Betelgeuse and Rigel are two super giants in the constellation of Orion. Constellation: Stellar cluster:...

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1 IB Physics Astrophysics Option Summer Assignment Name Due 2 nd Rotation Fall This question is about stars. Betelgeuse and Rigel are two super giants in the constellation of Orion. Distinguish between a constellation and a stellar cluster. Constellation: Stellar cluster: The star Betelgeuse has a parallax of arc second. Deduce that its distance from Earth is approximately 130 pc. (c) State why the Hipparcos satellite which orbits Earth is able to measure stellar parallaxes for stars at considerably greater distances than 130 pc. (d) The table below gives some information about the types and magnitudes of Betelgeuse and Rigel. Star Type Apparent magnitude Colour Apparent brightness Betelgeuse M W m 2 Rigel B W m 2 (i) (ii) Complete the above table for the colours of the stars. State why Betelgeuse has a lower apparent magnitude than Rigel. 1

2 (iii) Given that the distance of Betelgeuse from Earth is 130 pc, calculate the luminosity of Betelgeuse. (4) (iv) The luminosity of Rigel is W. Without any further calculation, explain whether Rigel is closer or further than Betelgeuse from Earth. (Total 14 marks) 2. This question is about Olbers paradox. Newton assumed that the universe is static and that the stars are uniformly distributed. State one further assumption of the Newtonian universe. Explain how Newton s assumptions led to Olbers paradox. (5) (Total 6 marks) 2

3 3. This question is about stars. Describe the final nuclear reaction in the core, and the final evolutionary state, of a low-mass star (of the order of 1 solar mass); nuclear reaction: evolutionary state: a high-mass star (of approximately 15 solar masses). nuclear reaction: evolutionary state: (Total 4 marks) 4. This question is about extragalactic astrophysics. In an observation of a distant galaxy, spectral lines are recorded. Spectral lines at these wavelengths cannot be produced in the laboratory. Explain this phenomenon. Describe how Hubble s law is used to determine the distance from the Earth to distant galaxies. 3

4 (c) Explain why Hubble s law is not used to measure distances to nearby stars or nearby galaxies (such as Andromeda). (Total 6 marks) 5. This question is about comets and stars. State one difference (other than size) between the orbit of a typical comet and the orbit of the Earth around the Sun..... The average distance between the stars in a galaxy is about 2 pc. A typical galaxy has a volume of pc 3. Estimate the number of stars in the galaxy (Total 3 marks) 6. This question is about magnitude and apparent brightness. Define apparent brightness and apparent magnitude. Apparent brightness: Apparent magnitude:

5 The table gives information on the peak absolute magnitude and the peak apparent brightness of two Cepheid stars. star (peak) absolute magnitude (peak) apparent brightness Delta Cephei Wm 2 Zera Geminorum Wm 2 State and explain whether Delta Cephei or Zeta Geminorum (i) appears brighter from Earth (ii) is closer to Earth (c) The luminosity of a Cepheid star is variable. Outline the reason for this variation

6 The graph shows the variation with period of the peak luminosity of Cepheid stars Luminosity Period/days 100 The luminosity is given in terms of the solar luminosity of W. (d) (i) Outline how data from the graph may be used to determine the distance of a galaxy from Earth (ii) The peak apparent brightness of Zeta Geminorum is Wm 2 and the period of variation of luminosity is approximately 10 days. Use data from the graph on previous page to deduce that the distance to Zeta Geminorum from Earth is about m (Total 12 marks) 6

7 7. This question is about cosmic microwave background radiation. State what is meant by cosmic microwave background radiation Describe how the cosmic microwave background radiation provides evidence for the expanding universe (Total 5 marks) 8. This question is about stellar evolution. A partially completed Hertsprung-Russel (H-R) diagram is shown below. I Luminosity S F Temperature The line indicates the evolutionary path of the Sun from its present position, S, to its final position, F. An intermediate stage in the Sun s evolution is labelled by I. 7

8 State the condition for the Sun to move from position S..... State and explain the change in the luminosity of the Sun that occurs between positions S and I..... (c) Explain, by reference to the Chandrasekhar limit, why the final stage of the evolutionary path of the Sun is at F (d) On the diagram on the previous page, draw the evolutionary path of a main sequence star that has a mass of 30 solar masses. (Total 6 marks) 9. This question is about Hubble s law. State Hubble s law..... Deduce an expression for the age T of the Universe in terms of the Hubble constant H (Total 4 marks) 10. This question is about luminosity. Define luminosity. 8

9 The sketch-graph below shows the intensity spectrum for a black-body at a temperature of 6000 K. intensity 0 0 wavelength On the axes above, draw a sketch-graph showing the intensity spectrum for a black-body at 8000 K. (c) A sketch of a Hertzsprung-Russell diagram is shown below. luminosity temperature On the diagram above, identify the (i) (ii) (iii) main sequence (label this M); red giant region (label this R); white dwarf region (label this W). 9

10 (d) In a Hertzsprung-Russell diagram, luminosity is plotted against temperature. Explain why the diagram alone does not enable the luminosity of a particular star to be determined from its temperature. (Total 8 marks) 11. This question is about stellar magnitudes and stellar distances. Define (i) apparent magnitude; (ii) absolute magnitude. Star A has an apparent magnitude of 5.0 and is 100 pc from Earth. The luminosity of star A is 4.0 times the luminosity of star B. The apparent brightness of star A is 100 times greater than the apparent brightness of star B. Deduce that (i) star B is 500 pc from Earth; 10

11 (ii) the absolute magnitude of star A is 0. (Total 7 marks) 12. This question is about cosmology. State one piece of evidence that indicates that the Universe is expanding. The rate at which the Universe is expanding depends on the density of the Universe. (i) Define critical density. (ii) Explain the importance of comparing the density of the Universe to the critical density in predicting the future of the Universe. (Total 5 marks) 13. This question is about stellar evolution. Outline the late stages in the evolution of a high-mass star that leads it to end its life as a neutron star. 11

12 Outline the mechanism that enables a neutron star to be detected from Earth. (Total 6 marks) 14. This question is about galactic motion. The K-line of light from singly ionized calcium has a wavelength of nm when measured in a laboratory. The same line in the spectrum of galaxy NGC 4889 has a wavelength of nm. The value of the Hubble constant may be assumed to be 70 km s 1 Mpc 1. Deduce a value for the distance of NGC 4889 from Earth (Total 4 marks) 12