Physics 341: Problem Set #1 Solutions
1. (a) Use dimensional analysis to derive a relationship between the total mass of a
gravitationally bound system M , its typical size R, and the typical speed v of its
components.
We can start by writing the dimensio
Phys 341: Homework #1 Due Sept. 13 I will give partial credit for partial solutions, but only if you show your work and explain your reasoning. Be careful with units. 1. (a) Consider a globular cluster containing about 106 stars in a sphere of radius
Physics 341: Problem Set #1 Solutions
1. (a) Use dimensional analysis to derive a relationship between the total mass of a
gravitationally bound system M , its typical size R, and the typical speed v of its
components.
We can start by writing the dimensio
Physics 341: Problem Set #8 Solutions
1. The vertical motion of stars in spiral galaxies depends on the gravity exerted by the
disk, so it allows us to weigh the disk.
(a) Use dimensional analysis to derive an estimate of the mass density of a spiral
gala
Physics 341: Problem Set #2 Solutions
1. To practice/review working with vectors, compute the specic angular momentum for straight
line motion r(t) = vt + b. Is angular momentum conserved? Should it be?
x
y
Recall that l = r v, and we can compute the cros
Phys 341: Homework #1 Solutions 1. To start, let's use dimensional analysis to estimate the speed of particles moving in a system of mass M and radius R. The things we have to work with are gravity G mass M radius R [M -1 L3 T -2 ] [M ] [L]
The comb
Physics 341: Problem Set #9 Solutions
1. The Plummer model for a spherical star cluster is given by the density prole
(r) =
3M
a2
4 (r2 + a2 )5/2
where M is the total mass, and a is a core radius.
(a) Show that the enclosed mass in the Plummer model is
M
Physics 341: Problem Set #3
due October 1
You are encouraged to work in groups on these problems, but each student must write up
the solutions individually. You must also list your collaborators on your solutions, and cite
any external sources you used (o
Physics 341: Problem Set #4
due October 8, 3:20PM
You are encouraged to work in groups on these problems, but each student must write up
the solutions individually. You must also list your collaborators on your solutions (or state
that there were none), a
Lecture 2
Physics 341: Principles of Astrophysics
Sept 3, 2015
What is your major/focus?
(for my own curiosity)
A. Engineering
30%
B. Physics (non-astro) 18%
C. Astrophysics
D. Other 23%
30%
What is your previous astro
experience?
A. None
47%
B. A class o
Lecture 4
Physics 341: Principles of Astrophysics
Sept 15, 2015
An object with mass m, at a position from the origin,
r
No outside force is
is moving with a velocity v.
applied.
Which of the following quantities is not conserved?
A
r
O
Correct
Answer
B
l
Lecture 8
Physics 341: Principles of Astrophysics
Sept 29, 2015
Astronomy Updates
New Horizons, yby of Pluto-Charon system on July
14, 2015.
High-res photos still being downloaded (1 kb/s)
Astronomy Updates
Water on Mars
Conrmation that liquid water exist
Lecture 3
Physics 341: Principles of Astrophysics
Sept 10, 2015
Lecture 2: Dimensional Analysis
from http:/xkcd.com/687/
Your good friend Al Friedmann sends you a letter deriving
a very important physical equation:
dR
dt
2
8
2
GR =
3
2
kc
He tells you tha
Lecture 5
Physics 341: Principles of Astrophysics
Sept 17, 2015
Gravity Mapping
NASAs GRACE
NASAs GRAIL
o as a rst approximation we will ignore its motion. We will come
n both bodies move.
from Carroll & Ostlie, Figure 2.4
n ellipse. a is the semi-major a
Lecture 7
Physics 341: Principles of Astrophysics
Sept 24, 2015
Images of the center of the Milky Way, without and with adaptive optics
from UCLA Prof. Andrea Ghez, http:/cosmicmatters.keckobservatory.org/
2007/dec/index.htm
Doppler effect
from http:/odin
Physics 341: Problem Set #5
due October 15
You are encouraged to work in groups on these problems, but each student must write up the
solutihttp:/inspirehep.net/ons individually. You must also list your collaborators on your
solutions, and cite any extern
Physics 341: Problem Set #2
due September 24
You are encouraged to work in groups on these problems, but each student must write up
the solutions individually. You must also list your collaborators on your solutions, and cite
any external sources you used
quantity
value
units
t
(yr)
G M_sun
39.478417604
AU^3 yr^-2
specific ang. momentum, ell
6.2831853
AU^2 yr^-1
time step, Delta t
0.001
yr
initial separation, r_0
1
AU
1.5
1
x (AU)
0.5
-1.5
-1
-0.5
0
0
-0.5
-1
-1.5
y (AU)
0.5
1
1.5
0
0.001
0.002
0.003
0.004
Physics 341: Problem Set #2 Solutions
1. We showed that for circular orbits, Keplers Third Law can be written as
P2 =
4 2 3
r
GM
where M is the mass of the central object.
(a) Use this expression and a Taylor expansion to derive the following approximatio
Physics 341: Problem Set #3 Solutions
1. For this problem you can use my orbit-ps03 spreadsheet, or you can write your own
program. You can download an Excel version of the spreadsheet from
http:/www.physics.rutgers.edu/ugrad/341/orbit-ps03.xls
To use the
Physics 341: Problem Set #4 Solutions
1. We showed in class that we can derive the total mass from a visual binary orbit,
4 2 d3 3
M = m1 + m2 =
2
GP
where M is the total mass, is the angular semi-major axis in radians ( = 1 + 2 ),
P is the orbital period
Physics 341: Problem Set #5 Solutions
1. In 2003 I helped discover a transiting planet orbiting OGLE-TR-56 (a faint star in
the constellation Sagittarius). We used the Keck telescope on Mauna Kea, Hawaii to
measure the stars Doppler shift. The radial velo
Physics 341: Problem Set #6 Solutions
1. Mars has a mass of 6.4 1026 g (about one tenth M ) and a radius of 3400 km (about
half R ). Its small moon Phobos has a mass of 1.1 1019 g and a radius of just 11 km.
Phobos orbits Mars with a semimajor axis of 938
Physics 341: Problem Set #7 Solutions
1. Recall that the surface brightness of an exponential disk has the form
I (R) = I0 eR/hR
where I0 is the central surface brightness and hR is the disk scale length. The total
brightness is given by integrating this
Physics 341: Problem Set #10 solutions
1. In this problem you will calculate a microlensing light curve. In the gure below, the
dashed straight line represents the trajectory of a point source passing behind a point
mass lens (the solid dot in the center)
Phys 341: Final Exam Due Thursday Dec. 13 at 12:00 noon This is a take-home final exam, due on Thursday, December 13 at 12 noon. You may give it to me in person (room 305W in the Serin Physics Building), or email it as a PDF file (to keeton@physics.r