Supplementary Notes for
Introduction to Stars & Galaxies
arranged by Unit (1-4), and
mainly as background or course review material. The format of the files
mainly either .html or .gif, readable and printable in any browser;
a few are pdf format and are readable using the free-ware ADOBE
acrobat reader. There are also demonstrations of some of the key
through JAVA animations on the page containing this course's links to Astronomical
Images, Movies, Demos (search on
Unit 1: Introduction and Tools of Astronomy
- a worked
example of a practical use of the small angle approximation. Don't
I would never ask you to crank numbers through an equation on an exam.
(1) I thought you might like to see a concrete example of why the
between these quantities is important and (2) you should understand the
behind the equation and how the equation is applied.
- a set of numerical,
mathematical examples of how the observed intensity and apparent
of a star are related. You will not need to compute these on an exam,
many of you will be using the mathematical relationship in your lab
course. All you need to know for this course is that stars with
values of apparent magnitude appear dimmer and so have smaller
intensities (or lower observed brightnesses) than those with smaller
of apparent magnitude. Stars with the greatest observed brightnesses
the highest measured light intensities and negative values of apparent
The terms 'observed brightness' and 'measured intensity' will be used
in this class. The apparent magnitude system is a parallel and more
system of measuring how much light from a star or galaxy (or whatever)
here at Earth.
- What do we mean by fact and theory in science? This
is a succinct set of definitions, as used in science, for the terms:
fact, hypothesis, law, theory, and "It is not just
a theory...It is a theory!", "Contrary to
- a review of why
Kepler's Laws of Orbital ("Planetary") Motion work, using
laws of motion and gravity and minimizing the use of mathematics. You
better know how to answer the questions at the bottom of the
is an animation showing how the Sun and Jupiter (1047x less massive)
orbit their center of mass in
11.86 years. This "pivot point" always lies nearer to the more massive
object. In reality, the Sun's motion is complicated by pull of the
other planets, but most of the Sun's motion is due to the pull by
- a worked
example of how one can use the orbit of a man-made satellite
Earth to determine Earth's mass. I won't expect you to compute this on
exam, but you had better know how we can determine mass via the
of an orbit, as well as what role mass plays in Kepler's 3rd
Unit 2: Light, Matter, and the Observed Properties of Stars
- a review of the 4
forces of nature
- a quick review of the properties
- here are two examples (1,
2) of how astronomers
determine distances to
in the solar system,
the initial stepping stone to determining distances to the stars.
Sun's spectrum, as emitted by the dominant photosphere, and a comparison
to a thermal radiator of a single temperature equal to our Sun's
mean surface temperature.
is a plot of 6 of the 7 major spectral types of stars, as we showed
in class (O,B,A,G,K,M, from top to bottom; no F star). These are all
main sequence stars, and they all have very simliar elemental
is a plot of the main sequence of stars on the Hertzsprung-Russell
(H-R) diagram. Quiz yourself on the properties of stars lying at
various positions on the H-R diagram.
- Some nice animations illustrating orbits of two masses around the
equal masses (circular orbit), two
equal masses (elliptical orbit), different
but comparable masses, different
and more disparate masses, and very
different masses (the last 3 of these all had circular orbits).
Note that both masses in each case have the same orbital period. Which
is more massive? Which has a greater orbital acceleration? greater
orbit speed? Because of the conservation of linear momentum, m1v1
= m2v2, so that the ratio of masses is inversely
related to the ratio of the orbit speeds (it's also inversely related
to the ratio of their distances from the center of mass, as we've
- In your laboratory course PHYS 1050, you will be working with the
concept known as absolute magnitude (see "The
Magnitude System" on pp. 304-305 of your textbook). It is to
intrinsic measure of the total power of light emitted) what apparent
magnitude is to observed brightness. This
link summarizes what it is and how it's used. While I won't be
testing you on absolute magnitude, you may find the link useful for the
purposes of your PHYS 1050 labs.
- Here is a quick
review of how we determine basic stellar properties. I'll be going
quickly in class, so bring it along.
Unit 3: Stars: How They Work and Their Life Stories
- An overview
of how main sequence stars work - this one is pretty darned important.
- An overview
of why stars evolve as they age, and eventually die.
- The evolution
of protostars on the H-R diagram and the time it takes for a star
of a given mass to contract onto the main sequence.
- How the Sun
will evolve on the H-R diagram over time; we'll be referring to
diagram in class. I
will not be asking you about all the details that appear here,
but you should be familiar with the 4 major stages identified in
bold and underlined. You should
understand that what we see on the outside of the star (its L, R,
T) is a reflection of what is happening in the fusion generating region
the center of the star - cause and effect.
- A plot illustrating detailed computations of the
predicted locations on the H-R diagram of stars belonging to
clusters of a fixed age, and the location of the main sequence turn-off
point. We compare this to the observed distributions and find an
amazing match! Here are more schematic illustrations of such, as we
showed in class: 3
Gyr (Myr = megayear = millions of years old, Gyr = gigayear =
billions of years old).
- A plot
showing the ages of star clusters measured by two completely
independent methods, getting the same answer...
- A short
summary of the endstates of stars, by mass. If you think that you
memorize this summary, think again. As usual I am more interested that
understand why these things happen. There is a pertinent
in the sample
exam questions for Unit 3.
- A quantitative, worked out, example
of how one estimates the MS life span of our Sun.
Unit 4: Galaxies and Cosmology
is a summary of the methods to determine distances.
is a plot of a simplified overview of the history of star formation
in different types of galaxies, as we've put together from
is a discussion of the most important things you should understand
galaxies. VERY IMPORTANT! Notice
that I am trying to get you to puzzle about WHY galaxies have their
properties; I am much less interested in your ability to memorize what
properties are. That shouldn't come as a surprise, eh?
is a table that converts some (cosmological) redshifts into
how long light has traveled from there and then to here and now. This
you have some idea of how these correspond as we talk about galaxies at
redshifts. And this
is a plot that shows how the "distance now" and "distance then" and
lookback time scale with cosmological redshift, for a current leading
model of the expansion of the universe. The distances are given in Giga
light years (billions of light years) and the lookback time is given in
Gigayears (billions of years), with 1 billion = 1000 million. The
present age of the universe (14 billion years) is marked as the
horizontal blue line in the diagram. Don't worry - this diagram
is not somehow critical to doing well on the exam; I've provided it for
the very curious and also for those just curious enough to learn
something from it regarding the concept of an expanding universe.
is a really useful link (with a really cool animation) that
explains how this expanding universe business works, and what impact it
has on our notions of distance. This link
- A listing
of big ideas concerning cosmology in Unit 4.
Professor of Astronomy
Department of Physics
Western Michigan University
Kalamazoo, MI 49008-5252
back to Physics 1060