(II) At approximately what time had the universe cooled

Problem 1Q The Milky Way was once thought to be "murky' or "milky' but is now considered to be made up of point sources. Explain.

Problem 2Q A star is in equilibrium when it radiates at its surface all the energy generated in its core. What happens when it begins to generate more energy than it radiates? Less energy? Explain.

Describe a red giant star. List some of its properties.

Problemp 5Q Does the H-R diagram directly reveal anything about the core of a star?

Why do some stars end up as white dwarfs, and others as neutron stars or black holes?

Problem 8P (II) We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sun (the 'solar constant’) is about 1.3 X 103 W/m2. What is (a) the apparent brightness b of the Sun. and (b) the intrinsic luminosity L of the Sun?

Problem 8Q If you were measuring star parallaxes from the Moon instead of Earth, what corrections would you have to make? What changes would occur if you were measuring parallaxes from Mars'7

Problem 9Q Cepheid variable stars change in luminosity with a typical period of several days. The period has been found to have a definite relationship with the average intrinsic luminosity of the star How could these stars be used to measure the distance to galaxies?

Problem 10P (II) Estimate the angular width that our Galaxy would subtend if observed from the nearest galaxy to us (Table 33-1). Compare to the angular width of the Moon from Earth.

What is a geodesic? What is its role in General Relativity?

Problem 11 Q If it were discovered that the redshift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change7 Would there be conflicting evidence? Discuss.

Problem 12Q Almost all galaxies appear to be moving away from us. Are we therefore at the center of the universe? Explain.

Problem 13P (II) Calculate the density of a white dwarf whose mass is equal to the Sun's and whose radius is equal to the Earth's. How many times larger than Earth's density is this.

Problem 13Q If you were located in a galaxy near the boundary of our observable universe, would galaxies in the direction of the Milky Way appear to be approaching you or receding from you? Explain.

A neutron star whose mass is 1.5 solar masses has a radius of about 11 km. Calculate its average density and compare to that for a white dwarf (Problem 9) and to that of nuclear matter.

Problem 14Q Compare an explosion on Earth to the Big Bang. Consider such questions as: Would the debris spread at a higher speed for more distant particles, as in the Big Bang? Would the debris come to rest? What type of universe would this correspond to. open or closed?

Problem 15Q If nothing, not even light, escapes from a black hole, then how can we tell if one is there?

Problem 19P (II) What is the Schwarzschild radius for a typical galaxy (like ours)?

Problem 19Q Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of thousands of years after the Big Bang?

Problem 20Q Under what circumstances would the universe eventually collapse in on itself?

(II) What is the maximum sum-of-the-angles for a triangle on a sphere?

(II) What is the speed of a galaxy with z = 0.060?

(II) Starting from Eq. , show that the Doppler shift in wavelength is \(\Delta \lambda / \lambda \approx v / c\) (Eq. for \(v \ll c\). [Hint: use the binomial expansion.] to The Big Bang, CMB, Universe Expansion ________________ Equation Transcription: Text Transcription: Delta{lambda}/lambda{approx}v/c v{<<}c

(II) The critical density for closure of the universe is \(\rho_{\mathrm{c}} \approx 10^{-26} \mathrm{~kg} / \mathrm{m}^{3}\). State \(\rho_\mathrm c\) in terms of the average number of nucleons per cubic meter. ________________ Equation Transcription: Text Transcription: rho_c{approx}10^-26 kg/m^3 rho_c

Problem 32P (II) The scale factor of the universe (average distance between galaxies) at any given time is believed to have been inversely proportional to the absolute temperature. Estimate the size of the universe, compared to today, at (a)t = 106 yr. (b)t = 1s. (c)t = 10-6s. and (d)t = 10-35 s.

(II) At approximately what time had the universe cooled below the threshold temperature for producing (a) kaons \((M \approx 500\ \mathrm {MeV}/c^2) \), (b) Y \((M \approx 9500\ \mathrm {MeV}/c^2)\), and (c) muons \((M \approx 100\ \mathrm {MeV}/c^2)\)? ________________ Equation Transcription: Text Transcription: (M{approx}500 MeV/c^2) (M{approx}9500 MeV/c^2) (M{approx}100 MeV/c^2)

Suppose that three main-sequence stars could undergo the three changes represented by the three arrows, A, B, and C, in the H-R diagram of Fig. 33-28. For each case, describe the changes in temperature, luminosity, and size.

Problem 40GP Estimate what neutrino mass (in eV/c2) would provide the critical density to close the universe. Assume the neutrino density is. like photons, about 109 times that of nucleons, and that nucleons make up only (a) 2% of the mass needed, or (b) 5% of the mass needed.

Problem 41GP Two stars, whose spectra peak at 660 nm and 480 nm. respectively, both lie on the main sequence. Use Wien's law, the Stefan-Bottzmann equation, and the H-R diagram (Fig. 33-6) to estimate the ratio of their diameters.

In the later stages of stellar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnesium: \({ }_6^{12} \mathrm{C}+{ }_6^{12} \mathrm{C} \rightarrow{ }_{12}^{24} \mathrm{Mg}+\gamma \). (a) How much energy is released in this reaction (see Appendix B). (b) How much kinetic energy must each carbon nucleus have (assume equal) in a head-on collision if they are just to touch (use Eq. 30-1) so that the strong force can come into play? (c) What temperature does this kinetic energy correspond to?

(a) How much energy is released in this reaction (see Appendix B). (b) How much kinetic energy must each carbon nucleus have (assume equal) in a head-on collision if they are just to touch (use Eq. ) so that the strong force can come into play? (c) What temperature does this kinetic energy correspond to? Consider the reaction \({ }_{8}^{16} \mathrm{O}+{ }_{8}^{16} \mathrm{O} \rightarrow{ }_{14}^{28} \mathrm{Si}+{ }_{2}^{4} \mathrm{He}\) and answer the same questions as in Problem ________________ Equation Transcription: Text Transcription: _8^16O+_8^16O{rightarrow}_14^28Si+_2^4He

How large would the Sun be if its density equaled the critical density of the universe, \(\rho_{\mathrm{c}} \approx 10^{-26} \mathrm{~kg} / \mathrm{m}^{3}\)? Express your answer in light-years and compare with the Earth-Sun distance and the size of our Galaxy.

Problem 1P (I) The parallax angle of a star is 0.00029°. How far away is the star?

Problem 3P (I) If one star is twice as far away from us as a second star, will the parallax angle of the farther star be greater or less than that of the nearer star? By what factor?

(I) A star exhibits a parallax of 0.38 seconds of arc. How far away is it?

Problem 4P (II) What is the relative brightness of the Sun as seen from Jupiter, as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the Earth is.)

Problem 4Q Select a point on the H–R diagram. Mark several directions away from this point. Now describe the changes that would take place in a star moving in each of these directions.

Problem 5P (II) When our Sun becomes a red giant, what will be its average density if it expands out to the orbit of Mercury (6 X 1010 from the Sun)?

Problem 6P (II) We saw earlier (Chapter 14) that the rate energy reaches the Earth from the Sun (the “solar constant”) is about 1.3 X 103 W/m2. What is (a) the apparent brightness b of the Sun, and (b) the intrinsic luminosity L of the Sun?

(II) A star is 35 pc away. How long does it take for its light to reach us?

Problem 7Q Can we tell, by looking at the population on the H–R diagram, that hotter main-sequence stars have shorter lives? Explain.

(II) What is the relative brightness of the Sun as seen from Jupiter as compared to its brightness from Earth? (Jupiter is 5.2 times farther from the Sun than the Earth.)

Problem 11P (II) A star is 56 pc away. What is its parallax angle? State (a) in seconds of arc, and (b) in degrees.

(II) When our Sun becomes a white dwarf, it is expected to be about the size of the Moon. What angular width will it subtend from the present distance to Earth?

(II) Calculate the -values for the He burning reactions of Eq. . (The mass of the very unstable \({ }_{4}^{8} \mathrm{Be}\) is 8.005305 u. ________________ Equation Transcription: Text Transcription: _4^8Be

(II) Suppose two stars of the same apparent brightness l are also believed to be the same size. The spectrum of one star peaks at \(800 \mathrm{~nm}\) whereas that of the other peaks at \(400 \mathrm{~nm}\). Use Wien's law (Section 27-2) and the StefanBoltzmann equation (Eq. 14-5) to estimate their relative distances from us. [Hint: see Examples 33-4 and 33-5.]

Problem 16Q What mass will give a Schwarzschild radius equal to that of the hydrogen atom in its ground state?

Problem 17P (II) What is the Schwarzschild radius for a typical galaxy (like ours)?

The Earth's age is often given as about 4 billion years. Find that time on Fig.33-25. People have lived on Earth on the order of a million years. Where is that onFig.33-25?

(I) Show that the Schwarzschild radius for a star with mass equal to that (a) of our Sun is 2.95 km, and (b) of Earth 8.9 mm.

Problem 18Q Explain what the 2.7-K cosmic microwave background radiation is. Where does it come from? Why is its temperature now so low?

Problem 20P (II) Describe a triangle, drawn on the surface of a sphere, for which the sum of the angles is (a) 359o and (b) 179o.

(I) If a galaxy is traveling away from us at 1.0% of the speed of light, roughly how far away is it?

The redshift of a galaxy indicates a velocity of \(3500 \mathrm{~km} / \mathrm{s}\). How far away is it?

Problem 24P (II) A galaxy is moving away from Earth. The “blue” hydrogen line at 434 nm emitted from the galaxy is measured on Earth to be 455 nm. (a) How fast is the galaxy moving? (b) How far is it from Earth based on Hubble’s law?

(II) Estimate the observed wavelength for the \(656-\mathrm{nm}\) line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance from us is (a) \(1.0 \times 10^6 \mathrm{ly}\), (b) \(1.0 \times 10^8 \mathrm{ly}\), (c) \(1.0 \times 10^{10} \mathrm{ly}\).

Problem 28P (II) What would be the redshift parameter z for a galaxy traveling away from us at v = 0.075c?

Problem 26P (II) If an absorption line of calcium is normally found at a wavelength of 393.4 nm in a laboratory gas, and you measure it to be at 423.4 nm in the spectrum of a galaxy, what is the approximate distance to the galaxy?

Problem 30P (II) Estimate the speed of a galaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 610 nm.

Assume that the nearest stars to us have an absolute luminosity about the same as the Sun’s. Their apparent brightness, however, is about \(10^{11}\) times fainter than the Sun. From this, estimate the distance to the nearest stars. (Newton did this calculation, although he made a numerical error of a factor of 100.)

Use conservation of angular momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of our Sun \((7 \times 10^{8} \ \mathrm {m})\), of mass 1.5 times that of the Sun, and which rotated (like our Sun) about once a month.

Problem 37GP By what factor docs the rotational kinetic energy change when the star in Problem 36 collapses to a neutron star? Problem 36 Use conservation of angular momentum to estimate the angular velocity of a neutron star which has collapsed to a diameter of 20 km, from a star whose radius was equal to that of our Sun (7 × 108 m), of mass 1.5 times that of the Sun, and which rotated (like our Sun) about once a month.

Problem 38GP A certain pulsar, believed to be a neutron star of mass 1.5 times that of the Sun, with diameter 20 km, is observed to have a rotation speed of 1.0 rev/s. If it loses rotational kinetic energy at the rate of 1 part in 109 per day, which is all transformed into radiation, what is the power output of the star?

The nearest large galaxy to our Galaxy is about \(2 \times 10^6 \ \mathrm {ly}\) away. If both galaxies have a mass of \(3 \times 10^{41} \ \mathrm {kg}\), with what gravitational force does each galaxy attract the other?

Problem 42GP Assume that the nearest stars to us have an intrinsic luminosity about the same as the Sun’s. Their apparent brightness, however, is about 1011 times fainter than the Sun. From this, estimate the distance to the nearest stars.

Problem 43GP A certain pulsar, believed to be a neutron star of mass 1.5 times that of the Sun, with diameter 16 km, is observed to have a rotation speed of 1.0 rev/s. If it loses rotational kinetic energy at the rate of 1 part in 109 per day, which is all transformed into radiation, what is the power output of the star?

Astronomers have recently measured the rotation of gas around what might be a supermassive black hole of about 2 billion solar masses at the center of a galaxy. If the radius from the galactic center to the gas clouds is 60 light-years, what Doppler shift \(\Delta\lambda/\lambda_0\) do you estimate they saw? ________________ Equation Transcription: Text Transcription: Delta{lambda}/lambda0

What is the temperature that corresponds to 1.8-TeV collisions at the Fermilab collider? To what era in cosmological history does this correspond? [Hint : see Fig.33-25.]

A galaxy is moving away from Earth. The "blue" hydrogen line at \(434 \mathrm{~nm}\) emitted from the galaxy is measured on Earth to be \(650 \mathrm{~nm}\). (a) How fast is the galaxy moving? (b) How far is it from Earth?