Supplementary Notes for
Physics 1060

*Introduction to Stars & Galaxies*

Unit 1:

- a worked
example of a practical use of the small angle approximation. Don't
worry;
I would never ask you to crank numbers through an equation on an exam.
However,
(1) I thought you might like to see a concrete example of why the
relationship
between these quantities is important and (2) you should understand the
concepts
behind the equation and how the equation is applied.

- a set of numerical,
mathematical examples of how the observed intensity and apparent
magnitude
of a star are related. You will not need to compute these on an exam,
but
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 larger values of apparent magnitude appear dimmer and so have*smaller*measured intensities (or lower observed brightnesses) than those with smaller values of apparent magnitude. Stars with the greatest observed brightnesses have the highest measured light intensities and negative values of apparent magnitude. The terms 'observed brightness' and 'measured intensity' will be used interchangably in this class. The apparent magnitude system is a parallel and more compact system of measuring how much light from a star or galaxy (or whatever) arrives 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
Belief".

- a review of
of Orbital ("Planetary") Motion work, using Newton's laws of motion and gravity and minimizing the use of mathematics. You had better know how to answer the questions at the bottom of the page! This 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 Jupiter.*why*Kepler's Laws

- a worked
example of how one can use the orbit of a man-made satellite
orbiting
Earth to determine Earth's mass. I won't expect you to compute this on
an
exam, but you had better know how we can determine mass via the
observation
of an orbit, as well as what role mass plays in Kepler's 3
^{rd}Law.

Unit 2:

- a review of the 4 fundamental forces of nature
- a quick review of the properties of atoms
- here are two examples (1, 2) of how astronomers determine distances to objects in the solar system, the initial stepping stone to determining distances to the stars.
- Our 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.
- Here 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 compositions.
- This
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
center of
mass: two
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, m
_{1}v_{1}= m_{2}v_{2}, 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 already learned).

- 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 luminosity (an 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
over these
quickly in class, so bring it along.

- 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
this
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 also understand that what we see on the outside of the star (its L, R, surface T) is a reflection of what is happening in the fusion generating region at 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
Myr, 10
Myr, 100
Myr, 1
Gyr, 10
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
must
memorize this summary, think again. As usual I am more interested that
you
understand
__why__these things happen. There is a pertinent question 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

- Here is a summary of the methods to determine distances.
- This
is a plot of a simplified overview of the history of star formation
in different types of galaxies, as we've put together from
observations.

- Here
is a discussion of the most important things you should understand
about
galaxies.
**VERY IMPORTANT!**Notice that I am trying to get you to puzzle about WHY galaxies have their observed properties; I am much less interested in your ability to memorize what those properties are. That shouldn't come as a surprise, eh? - This
is a table that converts some (cosmological) redshifts into
"lookback times".
i.e.,
how long light has traveled from there and then to here and now. This
is so
you have some idea of how these correspond as we talk about galaxies at
different
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.

- This
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
also helps.

- A listing
of big ideas concerning cosmology in Unit 4.

Kirk Korista Professor of Astronomy

Department of Physics

Western Michigan University

Kalamazoo, MI 49008-5252