Supplementary Notes for Physics 106

Supplementary Notes for Physics 1060
Introduction to Stars & Galaxies

These are arranged by Unit (1-4), and are provided mainly as background or course review material. The format of the files are 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 concepts through JAVA animations on the page containing this course's links to Astronomical Images, Movies, Demos (search on 'JAVA').

Unit 1: Introduction and Tools of Astronomy

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 why Kepler's Laws 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.
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: Light, Matter, and the Observed Properties of Stars

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, 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 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.

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 over view 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 T. Korista

Professor of Astronomy
Department of Physics
Western Michigan University
Kalamazoo, MI 49008-5252
email: kirk.korista@wmich.edu

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