ASTR 10, Vista College, Spring 2004

Instructors: Dr. Korpela

What Was Important - Material for Exam #1

January 16

• Answer the question : "What is astronomy"
• Be familiar with Scientific Notation and metric system. Know how to convert to and from regular notation and to multiply/divide using scientific notation.
• Basic idea of the scale of the universe, and our place in it.
• Have the "big picture" of the hierarchy of the objects in the universe (planets, stars, solar systems, galaxies). Knowing the overall picture of the universe will help you later. If you have an overall picture, then you will be less confused when you have more information to attach to each object.
  Which is closest, the solar system or the stars or the galaxies? Which is biggest?
• Know definition (not numbers) of AU, light year, and why we use those units

January 22

• Understand the basics of "what is science" and "how science works"
• Know and understand the Scientific Method
• Know the celestial sphere as a scientific model
• Be able to estimate angles on the sky
• Become familiar with planets currently in the sky, and constellations currently in the sky.
• Know definitions of Zenith, Celestial Equator, Celestial Poles
• Be able to identify the locations of these for observers at various places on the Earth
• Understand how which stars you see (and their apparent daily motion) changes with latitude
• Understand how time of day relates to your longitude

January 29

• Be able to relate the positions of objects in the sky to their positions in the solar system.
• Know why we see different stars at different times of the year.
• Know how the orbital motion of the earth about the sun causes the Sun to move against the stars during a year.
• Know why the North Star changes over the course of centuries/millenia (vocabulary: sidereal time)
• Know how the orbital motion of the earth about the sun combines with the tilt of its spin axis to cause seasonal variations in the apparent motion of the Sun across the sky each day. (vocabulary: equinoxes and solstices)
• Understand the relationship between this and the cause for the climatic seasons (see below).
• Know the relationship between how and where the moon appears to you and its location relative to the Earth and the Sun.
• Know the difference between a solar eclipse and a lunar eclipse
• Be able to explain when and why eclipses occur. What is the lunar phase? Who can see them? Why don't they occur monthly?

• NOT caused by Earth being closer to Sun in summer (this doesn't explain summer in Australia when winter is here; and the Earth is closest to the Sun (by only about 3%!) on January 4!)
• Caused by the tilt between the Earth's rotation (spin) axis and the plane of the Earth's orbit about the Sun.
• The above means that the Sun is higher in the sky during the summer. This makes it stay up longer (more hours of sun = warmer). It is also warmer at noon in the summer than in the winter, because the Sun is higher (just as a noon summer sun is warmer than a morning or evening summer sun). There is less solar energy per unit area arriving at the earth in winter.
• The difference in the distance between the North Pole and the Sun summer and winter due to this tilt is SMALL relative to the total distance to the Sun - about 0.002%! This does NOT cause the seasons.

• You should understand the following points. Understanding which object is blocking the sunlight in each case is 90% of the battle - the rest can be figured out from there.
• Lunar eclipses are eclipses of the moon. The moon is in the Earth's shadow, so light from the sun is blocked from reaching the moon. Sometimes only part of the moon is in the shadow -- a partial lunar eclipse -- and other times the light is completely blocked (except a little red light that is bent by the Earth's atmosphere) -- a total lunar eclipse. Anyone on the night side of the Earth can see a lunar eclipse. Lunar eclipses occur at full moon (you should be able to explain why!).
• Solar eclipses are eclipses of the sun. The moon blocks some or all of the light from the Sun. The moon's shadow sweeps across the Earth. Those observeres completely outside the shadow see no eclipse. Those observers outside the darkest part of the shadow, in the "penumbra", see only part of the sun as blocked, and see a partial solar eclipse. Those lucky enough to be in the middle, darkest part of the shadow (umbra) see a total solar eclipse. Solar eclipses occur at new moon (why?).
• We are "lucky" in that the moon and the sun have the same angular size on the sky (meaning they appear to be about the same size). This means that total solar eclipses are spectacular, since the bright sun is entirely blocked, but we can still see the faint outer regions of the sun. Due to slight variations in the Earth-Moon distance and the Earth-Sun distance, sometimes the moon doesn't appear large enough to completely block the sun, and we see an annular eclipse (an annulus is a ring - this just means you are left with a ring of sun). Note that the Sun and the Moon are VERY different in size, but they are also VERY different in distance, allowing them to APPEAR to be the same size!
• NEVER look at the sun except during the total part of a total solar eclipse.

February 5

• Ancient astronomy: Calendar stones to the Greeks. Understand how the position of the sun and stars in the sky can tell you when to plant your crops or schedule a party.
• The heliocentric model (sun at the center): planets orbit the Sun, all in the same plane and direction, with the closer planets moving faster.
• Understand how the retrograde (occasional westward) motion of Mars relative to the stars is explained in both the geocentric (earth at the center) and heliocentric (sun at the center) models.
• Know why the observed phases of Venus strongly favour the heliocentric model.
• How this model explains the fact that the planets all follow nearly the same path against the stars (the ecliptic, same as the sun), and their directions of motion.
• The idea of parallax will return in a couple of weeks!
• Planets orbit in ellipses, moving faster closest to the Sun.
• Kepler's Third Law: P² r ³ where P is the orbital period and r is the semi-major axis of the orbit (1/2 the long diameter of the ellipse).
  This means that the planets closest to the sun are moving the fastest.
• Newton's 2nd Law: The acceleration 'a' (change in velocity (speed or direction or both)) of an object is proportional to the force (F) applied. The constant of proportionality is the mass (m): F = m a
  Any body therefore moves in a straight line at constant speed unless there is some force acting upon it.
• Newton's 3rd Law: If one body is exerting a force on a 2nd, the 2nd body is exerting an equal and opposite force on the first one (eg. gun and bullet)
• You should understand how this explains how a rocket works.
• Universal Gravitation: all matter attracts.
  The force between two masses separated by a distance r is: F = - G m₁ m₂ / r²
  In other words, the force increases with the mass of the objects involved, and decreases when they are farther apart. Changing the distance by a factor of 2 has a bigger effect than changing one of the masses by a factor of 2, because the dependence is on distance squared.
• Note: You won't need to use the equations, but you should understand in words what they mean.
• Combining this with Newton's 2nd Law, we find that the acceleration due to gravity of a mass m₁ is a = - G m₁ / r²
  This means that if you drop two objects of differing masses (from the same height), they hit the ground at the same time! Unless some other force (such as air resistance) is affecting the experiment!
• The Earth's gravity acts as though the Earth's entire mass were at the center (true of any sphere). The surface gravity is the acceleration due to gravity felt at the surface (use mass and radius of Earth or other planet)
• Weight is the force you feel due to gravity, measured in the absence of acceleration. Weight is NOT the same as mass! Astronauts are "weightless" not because there is no gravity in space, but because they are falling around the earth (that's what an orbit is), and therefore accelerating. You'd be weightless too if you strapped a scale to your feet and jumped out of an airplane.
• You should understand how gravity explains orbits.
• Newton, using gravity, was able to derive Kepler's 3rd Law more generally for any two masses: P² = 4²/G(m ₁ + m₂) * a³ If m₂ << m₁ (the second mass is much smaller than the first) then we may ignore m₂ and then the relation is just P² = 4²/Gm₁ * a³
  This simply describes the fact that an object in orbit about a larger body moves fast enough to keep from falling into the larger body. If the large body is more massive, or the object's orbit is smaller, then the object feels a larger force of gravity, and must be moving more quickly in order to overcome it. Examples of applications of this law: all planets orbiting around the Sun (use the mass of the Sun), Jupiter's moons (use the mass of Jupiter), planets around other stars (use mass of the other star).
• Total energy is conserved.
• Total momentum (mass*velocity) is conserved.
• Tides on the earth are due to the pull of the moon and sun. The side of the earth that is toward the moon gets pulled toward the moon a bit harder than the center of the earth does. The side away from the moon gets pulled on a bit less than the center of the earth does. This leads to bulges of water on the side of the earth facing the moon and the side of the earth away from the moon.

February 12

GOAL: Learn about the physics of matter, the physics of light, and the interaction between light and matter, so that we can apply this knowledge to astronomical bodies!

• Visible light is a form of electromagnetic wave. Radio waves, microwaves, X-rays are other examples of EM waves. Visible light and Radio waves are the only ones that easily penetrate the Earth's atmosphere.
• ALL EM waves travel through a vacuum with the same speed (the speed of light = c = 300 000 km/s)!
• The difference between red light and blue light is the wavelength (Greek symbol lambda) of the EM wave. Radio waves have very large wavelengths, X-rays have very small wavelengths. The frequency of the wave is small for long wavelengths, and large for short wavelengths. (wavelength * frequency = speed of light)
• Light can also be thought of as a particle. Each "photon" carries energy. Photons with long wavelengths carry more energy than photons with short wavelengths (E=hc/lambda)
• Astronomers split light up into a spectrum (they sort it by wavelength, like a rainbow) because they can learn more about objects that way.
• Astronomers use telescopes to collect more light, store light over time, analyze it by wavelength, see more details, analyze it later
• The amount of light collected is proportional to the collecting area of the telescope (diameter squared).
• The amount of detail that can be seen is best for large telescopes, but is also dependent on the wavelength of light. Resolution is better for large diameters.
• The atmosphere mucks up the resolution of visible ground-based telescopes because of its distortions and motions.
• Reasons to put a telescope in space: avoid atmospheric absorption, avoid atmospheric turbulence, avoid light pollution
• Atoms are made up of a nucleus of protons (positive charge) and neutrons, plus electrons (negative charge). Neutral atoms have equal numbers of protons and neutrons. An element is determined by the number of protons in the nucleus. Hydrogen has 1 proton, and therefore 1 electron.
• It takes energy to remove an electron from an atom and turn it into an ion. This is called the binding energy. There are only certain permitted values of binding energy. Every element has a different fingerprint of permitted binding energies.
• Can also cause an electron to change energy levels. To go up an energy level takes energy (which can come from collisions or from the absorption of a photon with the right energy (and therefore wavelength)). To go down an energy level releases energy, usually carried by a photon, again of a particular energy and wavelength.
• Temperature vs. heat
• Blackbody radiation: Hot objects glow and emit energy.
  • Hotter objects produce MUCH more energy than cooler objects.
  • Hotter objects are BLUER than cooler objects.
  • Stars behave very much like blackbodies.
• Hot, dense objects emit continuous spectra (all wavelengths)
• If this light passed through a cool cloud of gas, a few photons will have just the right energy to be absorbed by the gas and removed from the spectrum. The observer will see absorption lines.
• The gas can re-emit these photons in random directions. Observers viewing only the gas will see emission lines .
• Shape of the curve of stellar spectra tells us about the temperature of stars. (Position of the peak)
• Temperature also determines how much energy is radiated by a blackbody. (10 times hotter = 10,000 times brighter)
• Permitted energy levels are like a 'fingerprint' for the element, and therefore so are absorption and emission lines.
• Doppler Effect: motion towards (or away) from the observer makes the wavelength shorter (or longer). True for both sound (pitch of race car engine sounds higher when it's coming towards you) and light (blueshift for motion towards the observer, redshift for away).
• Scattering of light by dust or other small particles: Dust particles scatter blue light more than red light, so when looking at a star through a dust cloud, it will appear redder than if there were no dust. If you look at the dust cloud itself, you will see the scattered blue light, so the dust cloud will appear blue. This is why the sun is red at sunset and also why the sky is blue.
• Stars: Hot dense object producing a continuous spectrum, with a cooler outer atmosphere which produces absorption lines.
• Presence of particular absorption lines can tell us something about which elements are present (the absence of a line doesn't insure the absence of the element, however).
• The Doppler effect is also important, in that it is how we measure motions along the line of sight between us and a star. Understand how the effect works for sound waves, and how we use it to measure radial velocity.
• The inverse square law is also very important. The luminosity or intrinsic brightness of a star is the energy per second coming from the star. How bright the star really is. The apparent brightness is how bright it looks to you, or the energy per second per unit area that you see. The apparent brightness of a star depends on the inverse square of the distance to the star. In other words it is proportional to 1/(distance)². For two identical objects, something twice as far away looks 1/4 as bright. Something 10 times as far away looks 1/100th as bright.
• Understand that for a blackbody, the energy emitted per second per unit of surface area is proportional to (temperature)⁴. Something twice as hot emits 16 times as much energy in each square meter of its surface. So if two stars are the same size, but one has twice the temperature, that one has 16 times the luminosity (or intrinsic brightness).