Download A301LectureOutlinePart1 - University of Texas Astronomy

Some Introductory Concepts
Scientific notation for very large and small numbers (read Appendix 1 in
text).
Example: 3 x 106 = 3 million, 4 x 10-3 = 0.004. Spend time making up your
own examples.
 You will continuously encounter this notation, so become comfortable
with it now (even though I will not ask you to manipulate such numbers on
exams).
Units of length, size, mass, … Defined just for convenience, but difficult
adjustment to make. For example, wavelengths of light are sometimes given as
microns, Angstroms, nanometers, millimeters, ... This should end up causing no
difficulties at all but it is admittedly a nuisance, and can cause endless suffering if
students don’t recognize that it is some arbitrary unit that is convenient. Just
remember that the unit is being used to avoid very large and small numbers.
Example: For distance or size, could use “microns” for light or dust
particles, “centimeters” or “inches” for everyday objects, “astronomical units”
(AU) for distancces within the solar system, “light years” or “parsecs” for stars,
“megaparsecs” for galaxies. Appendix 2 in the textbook goes over some of this;
just skim it now and use it for future reference if you become confused about units.
Angular measure (box, p. 11) –degree, arcminute, arcsecond (especially
important). Most astronomy today tries to break the “arcsecond barrier” imposed
by our own Earth’s atmosphere. Angular measure using “arcsecond” terminology
will occur in many places throughout the course (first in connection with
“parallax”). The idea of “angular resolution” will be fundamental throughout the
course.
Distances: could get from angular size (see illustrations); but for stars we
can’t resolve their angular size (they look like points), so we get distances from
parallax (sec. 1.7). You should get the idea of measuring parallax because it is so
natural--if it seems confusing, you probably don’t understand it at all.
This introduces the unit of parsec = distance of object that has a parallax of
one second of arc. This is abbreviated “pc.”
Result: Nearest stars are about 1 pc (a few light years) away. This is also the
average distance between neighboring stars in most galaxies. Size of our Galaxy
and many others is about 10,000 pc, and the distances between galaxies range from
millions (Mpc) to billions of pc (1000 Mpc—make sure you are comfortable with
what this means). These are numbers you should memorize now.
For distances in the solar system, see sec. 2.6.
HISTORY OF ASTRONOMY: We are skipping most of the history of
astronomy, except for the most significant topic:
Geocentric (earth-centered) vs. heliocentric (sun-centered) models (sec.
2.2-2.4)
Be able to describe the story in terms of the following succession of names:
Ptolemy (~140 AD) … Copernicus (~1500 AD), Galileo (~1600),
Tycho Brahe, Kepler (2.5), Newton (2.6).
Notice that it took over 1500 years to dislodge a single conception (that the
Earth was at the center of the universe). This is the most important feature of the
history of ideas, that most of them turn out incorrect, and that it takes a lot of
evidence and time (and even people being burned at the stake--G. Bruno) to
displace them with better (but still incorrect) ideas. This applies to everyday life as
well.
Once the heliocentric model was taken seriously, Kepler was able to come
up with his 3 “laws” (sec.2.6—see later lecture notes), which led Newton to come
up with much more general laws of motion for any objects moving under any kind
of force (not just gravity), as well as his famous law of gravity (sec. 2.7 and later
lecture notes). Much of physics derives from Newton’s laws.
Kepler’s Laws (sec. 2.6)
Empirical, based on observations; NOT a theory (in the sense of Newton’s laws).
1. Orbits of planets are ellipses (not circles), with Sun at one focus.
Must get used to terms period (time for one orbit), semimajor axis (“size” of
orbit), eccentricity (how “elongated” the orbit is), perihelion (position of
smallest distance to Sun), aphelion (position of greatest distance to Sun)
2. Equal areas swept out in equal times; i.e. planet moves faster when closer to
the sun. This is very easy to remember if you know that the objects are
moving under the force of gravity (which Kepler didn’t know).
3. Square of the period is proportional to the cube of the semimajor axis
 P2 = a3
when P is expressed in Earth years and “a” is in units of A.U. (astronomical
unit; average distance from Earth to Sun).
(Absolute size of A.U. unit determined from radar observations of Venus and
Mercury, and other methods—see sec. 2.6.)
Example: The planet Saturn has a period of about 30 years; how far is it from the
Sun?
This is about as serious as the math will get in this course, and you might expect 1-2
such questions per exam.
Kepler’s 3rd law, as modified by Newton (see below), will be a cornerstone of
much of this course, because it allows us to estimate masses of astronomical objects
(e.g. masses of stars, galaxies, the existence of black holes and the mysterious “dark
matter”).
Newton’s laws of motion and gravity (sec. 2.7)
1.
Every body continues in a state of rest or uniform motion (constant velocity) in a straight
line unless acted on by a force. This tendency to stay at rest or keep moving is called
“inertia”. It is not trivial.
2. Acceleration (change in speed or direction) of object is proportional to: applied force F
divided by the mass of the object m
i.e. a = F/m or (more usual) F = ma
This law allows you to calculate the motion of an object, if you know the force acting on it. This is
because acceleration is rato of change of velocity, so you can solve this for velocity as a function
of time. This is how we calculate the motions of objects, fluids, … just about anything, in physics
and astronomy (but requires calculus—examples given in class). Think about it!
3. To every action, there is an equal and opposite reaction, i.e. forces are mutual.
Law of Gravity: Every object attracts every other object with a force
F (gravity)  (mass 1) x (mass 2) / R2 (distance squared)
Notice this is an “inverse square law”.
How is this “force” transmitted instantaneously, at a distance? Gravitons? Today, gravity
interpreted as a “field” that is a property of space-time itself, or even stranger interpretations…
But Newton’s law of gravity is sufficient for us to calculate the orbits of nearly all astronomical
objects.
Consequences: Can derive Kepler’s laws from Newton’s laws of motion and the form of
the gravitational force. The result contains a new term:
---->
P2 = a3/ (m1+ m2)  Newton’s form of Kepler’s 3rd law.
(Masses expressed in units of solar masses).
--> Used to get masses of cosmic objects, by observing their periods and how far away
from each other they are (a). Cannot emphasize the importance of this relation enough!
LIGHT (Radiation, Chapter 3)
Can consider light as waves or as particles, depending on circumstance.
(One of the “big mysteries” of physics.) Either way, it is common practice to call
them “photons.”
Waves: Need to understand and become familiar with the following
properties of light (will discuss in class):
Wavelength—Always denoted by Greek letter “”.
Frequency—how many waves pass per second, denoted “f”
Speed—All light waves travel at the same speed, the “speed of light”,
“c”(=3x105 km/sec = 2x105 mi/sec; no need to memorize these numbers!)
The fact that light travels at a finite speed means that we see distant objects
as they were in the past. Consider our neighbor, the Andromeda galaxy shown in
Fig. 3.1 in your text—it is about 2 million light years away… Later we will “look
back” to times near the beginning of the universe using very distant galaxies.
Light is a wave that arises due to an oscillating (vibrating) electromagnetic
field (see text). Unlike other kinds of waves, light does not require a material
medium for its propagation (travel); light can propagate in a vacuum.
(Don’t worry about “polarization” if it is confusing to you.)
Spectrum: A most important term! It refers to the mixture of light of
different wavelengths from a given source; best to remember it as a graph of
“intensity” (or brightness) of radiation in each wavelength (or frequency) interval.
Will discuss in class. (Note: much of the rest of the course is concerned with
analyzing the spectra of different types of astronomical objects—so get used to the
concept now.)
Light from all objects covers an extremely large range of wavelengths (or
frequencies), from radio waves to gamma rays.
Memorize this list, and study figs. 3.4 and 3.9 carefully:
radio, infrared (IR), visible, ultraviolet (UV), x-rays, gamma rays
Human vision is only sensitive to a very tiny fraction of all this radiation—
astronomy in the last 50 years has been mostly concerned with getting out of this
region.
Other important point: Earth’s atmosphere is very opaque (light can’t get
through) except in the visible (also called “optical”) and radio parts of the spectrum
(the so-called optical and radio “windows”)
 That’s why much of recent astronomy is done from space.
Black-Body Spectrum—it’s only a simplified mathematical model, but
works well for the continuous (smooth) spectra of objects. Gives spectrum as a
function of temperature. (Don’t worry about different temperature scales in the
box on p. 72—we will always use units of degrees in Kelvins, but there will be no
confusion.) There are two ways in which this idealized blackbody spectrum is
related to temperature:
1. Wien’s law: relates wavelength at which most energy is emitted in the
spectrum (“wavelength of peak emission”) to the temperature:
max  1/(temperature of object)
So hotter object bluer, cooler object  redder. So we can get temperature
from the spectrum. (See fig.3.11 in text). Actually this is a crude measure, but you
learn a lot from it, e.g. solids like planets, dust grains, etc., near stars will be heated
to temperatures ~ few hundred degrees so emit most of their radiation in the
infrared part of the spectrum. (Same for the surface of the Earth.)
2. Stefan’s law: TOTAL energy E radiated at all wavelengths (per unit
surface area) is related to the temperature by:
E  (temperature)4  hotter objects will be brighter (per unit area)
Notice the steep temperature dependence!
Study Fig. 3.12 (BB curves for 4 cosmic objects).
Doppler Effect : one of most useful and important techniques used in all of
astronomy. We will encounter it again and again.
Wavelength (or frequency) of a wave depends on the relative radial speed of
the source and observer.
Radial motion means: motion towards or away; along the line of sight. The
Doppler effect involves only this component of motion.
Moving away: wavelengths increase (“redshift”)
Moving toward: wavelengths decrease (“blueshift”)
Shift in   radial velocity  this is how we get speeds of cosmic objects,
stars, galaxies, even expansion of universe.
Actual formula is: (apparent)/ (true) = 1 + (vel./speed of light)
For most objects in the universe, this relative shift is tiny, so we can’t detect
it using the “shift” of the whole spectrum. But we can use places in the spectrum
whose wavelengths are precisely known  spectral lines (the subject of Chapter 4,
on exam 2).
Exam #1 will test you on material up to this point. Remember that
these lecture outlines are only outlines, and do not contain all material
covered in class or that you are responsible for in the textbook.