2 student book
or any of a large number of websites. This pack does not cover relativity – we’ll do
that in school!
Chapter 1
At the beginning of the twenty-first century it is accepted that the observable
Universe is BIG. Measuring the Universe has not been simple. Scientists have
developed methods to estimate distances using a number of different observations.
Section 12.1 in the Student Guide deals with this area.
It is also accepted that the Universe was formed during the so-called Big Bang. This
occurred around 14 billion (14 x 109) years ago.
Section 12.2 in the Student Guide considers the evidence for the Big Bang and
describes what it shows us.
12.1 Radar Maps, Killer Asteroids and Unstable Stars.
a. The Light Year
Distances in the laboratory are measured in metres or millimetres. That’s sensible
because things in the lab are that sort of size. Journey distances, for example, from
Southampton to Scunthorpe, are measured in kilometres because using metres
would be unwieldy.
Astronomers are scientists who study the Universe using a range of wavelengths
including visible, radio waves and X-rays.
Astronomers consider distances much greater than Southampton to Scunthorpe.
The light year is the measurement that is most frequently used for large distances.
One light year is the distance that light travels in one year.
oistance
= speed x time
one light year = speed of light x number of seconds in a year
= 3 x 108 x 365.25 x 24 x 60 x 60
=
The Earth-Sun distance is 149.5 x 109 m.
Calculate this distance in light-minutes.
The nearest star to the Sun is called Proxima Centauri. It is at a distance of 4.3 light
years.
Calculate this distance in metres.
It is said that when you look up at the night sky you are looking back in time. Explain
why the statement is correct.
b. Echoes in Space
This is a picture of a volcano on Venus. But Venus has an atmosphere that is
impenetrable to visible light. The picture is an image formed from data using radar.
Radar uses pulses of electromagnetic radiation to image distant objects.
The principle of radar mapping is the same as ultrasound imaging or echo location.
A pulse is sent to a distant object and the time delay before the reflected pulse is
received is measured. The distance is calculated like this:
distance = speed of pulse x trip time
2
A radar pulse is directed at the Moon. The reflected pulse is detected 2.6 seconds
later.
Calculate the distance to the Moon.
c = 3 x 108 m s-1
The radar image of Venus shown above resolves height distances of about 100m.
Explain why the detection circuit must be able to detect trip times of 6  s or smaller.
The principle of radar mapping can be extended to velocity measurement.
The next page shows distances in the Universe related to the trip time of light. Note
that it uses a logarithmic scale.
Radar ranging and velocity of asteroid
relative
velocity v
relative
velocity v
asteroid
asteroid
first radar
pulse out
speed of light
= 3  108 m s–1
first radar
pulse returns
0.2 s later
second radar second radar
pulse out
pulse returns
0.22 s later
first pulse
second pulse
time between first and
second pulses 100 s
first pulse
out
second pulse second pulse
returns
out
first pulse
returns
0.2 s
0.22 s
100 s
distance out and back
= 0.2 light-seconds
distance out and back
= 0.22 light-seconds
distance of asteroid
= 0.1 light-seconds
= 30000 km
distance of asteroid
= 0.11 light-seconds
= 33000 km
time taken
= 100 s
increase in distance
3000 km = 0.01 light-seconds
relative velocity v =
3000 km
100 s
v = 30 km s–1
v/c = 0.01 s/100 s = 10–4
You need to look at this diagram very carefully to ensure that you understand it.
You could try exam question E1 at this point.
Looking Further.
Why can’t astronomers use radar techniques to measure distances to distant stars
and galaxies?
The distance to nearby stars can be found using ‘parallax’.
A relatively nearby star moves slightly against the background of more distance stars
because of the Earth’s rotation around the Sun.
In December the foreground star will be near A, in June it will appear near B. If we
know the radius of the Earth’s orbit then simple trig will allow us to calculate the
distance to the star.
As stars get further away the parallax gets smaller and smaller. In fact we can onoly
measure particularly close stars by this method.
Nearby star – big parallax
More distant star – smaller parallax.
So how to measure greater distances ?
To get round this problem astronomers first used the ‘inverse-square law’ of
radiation.
The brightness of a light source is proportional to 1/distance2.
This means that if the distance to a light source is doubled the brightness will fall to a
quarter of its original value.
So, brighter stars are nearer, dimmer stars are further, right?
Wrong. This only works if all stars are the same, but they’re not. Some stars are
simply brighter than others. They’re bigger. So the inverse-square law can only be
used as a very rough guide.
Astronomers needed to find a ‘standard candle’ , a type of star that was clearly
recognisable and always had the same actual brightness (‘intrinsic brightness’).
An astronomer with the delightful name of Henrietta Swan Leavitt solved the
problem.
1912 she discovered that a certain type of star called a Cepheid variable changes its
brightness with a regular period. She also found that the length of time for a star to
complete a cycle of bright to dim to bright again depended on the size of the star.
She did this by looking at nearby Cepheids of known distance. So if you observed a
Cepheid variable and measured the changes in brightness then you could work out
the size of the star. This allowed you to work out how far away it was!
Luckily, Cepheid variables are very big, very bright stars. This means that individual
stars can be observed in galaxies beyond the Milky Way (our home galaxy).
Henrietta, you’ve just blown up the Cosmos !
As telescopes got bigger and better during the nineteenth century astronomers
discovered more and more cloudy objects called ‘nebulae’ . But what were these
nebulae, and were they in our galaxy or outside it? You see, at this time sensible
people thought that the Universe and the galaxy were the same thing – because
nothing had been detected
beyond its bounds.
Lord Rosse’s drawing of a
spiral nebula, 1848.
Here is a picture of a Cepheid in what we now know is a distant galaxy – you can see
its variation of brightness over the period during which the photographs were taken.
Now the discovery of Cepheids in nebulae meant that the distance to the nebula
could be found – and it was long ! Our galaxy is about 100,000 light years in
diameter. When a Cepheid was measured in the Andromeda Nebula it was
calculated that the distance to the nebula must be around 2 million light years distant.
And if you find one distant galaxy (as that is what the cloudy thing is) it is likely that
there are more. Overnight the Universe had grown out of all proportion, Henrietta
had blown up the Cosmos.
So, what do we know? We can use radar for small distances. We can use parallax
for distances to nearby stars and Cepheids seem to allow us to measure distances
to nearby galaxies. What next ?
The astronomer Edwin Hubble (pictured below) found a relationship between
distance and red shift that really put the cat amongst the pigeons.
Chapter 2
Big Bangs and Microwave Echoes.
You should be reading this ready to search the web. Your challenge is to find the
answers to the questions below and write them down, as well as you can in a file that
can be emailed to the School.. Your work will be marked by a physics teacher.
Here are the questions with gaps for your answers. When researching the answers
don’t just use Wikipedia as there are other more detailed pages available.
Don’t just copyand paste. Think about what you are going to write. You may also find
the notes at the end of this section useful.
Question 1.
Explain what is meant by the term redshift.
Question 2.
Explain what is meant by cosmological redshift.
Question 3. Explain how Hubble linked redshift to distance of separation between the
observed galaxy and the Earth.
Question 4: State Hubble’s Law.
Question 5: Explain what ‘Hubble’s Law’ shows.
Question 6: Explain what happened at the ‘era of recombination’ and why the
Universe was transparent after that time.
Question 7: Explain what the microwave background radiation is and why it has a
wavelength of about 1mm.
Chapter 3:
Putting it all together
Look back at the specification given at the top of the document. Prepare an illustrated
article that explains all the areas covered. This should be about 2000 words long
and you should reference your sources.
Chapter 4
Try these questions from the disk.
Question 50S: Short Answer
Electromagnetic waves travel at constant speed. Choose a wavelength that is not
absorbed too much, find a good reflector, and then you can use a pulse of waves to
see how far away the reflector is. Take the speed of light, c = 3 x 108 m s–1.
1.
A radar measurement of the distance to the Moon gives a round-trip time of
2.57 s.
Calculate how far away the Moon is.
2.
The Sun is said to be 8 light-minutes away.
How far is this in km?
3.
Earth has a radius of orbit of 1.496 x 1011 m. Venus has a radius of orbit of
1.082 x 1011 m.
Based on this information alone, what might you expect to be the minimum
and maximum round-trip times for radar pulses reflected from Venus?
Pluto has a radius of orbit of 59.13 x1011 m, and a radius of 1151 km.
Outline the problems that might arise in trying to radar range Pluto. Provide
some calculated estimates to support your assertions where possible.
4.
Question 100S: Short Answer
The Universe as a perfect (black-body) radiator at 2.7 K
This question is about the temperature of the Universe and the radiation that has
filled it since neutral atoms were first produced.
Plasma absorbs photons
It is thought that the early Universe was too hot for electrons and protons to combine
together to form neutral atoms, but they existed as a mixture of positive ions and
electrons (a plasma). In these conditions photons cannot travel freely, as
electromagnetic photons continually interact with the ions, so dense plasma is not
transparent.
1.
'Hot atoms' are atoms with large quantities of random kinetic energy. Explain
why such atoms would break down into electrons and positive ions.
2.
The radiative zone of a star like our Sun consists of dense plasma. Explain
why the photons generated in the Sun’s core take millions of years to travel across
the radiative zone.
The photons generated in the core are gamma photons of frequency ~ 4 × 1017 Hz.
The radiative zone gets cooler and cooler from the core to the convective zone. By
continual absorption and emission in the radiative zone, photons of lower energy are
produced. Eventually, the photon energy is transferred by convection to the
photosphere (the Sun’s surface), where photons of frequency ~ 6 × 1014 Hz are
emitted.
3.
Show that, for each gamma photon produced in the core, about 600 photons
are emitted from the Sun’s surface.
The Universe becomes transparent
Electromagnetic radiation could not travel through the early Universe, filled with
charged particles like the radiative zone of a star. As the Universe expanded, it
cooled.
About 105 years after the Big Bang, the Universe had cooled to 3000 K, when the
ions in the plasma combined to form stable neutral atoms. The photons produced in
the combination were now free, in the absence of the plasma, to travel throughout
the Universe.
Wilhelm Wien investigated the radiation emitted by a ‘black-body’ (a perfect emitter)
at a temperature T (in kelvin) and deduced that the peak of the distribution of
energies it emits occurs at a wavelength  given by
T = 2.9 × 10–3 m K
This is Wien’s displacement law, for which he received the Nobel Prize in 1911. You
can apply this to the entire Universe, which acts as a perfect emitter, giving out the
radiation with which it fills itself.
4. Use Wien’s law to find the peak wavelength emitted by the Universe at 3000 K.
5.
In what region of the electromagnetic spectrum would you expect to detect
this radiation?
6.
3000 K is about the temperature of the tungsten wire in a light bulb. Why
do tungsten light bulbs produce so much heat? Why does the glass
envelope get so hot?
The Universe expands to its current size
As the Universe has expanded, the photons that fill it have been stretched in
wavelength.
7.
Theory suggests that the Universe has now cooled to a temperature of 2.7 K.
Use Wien’s law to find the peak wavelength emitted by the Universe at 2.7 K. Why is
this radiation referred to as Cosmic Microwave Background Radiation?
8.
Show that the diameter of the Universe is currently about 1000 times larger
than it was when it became transparent.
9.
Arno Penzias and Robert Wilson first detected the Cosmic Microwave
Background Radiation from an observatory on Earth's surface. Suggest reasons why
accurate measurements of this radiation, which confirm the temperature of the
Universe as 2.735 K, needed to be done from a satellite.