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The Milky Way was once thought to be “murky” or “milky” but is now considered to be made up of point sources. Explain.
A star is in equilibrium when it radiates at its surface all the energy generated at 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?
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.
Does the H-R diagram 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?
Can we tell, by looking at the population on the H-R diagram, that hotter main-sequence stars have shorter lives? Explain.
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?
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 absolute luminosity of the star. How could these stars be used to measure the distance to galaxies?
What is a geodesic? What is its role in General Relativity?
If it were discovered that the red shift of spectral lines of galaxies was due to something other than expansion, how might our view of the universe change? Would there be conflicting evidence? Discuss.
All galaxies appear to be moving away from us. Are we therefore at the center of the universe? Explain.
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.
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?
If nothing, not even light, escapes from a black hole, then how can we tell if one is there?
What mass will give a Schwarzschild radius equal to that of the hydrogen atom in its ground state?
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 on Fig. 33-25?
Explain what the 2.7-K cosmic microwave background radiation is. Where does it come from? Why is its temperature now so low?
Why were atoms, as opposed to bare nuclei, unable to exist until hundreds of thousands of years after the Big Bang?
Under what circumstances would the universe eventually collapse in on itself?
Using the definitions of the parse and the light-year, show that 1 pc = 3.26ly.
A star exhibits a parallax of 0.38 seconds of arc. How far away is it?
The parallax angle of a star is 0.00019o. How far away is the star?
A star is 36pc away. What is its parallax angle? State
(a) In seconds of arc, and
(b) In degrees.
What is the parallax angle for a star that is 55ly away? How many parsecs is this?
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 why factor?
A star is 35pc away. How long does it take for its light to reach us?
We saw earlier 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 l of the Sun and
(b) The absolute luminosity L of the Sun?
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).
Estimate the angular width that our Galaxy would subtend if observed from the nearest galaxy to us. Compare to the angular width of the Moon from Earth.
When our sun becomes a red giant, what will be its average density if it expands out to the orbit of Earth (1.5 X 1011m from the Sun)?
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?
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?
A neutron star whose mass is 1.5 solar masses has a radius of about 11km. Calculate its average density and compare to that for a white dwarf and to that of nuclear matter.
Calculate the Q-values for the he burning reaction of Eq. 33-2. (The mass of the very unstable 8/4Be is 8.005305u.)
Suppose two stars of the same apparent brightness are also believed to be the same size. The spectrum of one star peaks at 800nm whereas that of the other peaks at 400nm. Use Wien’s law and the Stefan-Boltzmann’s equation (Eq. 14-5) to estimate their relative distance from us.
Stars located in a certain cluster are assumed to be about the same distance from us. Two such stars have spectra that peak at λ1 = 500 nm and λ2 = 700nm, and the ratio of their apparent brightness is l1/l2 = 0.091. Estimate their relative sizes (give ratio of their diameters).
Show that the Schwarzschild radius for a star with mass equal to that
(a) Of our Sun is 2.95km, and
(b) Of Earth is 8.9mm.
What is the Schwarzschild radius for a typical galaxy (like ours)?
Describe a triangle, drawn on the surface of a sphere, for which the sum of the angles is
(a) 359o, and
What are the maximum sum-of-the-angles for a triangle on a sphere?
If a galaxy is traveling away from us at 1.0% of the speed of light, roughly how far away is it?
The red shift of a galaxy indicates a velocity of 3500km/s. How far away is it?
Estimate the speed of a galaxy (relative to us) that is near the observable “edge” of the universe, say 12 billion light-years away.
Estimate the observed wavelength for the 656-nm line in the Balmer series of hydrogen in the spectrum of a galaxy whose distance from us is
(a) 1.0 x 106 ly,
(b) 1.0 x 108 ly,
(c) 1.0 x 1010 ly.
Estimate the speed of a galaxy, and its distance from us. If the wavelength for the hydrogen line at 434nm is measured on Earth as being 610nm.
What is the speed of a galaxy with z = 0.600?
What would be the red shift parameter z for a galaxy traveling away from us at v = 0.50c?
Starting from Eq. 33-3, show that the Doppler shift in wavelength is ∆Λ/Λ0 ≈ v/c (Eq. 33-5b) for v << c.
The critical density for closure of the universe is pc ≈ 10 –26 kg/m3 state pc in terms of the average number of nucleons per cubic meter.
The scale of the universe (the average distance between galaxies) at any one moment 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 = 10–35s.
At approximately what time had the universe cooled below the threshold temperature for producing
(a) Kaons (M ≈ 500 MeV/c2).
(b) Y (M ≈ 9500MeV/c2), and
(c) Muons (M ≈ 100MeV/c2)?
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.
Assume that the nearest stars to us have an absolute luminosity about the same as the Sun’s. Their apparent brightness, however, is about 1011 times fainter than the Sun. Form 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 20km, from a star whose radius was equal to that of our Sun (7 x 108m), of mass 1.5 times that of the Sun, and which rotated (like our Sun) about once a month.
By what factor does the rotational kinetic energy change when the star in Problem 36 collapses to a neutron star?
A certain pulsar, believed to be a neutron star of mass 1.5times that of the Sun, with diameter 20km, is observed to have a rotation speed of 1.0rev/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 x 106 ly away. If both galaxies have a mass of 3 x 1041kg, with what gravitational force does each galaxy attract the other?
Estimate what neutrino rest mass (in eV) 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.
Two stars, whose spectra peak at 600nm and 400nm, respectively, both lie on the main sequence. Use Wien’s law, the Stefan-Boltzmann’s equation, and the H – R diagram (Fig. 33-6) to estimate the ratio of their diameters.
Suppose we can measure distances with parallax at 100 parsecs. What is our minimum angular resolution (in degrees), based on this information.
Through some coincidence, the Balmer lines from singly ionized helium in a distant star happen to overlap with the Balmer lines from hydrogen (Fig. 27-22) in the Sun. How fast is the star receding from us?
What is the temperature that corresponds to 1.8-TeV collisions at the Fermilab Collider? To what era in cosmological history does this correspond?
Astronomers have recently measured the rotation of gas around what might be a super massive 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 ∆λ/λ0 do you estimate they saw?
A galaxy is moving away from Earth. The “blue” hydrogen line at 434nm emitted from the galaxy is measured on Earth to be 650nm.
(a) How fast is the galaxy moving?
(b) How far is it from Earth?
In the later stages of stellar evolution, a star (if massive enough) will begin fusing carbon nuclei to form, for example, magnesium;
(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?
How large would the Sun be if its density equaled the critical density of the universe, pc ≈ 10 – 26 kg/m3? Express your answer in light-years and compare with the Earth-Sun distance and the size of our Galaxy.