Lesson 55 the Structure of the Universe

Name……………..

Class…………..

Plymstock School Physics Department

Module G485.5 Modelling the Universe

student booklet Lesson 52 – The Structure of the Universe

Objectives

(a) describe the principal contents of the universe, including stars, galaxies and radiation;

(b) describe the solar system in terms of the Sun, planets, planetary satellites and comets;

Outcomes

Be able to describe the principal contents of the universe, including stars, galaxies and radiation.

Be able to describe the solar system in terms of the Sun, planets, planetary satellites and comets.

Write your own definitions of these Keywords:

Universe

……………………………………………………………………………………

Star

……………………………………………………………………………………

Galaxy

……………………………………………………………………………………

Sun

……………………………………………………………………………………

Planet

……………………………………………………………………………………

Moon

……………………………………………………………………………………

……………………………………………………………………………………

Nebulae

……………………………………………………………………………………

Comet

……………………………………………………………………………………

Red giant

……………………………………………………………………………………

White dwarf

……………………………………………………………………………………

Main sequence star

……………………………………………………………………………………

Super red giant

……………………………………………………………………………………

Neutron star

……………………………………………………………………………………

Black hole

……………………………………………………………………………………

Supernova

……………………………………………………………………………………

Binary star

……………………………………………………………………………………

Quasar

……………………………………………………………………………………

Radiation

……………………………………………………………………………………

The Structure of the Universe Research Project

Create a presentation that describes the principal contents of the universe, including:

stars,

galaxies and

radiation

and describes the solar system in terms of the

Sun,

planets,

planetary satellites and

comets.

ALL (E-D) must define each term above

MOST (C-B) will give examples of each in and out of the Solar System as appropriate

SOME will explain the origin of the above elements and create a neat and logical presentation using keywords correctly.

Lesson 53 notes – Stars

Objectives

(d) describe the Sun’s probable evolution into a red giant and white dwarf;

(e) describe how a star much more massive than our Sun will evolve into a super red giant and then either a neutron star or black hole;

Outcomes

Be able to describe the formation of a star, such as our Sun, from interstellar dust and gas.

Be able to describe the Sun’s probable evolution into a red giant and white dwarf.

Be able to describe how a star much more massive than our Sun will evolve into a super red giant and then either a neutron star or black hole.

The Hertzsprung-Russell diagram and the evolution of stars

The Hertzsprung-Russell diagram can be used to show the evolution of stars. Two paths are shown:

(a) Figure 1 for stars of similar mass to the Sun (<3 solar masses)

(b) Figure 2 for stars of three or more times the mass of the Sun (> 3 solar masses)

Lesson 54 questions – Stars

Name………………………… ( /14)………%………

Class……………..

ALL

1. Describe and explain the stages which take place in the birth of a Main Sequence star.

......

[Total 5 marks]

2. When a star ceases to be Main Sequence, it may evolve in several different ways.
Explain the circumstances which will lead to the formation of a neutron star.

......

[Total 4 marks]

3. (i) A star of mass 7 × 1030 kg becomes a neutron star of radius 10 km. Calculate the average density of the neutron star, assuming that 50% of the original star’s mass has been lost.

density = ……………….. kg m–3

[3]

(ii) State how the density of a neutron star compares to that of materials commonly found on Earth.

......

[2]

[Total 5 marks]

Lesson 55 notes – Astronomical distances

Objectives

(f) define distances measured in astronomical units (AU), parsecs (pc) and light-years (ly);

(g) state the approximate magnitudes in metres, of the parsec and light-year;

(h) state Olbers’ paradox;

(i) interpret Olbers’ paradox to explain why it suggests that the model of an infinite, static universe is incorrect (HSW 7);

Outcomes

Be able to define distances measured in astronomical units (AU), parsecs (pc) and light-years (ly);

Be able to state the approximate magnitudes in metres, of the parsec and light-year;

Be able to state Olbers’ paradox.

Be able to interpret Olbers’ paradox to explain why it suggests that the model of an infinite, static universe is incorrect.

Be able to convert distances from metres to parsecs to light-years.

Radar

A radio pulse can be sent out and the time taken for the reflected pulse to be received is recorded. If we know the speed of electromagnetic radiation in free space and the time between transmission and reception the radar pulse enables us to find the distance of the object.

Parallax

The difference in direction of a star viewed from the two ends of a line with a length equal to the radius of the Earth’s orbit is called the PARALLAX of the star.

Stars that are close to the earth have a larger parallax than ones far away. In other words their position in the sky against far away stars when viewed from the Earth changes significantly as the Earth orbits the Sun.

By significantly we mean a fraction of a second of arc. In the example shown a Centauri (distance 1.33 parsecs) has a parallax of 0.75 “ of arc.

Astronomical unit

One Astronomical unit (AU) is defined as the mean distance of the Earth from the Sun (1.5x1011 m)

The light year

This is the distance that light travels in free space in one year = 9.5x1015 m

The Parsec

The radius of Earth’s orbit = 1.5x1011 m, and therefore the distance is found from:

tan(1”) = 1.5x1011/d so d = 3.06 x1016 m

1 parsec is the distance at which an object subtends an angle of one second using the radius of the Earth’s orbit as the baseline.

Distances between galaxies are usually measured in light years or Mega parsecs (Mpc).

1 Parsec = 3.06x1016 m = 2.04x105 AU = 3.26 light years

1 Mega parsec (Mpc) = 3.26x106 light years = 3.097x1022 m

The parallax of a number of stars is shown in the following table:

Star / Parallax
(" of arc) / Distance (l.y) / Star / Parallax
(" of arc) / Distance (l.y)
A Centauri / 0.750 / 4.3 / Vega / 0.133 / 25
Barnard's Star / 0.545 / 6.0 / Arcturus / 0.097 / 34
Sirius / 0.377 / 8.6 / Aldebaran / 0.054 / 60
Procyon / 0.285 / 11.4 / Castor / 0.001 / 570

At distances much greater than this the parallax method becomes impossibly difficult to measure. Remember that 1" of arc is the angle subtended by a human head almost ¾ of a kilometer away. Therefore the parallax of Castor is the same as the angle subtended by a human head at a distance of almost 750 km!

Another method for measuring larger distances had to be found.

Cepheid variables

The solution came early in the twentieth century as a result of studies of a variable star (one whose brightness changes with time) in the constellation of Cepheus.

The brightness of the star varied in a particular way (see Figure 3) and in 1912 Miss Henrietta Leavitt of Harvard College observatory discovered an important connection between the period and brightness. This is now known as the period-luminosity relationship. Many other stars were found to vary in a similar way and the group of stars was called Cepheid variables. (There are actually two types of Cepheid variable but we will just consider one type here).

The period-luminosity relation means that if you can measure the period of a Cepheid variable you can find its luminosity. Knowing how bright the star really is and then measuring how bright it appears to be will then give the distance of the star from the Earth. The discovery of Cepheid variables in the Andromeda nebula (M31) enabled its distance from Earth (over two million light years) to be found.

Two ways of presenting the period luminosity law are shown by the graphs in Figure 4.

Olber’s Paradox

Lesson 56 – Astronomical distances

Name………………………… ( /8)…….%….……

Class………..

ALL

1. The average orbital radius of Jupiter is approximately 5.2 AU.
Calculate the orbital radius of Jupiter in metres.

radius = ...... m

[Total 1 mark]

MOST

2. (a) Suggest why many stars within our galaxy do not conform with Hubble’s law.

......

[2]

(b) Estimate the age of the Universe, giving your answer in seconds. Show your working and take the Hubble constant to be 75 km s–1 Mpc–1.

age = ...... s

[3]

[Total 5 marks]

ALL

3. Large distances in the Universe may be measured in parsecs. Explain what is meant by a parsec.

......

[Total 2 marks]

Lesson 57 - The Red Shift

Objectives

(j) select and use the equation

Δλ = v

λ c

(k) describe and interpret Hubble’s redshift observations;

(l) state and interpret Hubble’s law (HSW 1 & 2);

(m) convert the Hubble constant H0 from its conventional units (km s-1 Mpc-1) to SI (s1);

Outcomes

Be able to select and use the equation

Δλ = v

λ c

Be able to describe Hubble’s redshift observations;

Be able to state Hubble’s law (HSW 1 & 2);

Be able to describe and interpret Hubble’s redshift observations;

Be able to state and interpret Hubble’s law (HSW 1 & 2);

Be able to convert the Hubble constant H0 from its conventional units (km s-1 Mpc-1) to SI (s-1);

The Doppler Effect predicts that radiation from sources that are towards us will be shifted towards shorter wavelengths (the blue end of the spectrum in the case of visible light) and towards longer wavelengths (the red end of the spectrum) if they are moving away from us.

Observations of the spectra of galaxies show that the light coming from many of these is shifted significantly towards the red and this shows that they are moving away from us at high speeds, many tens of thousands of kilometres per second. This shift towards the red is called the Red Shift and is very good evidence for the expansion of the Universe and for the origin of the Universe in the Big Bang.

If the Doppler shift of lines within their spectra can be measured their speed of recession can be calculated. The speed (v) relative to the observer on the Earth is given by:

Velocity of galaxy (v) = Dlc/l where l is the wavelength of a line in the spectrum on Earth, Dl is the shift in wavelength and c is the speed of light.

A diagrammatic version of the shift of two absorption lines for three galaxies together with their speeds of recession is shown in the following diagram. The comparison spectrum of an element on Earth, at rest compared with the observer, is shown above and below each galactic spectrum.

For very high speeds the simple formula cannot be used and the effects of special relativity have to be allowed for.

It is important to realise that the Doppler shift will depend on the original wavelength and so lines in the red end of the spectrum will be shifted more than those towards the violet end.

Hubble’s Law

Hubble measured red shift and distances and plotted these on a graph:-

Olbers’ paradox was solved by Hubble’s discovery because an expanding universe means that the amount of light from a receding galaxy reaching the Earth per second is reduced and also the fact that it is red shifted means that it has less energy when it reaches us! Therefore, the more distant a galaxy, the less of a contribution it makes to the total amount of light here on Earth and hence it is dark at night because the Universe is expanding!

Converting Units

You can convert the value of H to SI units as follows:

Take the Hubble constant H to be 70 kms-1 Mpc-1

and one light year to be 9.46x1015 m

One Parsec = 3.26 light years = 3.0857x1016 m

therefore 1 Mpc = 3.0857x1022 m

So 70 kms-1Mpc-1 = 70x103/ 3.09x1016x106 = 2.27 x 10-18 ms-1m-1

Lesson 58 questions – Redshift

Name……………………. ( /31)……….%……..

Class………………

ALL

1. The mean density of the Universe, ρ0, is thought to be approximately 1 × 10–26 kg m–3.
Calculate a value for the Hubble constant H0.

H0 =...... s–1

[Total 2 marks]

2. State Hubble’s law and define any symbols used.

......

[Total 2 marks]

3. Describe Olbers’ paradox and explain how the work of Edwin Hubble provides an answer.

......

[Total 5 marks]

4. In 1929 Edwin Hubble showed that the Universe was expanding by studying the light from stars and galaxies. Explain how.

......

[Total 5 marks]

5. (a) Suggest why many stars within our galaxy do not conform with Hubble’s law.

......

[2]

(b) Estimate the age of the Universe, giving your answer in seconds. Show your working and take the Hubble constant to be 75 km s–1 Mpc–1.

age = ...... s

[3]

[Total 5 marks]

MOST

6. Astronomers are searching for planets which orbit distant stars. The planets are not visible from the Earth. Their existence is revealed by the star’s motion which causes a shift in the wavelength of the light it emits.
A large planet P is shown orbiting a star S in the Fig. 1. Both the star and the planet rotate about their common centre of mass C.

Fig. 1

When measured from a stationary source in the laboratory, a spectral line has a wavelength l of 656.3 nm.
The light from star S is examined over a period of 74 hours. The change in wavelength ∆l for the same spectral line is recorded. The velocity has been calculated and the data shown in Fig. 2.

time / h / ∆λ /10–15 m / velocity / m s–1
1 / 6.7 / 3.1
6 / 38.1 / 17.5
12 / 66.0 / 30.3
19 / 76.0 / 34.9
23 / 69.1 / 31.7
29 / 43.8 / 20.1
35 / 6.8 / 3.1
41 / –32.2 / –14.8
48 / –66.0 / –30.3
55 / –76.0 / –34.9
61 / –62.5 / –28.7
67 / –32.2 / –14.8
74 / 6.1

Fig. 2