Astro 4: HW #2 Solutions
1. Gravitational Force in the Solar System
(a) Write down the expression for the gravitational force between the Sun and the
planet Jupiter, neglecting the gravitational eects of other planets.
F =
GMSun MJupiter
d2
Jupiter
(b) Ap

Astro 4 Homework #1 Solutions
1) Workout with Scientific Notation and Units
A. Express 0.00000000000182 in scientific notation.
Answer: 1.82 10-12
B. Express 263000000000000000 in scientific notation.
Answer: 2.63 1017
C. Express 6.0 1014 km in terms of a

Astronomy 4, Winter 2015
Homework 2 - solutions
Problem 1
a)
The acceleration of gravity is given by
g=
GM
r2
Using G = 6.67 1011 m3 kg 1 s2 , M = 6 1024 Kg, and r = 6371000 m + 390000
m = 6.761 106 m, we get g = 8.75 m/s2 .
b)
The escape velocity is give

Astro 4
Midterm Study Guide
Below, you will find a series of questions based on the lectures from the first half of
the Astro 4 course. This list is by no means exhaustive, but represents a large chunk
of what is important for the course. If you have ques

Astronomy 4, Spring 2015
April 2, 2015
Session 1 - Math and Physics Review
Do not worry about your diculties in Mathematics. I can assure you mine are still
greater.
Albert Einstein.
My oce hours are posted in CCLE .
Today we will review some math concep

Astronomy 4 HW #3
1. (a) How many kilograms of hydrogen does the Sun fuse every second?
From the proton-proton chain, we know that 4 1H 4He, where the energy loss is
0.03mp c 2 for every four hydrogen atoms. So the efficiency is:
= 4m c2 = 4 = 0.007.
p
E

Astronomy 4: HW #2
Due date: Tuesday, October 15th
1. Gravitational Force in the Solar System
(a) Write down the expression for the gravitational force between the Sun and the planet
Jupiter, neglecting the gravitational eects of other planets. Express yo

Astro 4 Final Review
HR diagram
o
If star is moving horizontally:
o
How long before sun exhausts fuel
o
Its getting cooler, expanding (redder)
5 billion years
Ex. R = 166Rsun, T = 3100k; whats luminosity?
L/Lsun = R/Rsun2 T/Tsun4 = 1662 * 3100/58004 = 220

Astronomy 4: HW #3 Solutions
Spring 2015
1. Magnesium Energy Levels
(a) The conversion factor is 1 eV = 1.602 1019 J, so
4.3458 eV
1.6 1019 J
= 6.96 1019 J
1 eV
(b) The photons energy will be exactly equal to the energy dierence between level 3
and 1, E

Astronomy 4: HW #7 Solutions
Spring 2015
1. Gravitational Redshift
(a) The spaceship is at r = 2RS , so using the gravitational redshift formula the frequency as observed by Earth will be smaller (because time is dilated near the black hole):
1
= 0.707 mi

Name:
UID:
Astronomy 4
Midterm Exam, Version A
Tuesday, April 28th, 11:00 a.m. 12:15 p.m.
DO NOT OPEN THIS EXAM UNTIL TOLD TO DO SO
WHILE YOU ARE WAITING
This exam is closed book. Calculators are allowed, but any quantitative problems have been set up
so

Astronomy 4, Spring 2015
May 7, 2015
Session 5 - Stellar evolution (Part II)
High mass stars and stellar remnants
When a star goes supernova, the explosion emits enough light to overshadow an entire
solar system, even a galaxy. Such explosions can set o t

Astronomy 4, Spring 2015
April 23, 2015
Equations
This sheet follows the equations from the cheat sheet.
Here is a brief explanation of all the equations on your equation sheet. Remember, you not
only need to know what the equations are saying, but also h

Astronomy 4, Spring 2015
April 23, 2015
Session 4 - Stars
The sky calls to us. If we do not destroy ourselves, we will one day venture to the
stars.
Carl Sagan.
Remember my oce hours are posted in CCLE .
Before we begin, here is the astronomy picture of

Astronomy 4, Spring 2015
May 14, 2015
Session 7 - Black holes and Relativity
Everything should be as simple as possible, but not simpler.
Albert Einstein.
Remember my oce hours are posted in CCLE .
Next week, May 20, I will give a planetarium show. You s

Astronomy 4, Winter 2015
April 9, 2015
Session 2 - Gravity and Light
The most incomprehensible thing about the universe is that it is comprehensible.
Albert Einstein
Remember my oce hours are Mondays and Wednesdays 5-6 pm, PAB 1-704A (Tutoring
center), or

Astronomy 4, Spring 2015
May 28, 2015
Session 9 - Galaxies and AGNs
We on Earth marvel, and rightfully so, at the daily return of our single sun. But from
a planet orbiting a star in a distant globular cluster, a still more glorious dawn awaits.
Not a sun

Astronomy 4, Spring 2015
May 14, 2015
Session 8 - Black holes and Relativity II
The most beautiful thing we can experience is the mysterious. It is the source of all true
art and all science.
Albert Einstein.
Remember my oce hours are posted in CCLE .
Vi

Astronomy 4: HW #5 Solutions
Spring 2015
1. Properties of giant stars
(a) The escape velocity of an object at a distance r from an object of mass M is given
by vesc = 2GM/r. Applied to the surface of the Sun (using M = M = 2 1030 kg
and R = R = 7 108 m).

Astronomy 4: HW #7
Due date: Tuesday, May 26th
1. Gravitational Redshift
Consider a spaceship in orbit around a black hole. The spaceship is located at a radius of
r = 2.0RS , where RS is the Schwarzschild radius of the black hole. To communicate with
obs

Astronomy 4: HW #8
Due date: Tuesday, June 2nd
1. Accretion Power
An astronomer is monitoring the activity in a pair of QSOs. Based on their respective redshifts,
the astronomer determines that QSO B is at a distance from Earth ve times greater than QSO
A

Astronomy 4, Spring 2015
April 30, 2015
Session 5 - Stellar evolution
Every great dream begins with a dreamer. Always remember, you have within you the
strength, the patience, and the passion to reach for the stars to change the world.
Harriet Tubman.
Re

Astronomy 4, Spring 2015
Homework 4 - solutions
Problem 1
a)
Remember that parallax is one over the distance. So if a star has 4 times the parallax of
another, it means that it is 4 times closer. In symbols:
We know that,
A = 4B
Remember that
d[pc] =
1
[a

Astronomy 4: HW #1 Solutions
Spring 2015
1. Workout with Scientic Notation and Units
(a) 0.00000000000537 = 5.37 1012
(b) 26400000000000000 = 2.64 1016
(c) Using the conversion factor 1 AU = 1.5 1011 m:
7.0 1016 m
1 AU
= 4.67 105 AU
1.5 1011 m
(d) First

Astronomy 4: HW #6
Due date: Tuesday, May 19th
1. Schwarzschild Radii
(a) What is the Schwarzschild radius, RS , of the white dwarf from HW #4, given that it has a
mass of MW D = 1M ? Compare RS to the actual white dwarf radius that you obtained (i.e.,
RW

Astronomy 4: Black Holes and
Cosmic Catastrophes
Professor Alice Shapley
Lecture 4: Light & Thermal Radiation
(Ch. 5)
Announcements
Late hw turned in to TAs (Jesus or Danny)
HW #2, due Tuesday, April 14th, in class.
Check your e-mail, or download from

Astronomy 4: HW #1
Due date: Tuesday, April 7th
1. Workout with Scientic Notation and Units
(a) Express 0.00000000000537 in scientic notation.
(b) Express 26400000000000000 in scientic notation.
(c) Express 7.0 1016 m in terms of astronomical units (AU).

Astronomy 4, Winter 2015
April 16, 2015
Session 3 - Light and stars
Though my soul may set in darkness, it will rise in perfect light;
I have loved the stars too fondly to be fearful of the night.
Sarah Williams.
Remember my oce hours are posted in CCLE

Lecture115/5/15
Spectrafromneutralatomscomparedwithspectrafromionizedatomsofthesameelementhave
differentsetsofspectrallines
Pressurevsgravity
o
Catseyenebula
o
Idealgasdominatedbypressure,motionofmolecules
Strongemission,discretelinesfromnumerousmolecules

Astronomy 4: HW #5
Due date: Tuesday, May 16th
1. Properties of Giant Stars
(a) What is the escape velocity (in m/s) from the surface of the Sun?
(b) What is the escape velocity (in m/s) from the surface of a red giant star with a mass of
1M and a radius

Astronomy 4, Spring 2015
April 23, 2015
Equations
This sheet follows the equations from the cheat sheet.
Here is a brief explanation of all the equations on your equation sheet. Remember, you not
only need to know what the equations are saying, but also h

Astronomy 4: Black Holes and
Cosmic Catastrophes
Professor Alice Shapley
Lecture 4: Light & Thermal Radiation
(Ch. 5)
Announcements
Late hw turned in to TAs (Jesus or Danny)
HW #2, due Tuesday, April 14th, in class.
Check your e-mail, or download from

Astronomy 4: HW #1
Due date: Tuesday, April 11th
1. Workout with Scientific Notation and Units
(a) Express 0.00000000000371 in scientific notation.
(b) Express 28600000000000000 in scientific notation.
(c) Express 4.0 1016 m in terms of astronomical units

Astronomy 4: HW #2
Due date: Tuesday, April 18th
1. Gravity on Mars
The planet Mars has a mass of MM ars = 6.42 1023 kg, and a radius of RM ars = 3397 km.
(a) What is the acceleration of gravity (in m/s2 ) on the surface of Mars. Remember: at the
surface