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Name……………………………………………………………
BWS Y13 Physics
G485 Frontiers in Physics
Homework Booklet - Teacher 1
Cosmology
Grade Boundaries are:
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
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A 80%
B 70%
C 60%
D50%
E 45%
Mark
Structure of the Universe/34
Stellar Evolution/28
Olbers’ Paradox and Hubble’s Law/45
Critical Density and Fate of the
Universe/32
%
Grade
Equations and data for this unit that you may find useful:
c = 3.0 x 108 ms-1
G = 6.67 x 10-11 Nm2kg-2
1 light year ≈ 9.5 x1015 m
𝑉=
4 3
𝜋𝑟
3
𝑎𝑔𝑒 𝑜𝑓 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒 ≈
3𝐻2
𝜌=
8𝜋𝐺
𝑣 𝛥𝜆
=
𝑐
𝜆
1
𝐻
Structure of the Universe
1. (a) Rank these astronomical bodies in order of size, smallest first.
The moon, galaxy, Jupiter, Earth, red giant, neutron star.
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(b) Define the astronomical unit.
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(c) Define the light year.
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………………………………………………………………………………………………………...[1]
(d) The astronomical unit, AU is approximately 1.5 x108 km. Show that it takes light
approximately 8 minutes to travel 1 AU.
[2]
(e) Show that 1 light year is greater than 60 000 AU.
[2]
2.(a) By drawing a carefully labelled diagram to illustrate your answer, define the parsec.
……………………………………………………………………………………………………………
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……………………………………………………………………………………………………….. [3]
(b) Convert the following parallax angles in degrees into seconds of arc:
(i) 1
………………………
(ii) 0.05
……………………….
(ii) 0.017
……………………….
(iii) 0.00021 ………………………..
[4]
(c) A star is observed to have a parallax angle of 0.132 seconds of arc. Calculate its
distance from the observer in parsecs and light years.
………..………………………….pc
………………………….light years
[3]
(d) A red giant star is observed to be at a distance of 400 light years. Calculate its parallax
angle in seconds of arc.
…………………….” [3]
3. The radii of Venus and Earth’s orbits respectively are 1.08 x 1011 m and 1.50 x 1011 m.
Calculate the ratio of the maximum angular size to the minimum angular size of Venus when
viewed from Earth.
[4]
4. The Sun has a mass of about 2.0 x 1030 kg and a radius of 7.0 x 108 m. The Earth has a
mass of about 6.0 x 1024 kg and a radius of 6.4 x 106 m.
(a) Calculate the ratio of volume of the Sun to the volume of the Earth.
……………………………………….[2]
(b) (i) Calculate the ratio of density of the Earth to density of the Sun.
…………………………………………….[3]
(ii) The Sun’s power is sourced from the fusion of hydrogen to helium. Deduce what you can
about the density of the Sun’s core.
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………………………………………………………………………………………………………...[1]
(iii) Light from the Sun falls with an intensity of 1400 Wm-2 above the equator and outside
the Earth’s atmosphere. Show that the total power output of the Sun is about 4 x 1026 W.
[3]
END
Stellar Evolution
1. (a) Describe the formation of a star such as the Sun and its most likely evolution. Your
answer should make clear how the steps in the sequence are ordered.
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………………………………………………………………………………………………………...[6]
(b) Describe the probable evolution of a star much more massive than our Sun.
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……………………………………………………………………………………………………...…[2]
(c) State two properties of a white dwarf.
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………………………………………………………………………………………………………...[2]
(d) Describe why a star will be at its brightest when the star is at its coolest.
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…………………………………………………………………………………………………...……[2]
(e) A recently observed supernova in a distant galaxy was estimated to have released
approximately 1044 J of energy. The supernova was approximately 2 x107 light years distant.
(i) Calculate the distance in parsecs.
…………………………pc [2]
(ii) The Sun is radiating with a power of approximately 4 x 1026 W. Estimate how long it will
take the Sun to release the same amount of energy as the supernova.
……..…..…………..years [3]
(iii) After the supernova stage, the star becomes a black hole. State two properties of a
black hole.
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………………………………………………………………………………………………………...[2]
2. A giant molecular cloud can be detected through its radiation when the temperature
reaches approximately 2000 K. At this point a protostar has formed – the core is not yet hot
enough for fusion to take place. A protostar is composed almost entirely of molecular
hydrogen.
(a) (i) Calculate the mean kinetic energy per molecule at 2000 K.
…………..…………J [2]
(ii) Calculate the average speed of a hydrogen molecule at 2000 K. Molecular mass of
hydrogen gas is 3.35 x10-27 kg.
…..……………….ms-1[2]
(iii) The total mass of the giant molecular cloud is 1030 kg. Show that total number of moles
of molecular hydrogen present in this giant molecular cloud is 5 x1032. The molecular mass
of hydrogen gas is 2 g mol-1.
[1]
(iv) Early in its formation the cloud was approximately spherical with a diameter of 6 AU and
a temperature of 100 K. Show that the gas pressure inside the giant molecular cloud was
about 1 Pa. The gas cloud behaves as an ideal gas.
[4]
END
Olbers’ Paradox and Hubble’s Law
1. (a) Olbers’ paradox is based on two old ideas about the universe, both now though to be
incorrect. State these two assumptions:
1………………………………………………………………………………………………………….
2……………………………………………………………………………………………………….[2]
(b) (i) State Hubble’s law.
……………………………………………………………………………………………………………
………………………………………………………………………………………………………...[2]
(ii) Hubble observed a galaxy at a distance of 2Mpc from Earth receding at a velocity of 850
kms-1. Use this information to calculate a value for Hubble’s constant.
…….…………………unit…..……...……………[2]
(iii) Show that this leads to an approximate age of the universe of approximately 2 Gy.
[3]
2. (a) State the cosmological principle.
……………………………………………………………………………………………………………
………………………………………………………………………………………………………...[2]
(b)(i) Modern observations give a value for the Hubble constant to be 74 kms-1Mpc-1.
Convert this value to SI units.
……………………………unit……………………………..
[3]
(ii) Use the value above to obtain the age of the universe.
…………………………y [2]
3. (a) The universe is said to be both isotropic and homogenous. Describe the meaning of
these two terms.
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………………………………………………………………………………………………………...[2]
(b) (i) The dark lines on a spectrum from a distant galaxy are shifted by 15% from their
laboratory value. Calculate the recessional speed of the galaxy.
………………….……………..ms-1[2]
(ii) Using a value for the Hubble constant of 65 kms-1Mpc-1, estimate the distance of the
galaxy from the Earth.
…………………………………..km [3]
(iii) Calculate the age of the universe using the value of Hubble’s constant given.
……….………………………….y [3]
(c) Two scientific observations directly support the idea that the universe is expanding.
Describe two observations that support this idea.
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Recessional velocity/km/s
4. The graph below shows the recessional velocity of distant galaxies plotted against their
distance from Earth.
50000
45000
40000
35000
30000
25000
20000
15000
10000
5000
0
0
100
200
300
400
500
600
700
Distance/ MPc
(a) (i) State Hubble’s law and explain how the graph verifies it.
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………………………………………………………………………………………………………...[3]
(ii) Use the graph to obtain a value for the Hubble constant.
…..…….…………………unit…..……………….[3]
(iii) Use the value for Hubble’s constant to obtain the approximate age of the universe.
…………………….……………y [3]
(b) (i) Use your value for Hubble’s constant to obtain the recessional velocity for a nearby
galaxy, 3.0 Mpc away.
……………………………..kms-1 [2]
(ii) Calculate the red shift for this galaxy.
…………………………………% [2]
(c) One important other piece of evidence for the big bang is the cosmic microwave
background radiation. Explain how this radiation leads to a hot big bang model of the early
universe.
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………………………………………………………………………………………………………...[3]
END
Critical Density and Fate of the Universe
1. (a) (i) A distant galaxy is observed to have a redshift of 10%. Calculate its recessional
velocity.
……………………..…………..kms-1 [2]
(ii) The distant galaxy is at an estimated distance of 400 Mpc. Calculate a value for Hubble’s
constant. Include an appropriate unit.
……………………unit………………..[3]
(iii) Use the value calculated above to calculate the critical density of the universe. Include
an appropriate unit with your answer.
………………………unit……………….[3]
(b) In the far future the universe may be closed, flat or open.
Describe these three possible fates of the universe. For each, compare the density of the
universe with the critical density.
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………………………………………………………………………………………………………...[6]
2. Current estimates of the age of the universe give a value of approximately 13 Gy.
(a) Use the age above to calculate a value for the Hubble constant.
………….……………….s-1 [3]
(b) (i) Calculate a value for the critical density of the universe.
……..….…………….kgm-3 [3]
(ii) One hydrogen atom has a mass of 1.67 x10-27 kg. Calculate the critical density in terms
of number of hydrogen atoms per cubic metre.
………………………………[2]
(iii) A modern estimate for the density of the universe is 5.5 hydrogen atoms per cubic
metre. Describe the likely evolution of the universe in the far future.
……………………………………………………………………………………………………………
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………………………………………………………………………………………………………...[3]
3. The critical density of the universe is estimated to be 1.0 x 10-26 kgm-3.
(a) (i) Calculate the Hubble constant using the critical density above.
………….………………s-1[2]
(ii) Calculate the age of the universe.
………….…………..years [2]
(b) (i) The universe may be open, closed or flat. State the condition for a flat universe and
sketch a graph of radius of the universe against time if the universe is flat.
Condition:……………………………………………………………………………………………….
Graph:
[2]
(ii) When will the universe reach its flat state?
……………………………………………………………………………………………………….[1]
END