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Elementary Astronomy
Physics 1040
Credits: 3 Classroom Location: Science 109 Time: MW 5:15 – 6:30 PM
Instructor: Tobler Office: Science 121 Phone: (435)652-7759
Email: stobler@dixie.edu
Office Hours: M, W 10 – 11 am
Tutor Center: T, W 2 – 3 pm (Room Browning 115)
Required Stuff: Explorations: An Introduction to Astronomy, 6th Edition, by Arny and Schneider
Scientific calculator (One with buttons like: log, square root [√], trig functions, etc.)
(There is more required stuff for the lab. See all the fun we get to have?)
Please Note: These will be used immediately. Please get it quick.
Course Objectives:
General Physical Science: A student who successfully completes this course should:
1. Demonstrate knowledge of the skills required to make informed personal and social decisions
about issues that we will face locally as well as globally.
2. Demonstrate knowledge of basic fundamental laws, concepts, and theories in the physical
sciences and be able to apply them to everyday life.
3. Understand the process of science – scientific knowledge in generated and validated – so that
you can make independent, empirical inquiries about the natural world.
4. Demonstrate knowledge of the process of science by being able to utilize data in the form of
tables, graphs, and charts through interpretation and then communicate those findings in oral
or written form.
Specific to Physics 1040: A student who successfully completes this course should be able to:
1. Solve simple problems in astronomy by use of gravity, forces, and light propagation.
2. Understand the basic similarities and differences of the planets within our solar system.
3. Understand terminology used by astronomers is describing celestial objects.
Mastery of the course objectives will be evaluated by performance on homework assignments, unit
exams, class presentations, and the final exam.
Your Work Load: You will be expected to complete the following this semester:
- Homework Problems: Select homework problems are assigned from the end of each chapter.
These are taken from the categories “Review” and “Problems”. These are to be turned in at the
start of lecture period on the day due. A grace period of 15 minutes will be allowed. After 5:30
pm on the due date, homework will be late and receive a 50% late deduction. After 24 hours of
the initial due date and time homework will no longer be accepted.
o It is anticipated that you will work in groups. You are encouraged to work with others on
these homework problems. However, you must write your own answers and turn in
your own work. Copying will not be tolerated. Students who copy will receive a ZERO (0)
on that homework assignment.
o Questions requiring you to write an explanation are required to be written in full
sentences.
o Questions requiring a numerical answer need to have all steps written down, not just
the answer. See example in Appendix.
- Poster Project: You will be expected to do a poster presentation on an astronomical topic of
your choice, as approved by me. This is worth a large portion of your grade. Don’t
underestimate this project.
o Use the following to help guide your topic:
January 30: Approved astronomy topic turned in to Dr. Tobler
February 27: List of 4 or more relevant references on your topic submitted
April 16: In class poster presentation
o The class will be split up to do the poster session. The first half will stand by their
posters and discuss their poster with fellow students. The other half will walk around
and view the displayed posters, making comments on their fellow students’ posters.
Halfway through class we will switch roles and responsibilities.
o Your grade for this will be based on the following
10% Approved topic turned in on time
15% References turned in on time
50% Poster organization and content (per a rubric given out before the
presentation)
10% Professionalism (meaning appearance)
5% Fellow student comments and grades
10% Providing insightful comments and grade on others’ posters
- Tests: There will be 3 unit exams and a final comprehensive exam. The unit exams will be
offered in the testing center on the dates indicated on the schedule. Each exam will be a
combination of vocabulary, multiple choice, and possible short answer. A review sheet will be
provided before each exam. In addition, the multiple choice and short answer will be patterned
after the homework turned in and the practice exams at the end of each chapter. Normally, no
makeup exams will be given, and then only when previous arrangements have been made. (This
means you need to contact me BEFORE 11 pm on the last day of the exam to get permission to
take the test late. Otherwise, you miss the test, tough luck.) The final is worth 2 unit exams. The
final exam will be in class on the day indicated on the schedule and cannot be taken any other
time.
Grades: The overall grade for this course will be calculated according to the following breakdown:
Homework 25%
Poster 25%
Unit Exams (3) 3 x 10% = 30%
Final Exam 20%
Total 100%
Final grades will be determines on the overall percentage for the course as follows:
A 93 and above B- 80-82.9 D+ 67-69.9
A- 90-92.9 C+ 77-79.9 D 63-66.9
B+ 87-89.9 C 73-76.9 D- 60-62.9
B 83-86.9 C- 70-72.9 F Below 60
Attendance Policy: Attendance is vital to performing well in this course (and staying awake in lectures).
However, you will not be graded directly on attendance. The instructor will not give individual lectures
to those who miss class. If you miss class, you will be responsible to obtain lecture notes from a fellow
student.
Those who visit or cause other distractions for the teacher and fellow students will be asked to leave
class. Tablets, phones, and other devices can be used to enhance classroom experiences. Mostly, they
are used as a personal distraction from the lecture topic. If you are using one of these devices and a
fellow student complains to me about it, you will be asked not to use it again in class, or you will be
asked to leave the classroom. Please respect your instructor and your fellow students who are desiring
to learn potentially difficult physics topics.
Cell Phones: If you are expecting a call or a text more important than class, stay out of class. Please do
not answer a call or a text in class or stand up and leave class to answer a call. If you come to class, come
to listen and participate.
Disabilities: If you suspect or are aware that you have a disability that may affect your success in the
course you are strongly encouraged to contact the Disability Resource Center (DRC) located in the North
Plaza Building. The disability will be evaluated and eligible students will receive assistance in obtaining
reasonable accommodations. Phone # 435-652-7516.
Appendix A: Math stuff
It is expected that you are able to do some simple mathematics as part of your astronomy
education. Astronomy has always been intertwined with math, with many of the first math
advancements coming as a result of astronomical observations. To a degree, you cannot do astronomy
without math.
Now that you are scared, I will put you to rest with the matter. There are only a small number of
equations needed for you to successfully understand basic astronomy. This page can be used as a
reference to the math we will encounter.
Strategies: Recognition of what equation to use when dealing with math in astronomy is the
most important aspect of correctly solving these problems. Sadly, this is also the hardest part of the
math.
A good strategy for recognizing which equation to use is to start with the information you
currently have. Write down all the numbers you have been given in the problem, including a written
description of what you are trying to find. Your equation you use will include these values and nothing
more. Below is a table of these equations including what each symbol represents.
Beware of your units! There is a difference between kilometers and meters, years and seconds,
etc. This is why the equations have what the units should be for each symbol to correctly use that
equation. If you do not have the correct units, convert your value to the units you need. Ex: If you have
minutes and you need seconds, multiply by 60 as there are 60 seconds in every minute. If you want to
check you units as part of the calculation, remember that the units and the numbers can be treated
completely independently of one another. Group all the numbers together and the units together. The
normal combination rules of math (fractions, powers, etc.) apply to the units just as they do the
numbers.
You can expect to do some simple algebra. You cannot avoid this. It is best to do the algebra
before plugging in the numbers. Isolate the value in the problem you are asked to find. Only once that
value is isolated, then you can plug in the numbers. Many problems occur when the numbers are put
into the calculator. To reduce these types of errors, do the numerical calculations in steps, especially if
you are dealing with fractions. Compute the numerator first, then separately compute the denominator,
and finally divide the two values.
Last thing to remember, there is almost never one way to solve each problem. Look around,
perhaps a slightly different equation to find the same thing is the one you desire. The equations you
work with will depend on the information you have been given in the problem.
Now for those equations:
Name Equation Parts
Universal Law of Gravitation F = gravitational force in Newtons
G = Newton’s Constant
M = mass in kilograms
m = mass in kilograms
r = separation between two objects
Newton’s 2nd Law of motion F = Force in Newtons
(general formula) m = mass in kilograms
a = acceleration in meters per second per
second
Newton’s 2nd Law of motion F = Forces in Newtons
(circular motion) m = mass in kilograms
d = radius of orbit in meters
v = velocity of body in meters per second
Escape Velocity Vesc = velocity in meters per second
G = Newton’s Constant
M = mass in kilograms
R = radius of body to escape from in
meters
Kepler’s Third Law (Solar P = orbital period in years
System Version) a = semi-major axis in AU
Kepler’s Third Law (General P = orbital period in seconds
Version) a = semi-major axis in meters
G = Newton’s Constant
M = mass in kilograms
m = mass in kilograms
Scope Resolution (object size) L = size of object in meters
R = distance to object in meters
λ = wavelength of light in meters
D = diameter of telescope in meters
Scope Resolution (angular) α = angular size of object in degrees
λ = wavelength of light in meters
D = diameter of telescope in meters
Scope Resolution (angular) α = angular size of object in arcseconds
λ = wavelength of light in nanometers
D = diameter of telescope in centimeters
Light Gathering Power A = Area of telescope mirror in m2
D = diameter of telescope in meters
Small angle formula (degrees) s = length (or angular diameter) in meters
d = distance to object in meters
θ = angular size of object in degrees
Small angle formula s = length (or angular diameter) in meters
(arcseconds) d = distance to object in meters
θ = angular size of object in arcseconds
Light c = speed of light in meters per second
λ = wavelength in meters
f = frequency in Hertz
Distance Modulus for Stellar m = apparent magnitude
Brightness M = absolute magnitude
d = distance to object in parsecs
Wien’s Law T = temperature in Kelvin
λmax = wavelength in nanometers
Doppler Shift Δλ = Change in wavelength in nanometers
λ0 = wavelength in laboratory in
nanometers
V = Radial velocity of light source in
kilometers per sec
c = speed of light in kilometers per sec
Density of an object ρ = density in kilograms per cubic meters
M = mass in kilograms
R = radius of object in meters
= Volume of a sphere in cubic
meters
Kinetic Energy E = Kinetic Energy in Joules
m = mass in kilograms
V = velocity in meters per second
Rest Mass Energy E = Energy in joules
m = mass in kilograms
c = speed of light in meters per second
Luminosity L = luminosity in watts
R = radius in meters
σ = Stefan-Boltzmann constant
T = temperature in Kelvin
Mass-Luminosity relationship L = luminosity in solar units
M = mass in solar units
Angular Momentum Angular momentum = MVR M = mass in kilograms
V = velocity in meters per second
R = radius in meters
Schwarzschild radius RS = Schwarzschild radius in meters
G = Newton’s constant
M = mass in kilograms
c = speed of light in meters per second
Hubble law V = Hd V = velocity in kilometers per second
H = Hubble constant
d = distance in megaparsec
Example Problems of Math Stuff:
Ex 1: Chapter 4 Problem 5
A lightbulb radiates most strongly at a wavelength of about 3000 nm. How hot is its filament?
We are given a wavelength and asked to find a temperature:
λmax = 3000 nm
T=?
To solve this problem we will use Wien’s Law from Chapter 4, which states
“The wavelength at which an object radiates most strongly is inversely proportional to the object’s
temperature.” Or in equation form:
Plugging in our values we have:
This can also be converted to the following temperatures: 966.67 K = 693.52 °C = 1280.30 °F
Ex 2: Chapter 13 Problem 10
A line in a star’s spectrum lies at 400.0 nanometers. In the laboratory, that same line lies at 400.2
nanometers. How fast is the star moving along the line of sight? Is it moving toward or away from us?
We are given the wavelength of the spectrum line as observed by the star and in the laboratory:
Δλ = 0.2 nanometers
λ0 = 400.2 nanometers
V=?
For this problem we will also need to know the speed of light: c = 300,000 km/sec
To solve this problem we will use the Doppler shift:
Plugging in our values we have:
