1. This question is about the mean density of matter in the universe.
(a) Explain the significance of the critical density of matter in the universe with respect to the possible fate of the universe.
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The critical density ρ0 of matter in the universe is given by the expression
2 3H 0 ρ0 = , 8πG
where H0 is the Hubble constant and G is the gravitational constant.
–18 –1 An estimate of H0 is 2.7 × 10 s .
(b) (i) Calculate a value for ρ 0.
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(ii) Hence determine the equivalent number of nucleons per unit volume at this critical density.
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1 2. The question is about stellar radiation and the star Betelgeuse.
(a) Explain the term black-body radiation .
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The diagram below is a sketch graph of the black-body radiation spectrum of a certain star.
intensity
(b) Label the x-axis of the graph. (1)
(c) On the graph, sketch the black-body radiation spectrum of a star that has a lower surface temperature and lower apparent brightness than this star. (2)
The star Betelgeuse in the Orion constellation emits black-body radiation that has a maximum intensity at a wavelength of 0.97 µ m.
(d) Deduce that the surface temperature of Betelgeuse is about 3000 K.
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2 3. This question is about various bodies in the universe.
(a) Briefly describe the nature of a star.
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(b) Distinguish between a constellation and a galaxy.
Constellation: ......
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Galaxy: ......
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3 4. This question is about some of the properties of Barnard’s star.
Barnard’s star, in the constellation Ophiuchus, has a parallax angle of 0.549 arc-second as measured from Earth.
(a) With the aid of a suitable diagram, explain what is meant by parallax angle and outline how it is measured.
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(b) Deduce that the distance of Barnard’s star from the Sun is 5.94 ly.
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4 apparent brightness of Barnard' s star (c) The ratio is 2.6 × 10 –14 . apparent brightness of the Sun
(i) Define the term apparent brightness .
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luminosity of Barnard' s star (ii) Determine the value of the ratio (1 ly = 6.3 × luminosity of the Sun 10 4 AU). (4)
(d) The surface temperature of Barnard’s star is about 3 500 K. Using this information and information about its luminosity, explain why Barnard’s star cannot be
(i) a white dwarf.
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(ii) a red giant.
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5 5. This question is about the solar system.
(a) State the name of the planet in the solar system that has
(i) the greatest mass;
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(ii) an orbit around the Sun between that of Saturn and of Neptune.
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(b) State where, in the solar system, the asteroid belt is found.
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(c) State two features of the orbits of comets.
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6. State and explain two conditions that are necessary for nuclear fusion to be initiated in a star.
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6 7. This question is about stars.
(a) Stars are very massive. State why stable stars are not crushed inwards under gravitational pressure.
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(b) State the difference between a visual binary star and a spectroscopic binary star.
Visual binary: ......
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Spectroscopic binary: ......
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8. This question is about comets and stars.
(a) State one difference (other than size) between the orbit of a typical comet and the orbit of the Earth around the Sun.
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(b) The average distance between the stars in a galaxy is about 2 pc. A typical galaxy has a volume of 10 12 pc 3. Estimate the number of stars in the galaxy.
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9. This question is about stars.
7 Betelgeuse and Rigel are two super giants in the constellation of Orion.
(a) Distinguish between a constellation and a stellar cluster .
Constellation: ......
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Stellar cluster: ......
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(b) The star Betelgeuse has a parallax of 0.0077 arc second. Deduce that its distance from Earth is approximately 130 pc.
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(c) State why the Hipparcos satellite which orbits Earth is able to measure stellar parallaxes for stars at considerably greater distances than 130 pc.
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8 (d) The table below gives some information about the types and magnitudes of Betelgeuse and Rigel.
Star Type Apparent Colour Apparent magnitude brightness
Betelgeuse M −0.04 2.0 × 10 −7 W m −2
Rigel B 0.12 3.4 × 10 −8 W m −2
(i) Complete the above table for the colours of the stars. (2)
(ii) State why Betelgeuse has a lower apparent magnitude than Rigel. (1)
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(iii) Given that the distance of Betelgeuse from Earth is 130 pc, calculate the luminosity of Betelgeuse.
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9 (iv) The luminosity of Rigel is 2.3 × 10 31 W. Without any further calculation, explain whether Rigel is closer or further than Betelgeuse from Earth.
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