Ch 10   Homework

01. Calculate the escape speed from (a) the surface of the present-day Sun and (b) from the surface of the Sun when it becomes a red giant, with essentially the same mass as today but with a radius that is 100 times larger. (c) Explain how your results show that a red-giant star can lose mass more easily than a main-sequence star.
02. Calculate the average speed of a hydrogen atom (mass 1.67 x 10-27 kg) (a) in the atmosphere of the present-day Sun, with the temperature 5800K, and (b) in the atmosphere of a 1-M red giant, with the temperature 3500K. (c) Compare your results with the previous question.
03. What mass of hydrogen will the Sun convert into helium during its entire main-sequence lifetime of 1010 years? What fraction does this represent of the total mass of hydrogen that was originally in the Sun? Assume that the Sun's luminosity remains nearly constant during the entire 1010 years.
04. The earliest fossil records indicate that life appeared on the Earth about a billion years after the formation of the solar system. What is the highest mass that a star could have in order that its lifetime on the main sequence is long enough to permit life to form on one or more of its planets? Assume that the evolutionary processes would be similar to those that occurred on Earth.
05. The brightness of a certain Cepheid variable star increases and decreases with a period of 10 days. (a) What must this star's luminosity be if its spectrum has a strong absorption lines of hydrogen and helium, but no strong absorption lines of heavy elements? (b) Repeat part (a) for the case in which the star's spectrum also has strong absorption lines of heavy elements.
06. The star X Arietis is an RR Lyrae variable. Its apparent brightness varied between 2.0 x 10-15 and 4.9 x 10-15 that of the Sun with a period of 0.65 day. Interstellar extinction dims the star by 37%. Approximately how far away is the star?
07. The apparent brightness of δ Cephei (a Type I Cepheid variable) varies with a period of 5.4 days. Its average apparent brightness is 5.1 x 10-13 that of the Sun. Approximately how far away is δ Cephei? (Ignore interstellar extinction.)