ASTR 210 Homework Assignment 3
Due: Sep 21, 2012
1. Solar and lunar tides
Weve seen that the Sun and the Moon both have similar angular sizes as seen from the
Earth, and that the Suns gravitational tide is comparable in size to that of the Moon.
This is n
Astronomy 210
Spring 2014
Homework #9
Due online by 5:00 pm Friday, April 18
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show y
Astronomy 210
Spring 2014
Homework #3
Due online by 5:00 pm Friday, February 14
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you sho
ASTR 210 Homework Assignment 8
Due: November 6, 2013
1. Jeans equation
In lecture we derived the spherical Jeans equation,
d( 2 )
GM
+ 2 = 0,
dr
r
(1)
where M (r) is the total mass enclosed within radius r, (r) is the density of a population
of objects, a
Astronomy 210
Spring 2014
Homework #11
Due online by 5:00 pm Friday, May 2
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show you
Astronomy 210
Spring 2014
Homework #1
Due online by 5:00 pm Friday, January 31
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show
Astronomy 210
Spring 2014
Homework #2
Due online by 5:00 pm Friday, February 7
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show
Astronomy 210
Spring 2014
Homework #4
Due online by 5:00 pm Friday, February 28
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you sho
Astronomy 210
Spring 2014
Homework #5
Due online by 5:00 pm Friday, March 7
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show yo
Astronomy 210
Spring 2014
Homework #6
Due online by 5:00 pm Friday, March 14
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show y
ASTR 210 Lecture #4
Planetary motion and Kepler's laws
1. Elliptical orbits Kepler's first law
2. Equal areas in equal times Kepler's second law
3. Period-radius relation Kepler's third law
Announcements
Syllabus at https:/learn.illinois.edu/course/view.p
Astronomy 210
Spring 2014
Homework #10
Due online by 5:00 pm Friday, April 25
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show
Astronomy 210
Spring 2014
Homework #8
Due online by 5:00 pm Friday, April 11
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show y
ASTR 210 Homework Assignment 10
Due: November 20, 2013
1. The age of the universe
(a) Using H = a/a, show that the age of the universe today is
1
t=
0
da
=
a H (a)
0
dz
.
(1 + z ) H (z )
(1)
(b) Suppose that today, the universe is composed of m = 0.3, r =
ASTR 210 Homework Assignment 1 Solutions
1. Small angle formula
(a) Since 1 and 3 are small angles, we may use the small angle formula = s/D to
relate the lions angular size to its physical size s and its current distance D.
During one minute, the lions a
ASTR 210 Homework Assignment 3 Solutions
1. I, blackbody
(a) The body temperature of a human is about T = 37 C = 310 K. Using Wiens Law,
max 9.4m. So the camera should be optimized around 10 m wavelength.
(b) Again, use T =310 K and lets assume a surface
ASTR 210 Homework Assignment 2 Solutions
1. Solar and lunar tides
(a) Write M =
4
R3 .
3
Then
a =
2GM
8
G
r =
3
r
3
R
r
3
r.
(b) In the small-angle approximation, the bodys angular size is related to its physical size R and distance r by = R/r. Inserting
ASTR 210 Homework Assignment 4 Solutions
1. Giant impacts
(a) If an object is dropped from rest at distance rH , then by conservation of energy,
its velocity when it reaches the surface at radius R will be v = [2GM (R1
rH1 )]1/2 . Numerically, the Hill r
ASTR 210 Homework Assignment 7 Solutions
1. Supernova energetics
1
1
(a) K = 2 M v 2 = 2 (15M ) (3000 km/s)2 1.34 1034 J.
(b) Ephoton = L t = (1010 L ) (10 d) 3.3 1042 J. In comparison, over its 10 billion
year lifetime, the Sun will radiate energy E 1.2
ASTR 210 Homework Assignment 9 Solutions
1. Hubble expansion
(a) If a tn , then H a/a = n/t, which means t = n/H .
(b) If the Hubble parameter is constant with time, H = H0 , then a eH0 t .
2. Standard candles
(a) The observed ux fall o with distance like
ASTR 210 Homework Assignment 10 Solutions
1. The age of the universe
(a) The age of the universe is given by
t
t=
1
dt =
0
0
da
=
a
1
0
da
=
aH
0
dz
,
(1 + z )H
(1)
where we have used 1 + z = a1 and assumed that H > 0.
(b) For the assumed parameters of m
ASTR 210 Homework Assignment 5 Solutions
1. Exoplanet Properties
1/3
(a) From Keplers 3rd Law, a3 = (G M P 2 /4 2 )
1.01M and P = 1.63 days.
0.027 AU, using M M =
(b) vrel = 2a/P 182 km/s.
(c) in the center-of-mass frame, the total momentum is zero: ptot
ASTR 210 Homework Assignment 8 Solutions
1. Jeans equation
If rn for n > 0, then the Jeans equation is solved by =
GM/[(n + 1)r].
2. Rotation curve
(a) See Fig. 1. The maximal allowed total disk mass is Md = 7.5 1010 M .
(b) At r = 8 kpc, the enclosed dar
Astronomy 210
Spring 2014
Homework #7
Due online by 5:00 pm Friday, April 4
Note for quantitative questions: Answers must be legible and include all relevant calculations,
diagrams, and explanations to be graded. No credit will be given unless you show yo
ASTR 210 Lecture #5
Gravity and orbital mechanics
1. Newton's laws
2. Universal gravitation
3. Kinetic and potential energy
Announcements
Syllabus at https:/learn.illinois.edu/course/view.php?id=4051
Register your iClicker by Monday, February 3!
First hom
Welcome to Astronomy 210!
Please take a syllabus.
Instructor: Paul Ricker
[email protected]
TA:
Monica Huang
[email protected]
What you need in order to take this course
Text
iClicker
Foundations of Astrophysics
Ryden and Peterson
Either first or
ASTR 210 Lecture #7
Light
1. Light as a wave
2. Light as particles
Announcements
Register your iClicker!
Homework #2 due Friday, February 7 TODAY at 5:00 pm
Night observing projected to start February 24
Question
How large is the speed of light?
A. 186,00
ASTR 210 Lecture #18
Neutron stars and supernovae
1. Evolution of massive stars
2. Supernovae
3. Neutron stars
Announcements
Homework #7 due this Friday, April 4 at 5:00 pm
Night observing: one and done (check the website)
Observing reports may be submi
ASTR 210 Lecture #21
The Milky Way
1. Structure
2. Dynamics
Announcements
Homework #9 due this Friday, April 18 at 5:00 pm
Question
How are we situated within the Galaxy?
A. Near the center
B. In the disk, about halfway out
C. In the disk, near the edge
D