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Midterm

ASTRO 142 Exam 1Exam


Department
Astronomy
Course Code
AST 142
Professor
All
Study Guide
Midterm

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Astronomy 142 Practice Midterm Exam #2
Spring 2013
This practice exam will do you very little good unless (1) you have mastered the
homework and workshop problems, and tried to understand everything discussed in
the online solutions for all these problems; (2) you have already composed your one-
page Cheat Sheet and want to see if it really has everything you need on it, and nothing
you don’t. If you’ve done (1) and (2), feel free to proceed.
If this were a real exam, you would be advised here of the exam rules:
“You may consult only one page of formulas and constants and a calculator while
taking this test. You may not consult any books, nor each other. All of your work must
be written on the attached pages, using the reverse sides if necessary. The final answers,
and any formulas you use or derive, must be indicated clearly. Exams are due an hour
and fifteen minutes after we start, and will be returned to you during the next lecture.
Good luck.
“Note:
“Work first on the problems you find easiest, and come back to harder or less
familiar material later. Don’t get stuck.
“The amount of space left for each problem is not necessarily an indication of the
amount of writing it takes to solve it.”
Name: _______________________

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- 2 -
Problem 1. (40 points)
a. A
8
10 M
black hole at the center of an elliptical galaxy accretes matter from a
surrounding disk at a rate limited by radiation pressure. What is the luminosity
thus produced (in
L
)?
b. We usually think of the radiated energy in black hole accretion as originally
comprising a fraction
0.1
ε
=
of the rest energy of the infalling material. What is
the rate (in
-1
yearM
) at which the black hole in part (a) must accrete mass in
order to produce its luminosity?

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- 3 -
Problem 1. (continued)
c. A very young
1M
protostar, still completing its formation, accretes matter from
a surrounding disk at a rate limited by radiation pressure. What is the luminosity
thus produced (in
L
)?
d. In this case we account for the radiated energy in the gravitational potential
energy of the infalling material. Gas originating hundreds of AU away from the
star is passed through the disk and deposited on the surface of the star,
considered here to lie 1
R
from the star’s center. According to the virial theorem
only half of the potential energy drop shows up as an increase in thermal kinetic
energy; the rest is available for radiation. What is the rate (in
-1
yearM
) at
which the star in part (c) must accrete mass in order to produce its luminosity?
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