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Concept explainers
To:
(a) show that when a light wave of Figs. 44.16 a and b travels at speed c from galaxy A to Earth, then
(b) show that the change in the wavelength ∆λ is given by
(c) use binomial equation to expand the right side of equation given in (b). Then write the resulting equation for
(d) retain the first expression in the binomial expansion in (c), and then write the resulting equation for ∆λ/λ.
(e) use Hubble’s Law to compare Doppler Effect result with cosmological expansion result of (d) and find the value of α.Then analyze the results.
(f) find the distance between the galaxy A and Earth when the light was emitted by using the result in (b), and the galaxy has a red shift of 0.050. (Assuming that the expansion rate of the universe is constant, as given in the chapter.)
(g) using the result in (a) calculate how long ago was the light emitted from galaxy A.
(h) using the Doppler Effect, calculate how long ago the light was emitted from galaxy A.
(i) find the distance between the galaxy A and the Earth.
(j) find the distance between the galaxy B and Earth when the light was emitted by using the result in (b), and the galaxy has a red shift of 0.080.
(k) using the result in (a) calculate how long ago was the light emitted from galaxy B.
(l) calculate the distance between galaxy A and B, when the light from galaxy A was emitted.
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Chapter 44 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
- Show that the velocity of a star orbiting its galaxy in a circular oibit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.arrow_forward(a) What Hubble constant corresponds to an approximate age of the universe of 1010 y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of 1010 y. (b) Similarly, what Hubble constant corresponds to a universe approximately 21010years old?arrow_forwardThe distance of a galaxy from our solar system is 10 Mpc. (a) What is the recessional velocity of the galaxy? (b) By what fraction is the starlight from this galaxy red shifted (that is, what is its z value)?arrow_forward
- Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.arrow_forwardFigure P38.21 shows a jet of material (at the upper right) being ejected by galaxy M87 (at the lower left). Such jets are believed to be evidence of supermassive black holes at the center of a galaxy. Suppose two jets of material from the center of a galaxy are ejected in opposite directions. Both jets move at 0.750c relative to the galaxy center. Determine the speed of one jet relative to the other. Figure P 38.21arrow_forward1- As the universe expands, a galaxy which is at a distance of 5.0 x 106 pc, is moving away from you. What is the velocity of the galaxy relative to you? [You are given that Hubble's Constant is H = 73(km/s) / (106 pc). 2- a) The distance to Alpha Centauri (the nearest large star to Earth) is 4.37 Ly (Light Years). What is the distance in miles (given that one Ly = 5.88 x 1012 miles?) b) Present rocket ship speeds are roughly 100,000 miles per hour, which is the same as 8.766 x 108 miles per year. At this speed, and using the distance you calculated in (a), how many years would it take to travel to Alpha Centauri?arrow_forward
- The bright radio galaxy, 3c84, is observed to be moving away from the Earth at such high speed that the emitted blue 434-nm Hγ line of hydrogen is Doppler-shifted to 442 nm. Edwin Hubble discovered that all objects outside the local group of galaxies are moving away from us, with speeds v proportional to their distances R. Hubble's law is expressed as v = HR, where the Hubble constant has the approximate value H ≈ 22 ✕ 10−3 m/(s · ly). Determine the distance from the Earth to this galaxy. _________ lyarrow_forwardThe farthest objects in our Universe discovered by modern astronomers are so distant that light emitted by them takes billions of years to reach the Earth. These objects (known as quasars) have many puzzling features, which have not yet been satisfactorily explained. What is the distance in km of a quasar from which light takes 3.0 billion years to reach us ?arrow_forwardCertain wavelengths in the light from a galaxy in the constellation Virgo are observed to be 0.4% longer than the corresponding light from Earth sources. (a) What is the radial speed of this galaxy with respect to Earth? (b) Is the galaxy approaching or receding from Earth?arrow_forward
- Hubble's law can be stated in vector form as v = HR. Outside the local group of galaxies, all objects are moving away from us with velocities proportional to their positions relative to us. In this form, it sounds as if our location in the Universe is specially privileged. Prove that Hubble's law is equally true for an observer elsewhere in the Uni- verse. Proceed as follows. Assume we are at the origin of coordinates, one galaxy cluster is at location R, and has velocity v, = HR relative to us, and another galaxy cluster has position vector R, and velocity v, = HR, Suppose the speeds are nonrelativistic. Consider the frame of reference of an observer in the first of these galaxy clusters. (a) Show that our velocity relative to her, together with the position vector of our galaxy cluster from hers, satisfies Hubble's law. (b) Show that the position and velocity of cluster 2 rel- ative to cluster 1 satisfy Hubble's law.arrow_forwardWhat about when t=7s? How do we calculate that?arrow_forwardIf a galaxy moving away from the Earth has a speed of 1000 km/s and emits 656 nm light characteristic of hydrogen (the most common element in the universe). Why is the speed of the Earth in its orbit negligible here?arrow_forward
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