AST 444

Problems

Ch-231. An astronomer looking through the Hubble Space Telescope can see a star with solar luminosityw at a distance of 100,000 pc. The brightest Cepheids have luminosities 30,000 times greater than that of the Sun. Taking the Sun’s absolute magnitude to be 5, calculate the absolute magnitudes of these bright Cepheids. Neglecting interstellar absorption, how far away can HST see them?

2. Using the data presented in Figure 23.21, estimate the distance from the Galactic center at which matter takes (a) 100 million years, (b) 500 million years to complete one orbit

3. Material at an angular distance of 0.2'' from the Galactic center is observed to have an orbital speed of 1200 km/s. If the Sun’s distance to the Galactic center is 8 kpc, and the material’s orbit is circular and is seen edge-on, calculate the radius of the orbit and the mass of the object around which the material is orbiting.

Chapter 24

1. According to Hubble’s law, with H0 = 70 km/s/Mpc, how long will it take for the distance from the Milky Way Galaxy to the Virgo Cluster to double?

2. Assuming Hubble’s law with H0 = 70 km/s/Mpc, what would be the angular diameter of an E0 galaxy of radius 80 kpc, if its 656.3 nm Hα line is actually observed at 700 nm?

3. A certain quasar has a redshift of 0.25 and an apparent magnitude of 13. Using the data from Table 24.2, calculate the quasar’s absolute magnitude and hence its luminosity. Compare the apparent brightness of the quasar, viewed from a distance of 10 pc, with that of the Sun as seen from Earth.

4. A quasar consumes 1 solar mass of material per year, converting 15 percent of it directly into energy. What is the quasar’s luminosity, in solar units?

1. Based on the data in Figure 25.1, estimate the mass of the galaxy NGC 4984 inside 20 kpc.

Chapter 25

2. Use Kepler’s third law to estimate the mass required to keep a galaxy moving at 750 km/a in a circular orbit of radius 2 Mpc around the center of a galaxy cluster. Given the approximations involved in calculating this mass, do you think it is a good estimate of the cluster’s true mass?

3. The spectrum of a quasar with a redshift of 0.20 contains two sets of absorption lines, redshifted by 0.15 and 0.155, respectively. If H0 = 70 km/s/Mpc, estimate the distance between the intervening galaxies responsible for the two sets of lines.

FinalChapter 26

1. What is the greatest distance at which a galaxy survey sensitive to objects as faint as 20th magnitude could detect a galaxy as bright as the Milky Way (absolute magnitude -20)?

2. If the entire universe were filled with Milky Way-like galaxies, with an average density of 0.1 per cubic megaparsec, calculate the total number of galaxies observable by the survey in Problem 1, if it covered the entire sky.

3. The Virgo Cluster is observed to have a recessional velocity of 1200 km/s. Assuming H0 = 70 km/s/Mpc and a critical-density universe, calculate the total mass contained within a sphere centered on Virgo and just enclosing the Milky Way Galaxy. What is the escape speed from the surface of this sphere?

1. Assuming critical density today, what were the temperature and density of the universe at the time the first quasars formed?

Chapter 27

2. Which component—matter or radiation—dominated the universe, and by what factor in density (assuming a critical-density universe today), at the start of (a) decoupling, (b) nucleosynthesis?

3. Estimate the temperature needed for electron–positron pair production. The mass of an electron is 9.1 10-31 kg. Use E = mc2 to find the energy (Section 16.5), E = hf and λ f = c to find the wavelength λ of a photon having that energy, and finally Wien’s law to find the temperature for which a blackbody spectrum peaks at that wavelength. How does your answer compare with the threshold temperature given in the text?

Ch 281. A planet orbits one component of a binary-star system at a distance of 1 A.U. (see Figure 28.14a). If both stars have the same mass, and their orbit is circular, estimate the minimum distance between the stars for the tidal force due to the companion not to exceed a “safe” 0.01 percent of the gravitational force between the planet and its parent star.

2. Suppose that each of the “fraction” terms in the Drake equation turns out to have a value of , that stars form at an average rate of 20 per year, and that each star has exactly one habitable planet orbiting it. Estimate the present number of technological civilizations in the Milky Way Galaxy if the average lifetime of a civilization is (a) 100 years (b) 10,000 years (c) 1 million years.

3. Convert the water hole’s wavelengths to frequencies. For practical reasons, any search of the water hole must be broken up into channels, much like you find on a television, except these channels are very narrow in radio frequency, about 100 Hz wide. How many channels must astronomers search in the water hole?