ast301probs5-sol

ast301probs5-sol - Homework 5 University Astronomy...

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Homework 5 University Astronomy 5/15/10 1 University Astronomy 1017-301 Homework Assignment 5 Instructor: Dr Andrew Robinson Due Date: 9am Friday, 14 May 2010. To tackle some of the following problems you will need to do some research, using either the textbook or other resources, to find various pieces astronomical data and the values of certain physical constants. For calculations, show all your workings in order to receive full credit . 1. a. Estimate the total number of orbits around the galactic center that the sun will make during its main sequence lifetime . b. How far would an O star, 5 × 10 5 times more luminous than the sun, travel along its orbit, if it formed at the same distance from the galactic center as the sun? 2. The quasar PG1700+518 has a redshift z = 0.292 and a flux in the visible band F V = 1.0 × 10 -14 W/m 2 . a. What is the distance to this quasar in Mpc. (Note: use the formula for relativistic redshift given in Lecture 22). b. What is its luminosity in the visual band, L V . c. Assuming that its bolometric (i.e., Assuming that its bolometric (i.e., total) luminosity is 9 L V , calculate the mass of the smallest black hole that is required to power this quasar. a) The Sun’s main sequence lifetime is 1.2x10 10 yr. The period of a single orbit around the galactic center is P = 2 π r/v, where r = 8.0 kpc and v = 220 km/s. After the unit conversions, this yields P = 7.05x10 15 s = 2.24x10 8 y. The number of orbits completed during the Sun’s M-S lifetime is, therefore, N = (1.2x10 10 yr)/( 2.24x10 8 y) 54. b) We can find the lifetime of the O star using the same method as in HW4 Q1: t O = (1/5x10 5 ) 5/7 x1.2x10 10 y 1.0x10 6 y. If it formed at the same distance from the galactic center as the Sun, it will have the same orbital speed and hence it will travel a distance d= vt O = 220 km/s x 3.2x10 13 s = 7.1x10 15 km around it orbit during its lifetime. This is only about 0.4 % of the circumference of the orbit. Massive stars don’t move far from their birth places in the spiral arms before they die.
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Homework 5 University Astronomy 5/15/10 2 3. The Galactic Center black hole is a relatively weak X-ray source, which suggests that it is currently dormant through lack of “fuel” in the form of interstellar gas. What if, for example, the tidal disruption of a passing star (as in HW 4 problem 9) was to suddenly provide a fuel supply? a. Calculate the luminosity of the black hole if it were accreting gas at the maximum possible rate (think Eddington). b.
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ast301probs5-sol - Homework 5 University Astronomy...

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