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
à 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) µ (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) Þ 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 “l”.
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.
àMemorize 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”)
à 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: lmax µ 1/(temperature of object)
So hotter object Þ bluer, cooler object Þ 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 µ (temperature)4 Þ 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 l µ radial velocity Þ this is how we get speeds of cosmic objects, stars, galaxies, even expansion of universe.
Actual formula is: l(apparent)/ l(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 Þ 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.