1. Chapter 0 Charting the Heavens

2. 0.1 The “Obvious” View
Stars that appear close in the sky may not actually be close in space.

3. 0.1 The “Obvious” View The celestial sphere:
Stars seem to be on the inner surface of a sphere surrounding the Earth.
They aren’t, but we can use two-dimensional spherical coordinates (similar to latitude and longitude) to locate sky objects.

4. 0.1 The “Obvious” View
Declination: Degrees north or south of celestial equator
Right ascension: Measured in hours, minutes, and seconds eastward from position of the Sun at vernal equinox

5. 0.2 Earth’s Orbital Motion
Daily cycle, noon to noon, is diurnal motion – solar day.
Stars aren’t in quite the same place 24 hours later, though, due to Earth’s rotation around the Sun; when they are in the same place again, one sidereal day has passed.

6. 0.2 Earth’s Orbital Motion
The 12 constellations the Sun moves through during the year are called the zodiac; path is ecliptic.

7. 0.2 Earth’s Orbital Motion
Ecliptic is plane of Earth’s path around the Sun; at 23.5° to celestial equator.
Northernmost point (above celestial equator) is summer solstice; southernmost is winter solstice; points where path crosses celestial equator are vernal and autumnal equinoxes.
Combination of day length and sunlight angle gives seasons.
Time from one vernal equinox to next is tropical year.

8. 0.2 Earth’s Orbital Motion
Precession: Rotation of Earth’s axis itself; makes one complete circle in about 26,000 years

9. 0.2 Earth’s Orbital Motion
Time for Earth to orbit once around the Sun, relative to fixed stars, is sidereal year.
Tropical year follows seasons; sidereal year follows constellations – in 13,000 years July and August will still be summer, but Orion will be a summer constellation.

10. 0.3 The Motion of the Moon
The Moon takes about 29.5 days to go through whole cycle of phases – synodic month.
Phases are due to different amounts of sunlit portion being visible from Earth.
Time to make full 360° around Earth, sidereal month, is about 2 days shorter than synodic month.

11. 0.3 The Motion of the Moon Lunar eclipse:
Earth is between the Moon and Sun
Partial when only part of the Moon is in shadow
Total when all is in shadow

12. 0.3 The Motion of the Moon
Solar eclipse: the Moon is between Earth and Sun

13. 0.3 The Motion of the Moon
Solar eclipse is partial when only part of the Sun is blocked, total when all is blocked, and annular when the Moon is too far from Earth for total.

14. 0.3 The Motion of the Moon
Eclipses don’t occur every month because Earth’s and the Moon’s orbits are not in the same plane.

15. 0.4 The Measurement of Distance
Triangulation: Measure baseline and angles, and you can calculate distance.

16. 0.4 The Measurement of Distance
Parallax: Similar to triangulation, but looking at apparent motion of object against distant background from two vantage points

17. 0.5 Science and the Scientific Method
Scientific theories:
Must be testable
Must be continually tested
Should be simple
Should be elegant
Scientific theories can be proven wrong, but they can never be proven right with 100% certainty.

18. 0.5 Science and the Scientific Method
Observation leads to theory explaining it.
Theory leads to predictions consistent with previous observations.
Predictions of new phenomena are observed. If the observations agree with the prediction, more predictions can be made. If not, a new theory can be made.

19. Summary of Chapter 0 Astronomy: Study of the universe
Stars can be imagined to be on inside of celestial sphere; useful for describing location.
Plane of Earth’s orbit around Sun is ecliptic; at 23.5° to celestial equator.
Angle of Earth’s axis causes seasons.
Moon shines by reflected light, has phases.
Solar day ≠ sidereal day, due to Earth’s rotation around Sun.

20. Summary of Chapter 0, cont.
Synodic month ≠ sidereal month, also due to Earth’s rotation around Sun
Tropical year ≠ sidereal year, due to precession of Earth’s axis
Distances can be measured through triangulation and parallax.
Eclipses of Sun and Moon occur due to alignment; only occur occasionally as orbits are not in same plane.
Scientific method: Observation, theory, prediction, observation …

21. Electromagnetic Radiation
(How we get information about the cosmos)
Examples of electromagnetic radiation?
Light
Infrared
Ultraviolet
Microwaves
AM radio
FM radio
TV signals
Cell phone signals
X-rays

22. Units of Chapter 1 The Motions of the Planets
The Birth of Modern Astronomy
The Laws of Planetary Motion
Newton’s Laws
Summary of Chapter 1

23. 1.1 The Motions of the Planets
The Sun, Moon, and stars all have simple movements in the sky, consistent with an Earth-centered system.
Planets:
Move with respect to fixed stars
Change in brightness
Change speed
Have retrograde motion
Are difficult to describe in earth-centered system

24. 1.1 The Motions of the Planets
A basic geocentric model, showing an epicycle (used to explain planetary motions)

25. 1.1 The Motions of the Planets
Lots of epicycles were needed to accurately track planetary motions, especially retrograde motions. This is Ptolemy's model.

26. 1.1 The Motions of the Planets
A heliocentric (Sun-centered) model of the solar system easily describes the observed motions of the planets, without excess complication.

27. 1.2 The Birth of Modern Astronomy
Observations of Galileo:
The Moon has mountains, valleys, and craters.
The Sun has imperfections, and it rotates.
Jupiter has moons.
Venus has phases.
All these were in contradiction to the general belief that the heavens were constant and immutable.

28. 1.2 The Birth of Modern Astronomy
The phases of Venus are impossible to explain in the Earth-centered model of the solar system.

29. 1.3 The Laws of Planetary Motion
Kepler’s laws:
1. Planetary orbits are ellipses, Sun at one focus.

30. 1.3 The Laws of Planetary Motion
Kepler’s laws:
2. Imaginary line connecting Sun and planet sweeps out equal areas in equal times.

31. 1.3 The Laws of Planetary Motion
Kepler’s laws:
3. Square of period of planet’s orbital motion is proportional to cube of semimajor axis.

32. 1.3 The Laws of Planetary Motion
The Dimensions of the solar system
The distance from Earth to the Sun is called an astronomical unit. Its actual length may be measured by bouncing a radar signal off Venus and measuring the transit time.

33. 1.4 Newton’s Laws
Gravity
On Earth’s surface, the acceleration due to gravity is approximately constant, and directed toward the center of Earth.

34. 1.4 Newton’s Laws
Gravity
For two massive objects, the gravitational force is proportional to the product of their masses divided by the square of the distance between them.

35. 1.4 Newton’s Laws
Gravity
The gravitational pull of the Sun keeps the planets moving in their orbits.

36. 1.4 Newton’s Laws
Massive objects actually orbit around their common center of mass; if one object is much more massive
than the other, the center of mass is not far from the center of the more massive object. For objects more equal in mass, the center of mass is between the two.

37. 1.4 Newton’s Laws
Kepler’s laws are a consequence of Newton’s laws.

38. Summary of Chapter 1
First models of solar system were geocentric, but couldn't easily explain retrograde motion.
Heliocentric model does.
Galileo's observations supported heliocentric model.
Kepler found three empirical laws of planetary motion from observations.

39. Summary of Chapter 1, cont.
Laws of Newtonian mechanics explained Kepler’s observations.
Gravitational force between two masses is proportional to the product of the masses, divided by the square of the distance between them.

40. Units of Chapter 2 Information from the Skies Waves in What?
The Electromagnetic Spectrum
Thermal Radiation
Spectroscopy
The Formation of Spectral Lines
The Doppler Effect
Summary of Chapter 2 40

41. 2.1 Information from the Skies
Electromagnetic radiation: Transmission of energy through space without physical connection through varying electric and magnetic fields
Example: Light 41

42. 2.1 Information from the Skies
Example: Water wave
Water just moves up and down.
Wave travels and can transmit energy. 42

43. 2.2 Waves in What?
Diffraction: The bending of a wave around an obstacle
Interference: The sum of two waves; may be larger or smaller than the original waves 43

44. 2.2 Waves in What?
Water waves, sound waves, and so on, travel in a medium (water, air, …).
Electromagnetic waves need no medium.
Created by accelerating charged particles 44

45. Radiation travels as waves. Waves carry information and energy.
Properties of a wave
wavelength (l)
crest
amplitude (A)
trough
velocity (v)
l is a distance, so its units are m, cm, or mm, etc.
Period (T): time between crest (or trough) passages
Frequency (n): rate of passage of crests (or troughs), n =
Also, v = l n
h 1 T
(units: Hertz or cycles/sec)

46. } Radiation travels as Electromagnetic waves.
That is, waves of electric and magnetic fields traveling together.
Examples of objects with magnetic fields:
a magnet
the Earth
Clusters of galaxies
Examples of objects with electric fields:
Power lines, electric motors, …
Protons (+)
Electrons (-) }
"charged" particles that make up atoms.

47. Scottish physicist James Clerk Maxwell showed in 1865 that waves of electric and magnetic fields travel together => traveling “electromagnetic” waves.

48. The Doppler Effect
Applies to all waves – not just radiation. The frequency or wavelength of a wave depends on the relative motion of the source and the observer.

49. Applies to all kinds of waves, not just radiation.
The Doppler Effect
Applies to all kinds of waves, not just radiation.
at rest
velocity v1
velocity v1
velocity v2
you encounter more wavecrests per second => higher frequency!
velocity v1
velocity v3
fewer wavecrests per second => lower frequency!

50. Waves bend when they pass through material of different densities.
Things that waves do
1. Refraction
Waves bend when they pass through material of different densities.
air
water
swimming pool
prism
glass
air
air

51. 2. Diffraction
Waves bend when they go through a narrow gap or around a corner.

52. The Electromagnetic Spectrum
1 nm = m , 1 Angstrom = m
c =
l n

53. The "Inverse-Square" Law Applies to Radiation
Each square gets 1/4 of the light
Each square gets 1/9 of the light 1 D2
apparent brightness α
α means “is proportional to”. D is the distance between source and observer.

54. Approximate black-body spectra of stars of different temperature
cold dust
average star (Sun)
Brightness
infrared visible UV
“cool" stars
very hot stars
infrared visible UV
frequency increases, wavelength decreases

55. Laws Associated with the Black-body Spectrum
Wien's Law: 1 T
λmax energy α
(wavelength at which most energy is radiated is longer for cooler objects)
Stefan's Law:
Energy radiated per cm2 of area on surface every second α T 4
(T = temperature at surface)
1 cm2

56. The total energy radiated from entire surface every second is called the
luminosity. Thus
Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2)
For a sphere, area of surface is 4πR2, where R is the radius.
So Luminosity α R2 x T4

57. Types of Spectra and Kirchhoff's (1859) Laws
1. "Continuous" spectrum - radiation over a broad range of wavelengths (light: bright at every color). Produced by a hot opaque solid, liquid, or dense gas.
2. "Emission line" spectrum - bright at specific wavelengths only. Produced by a transparent hot gas.
3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines. Produced by a transparent cool gas absorbing light from a continuous spectrum source.

58. When an atom absorbs a photon, it moves to a higher energy state briefly
When it jumps back to lower energy state, it emits a photon - in a random direction

59. So why do stars have absorption line spectra?
Simple case: let’s say these atoms can only absorb green photons. Get dark absorption line at green part of spectrum. . . . . . . . . . . .
“atmosphere” (thousands
of K) has atoms and ions
with bound electrons
hot (millions of K), dense interior
has blackbody spectrum,
gas fully ionized

60. Stellar Spectra
Spectra of stars differ mainly due to atmospheric temperature (composition differences also important).
“hot” star
“cool” star

61. Why emission lines?
hot cloud of gas . . . . . .
- Collisions excite atoms: an electron moves to a higher energy level
- Then electron drops back to lower level
- Photons at specific frequencies emitted.

62. 2.7 The Doppler Effect
If one is moving toward a source of radiation, the wavelengths seem shorter; if moving away, they seem longer.
Relationship between frequency and speed: 62

63. 2.7 The Doppler Effect
The Doppler effect shifts an object’s entire spectrum either toward the red or toward the blue. 63

64. Summary of Chapter 2 Wave: period, wavelength, amplitude
Electromagnetic waves created by accelerating charges
Visible spectrum is different wavelengths of light.
Entire electromagnetic spectrum:
includes radio waves, infrared, visible light, ultraviolet, X-rays, gamma rays
can tell the temperature of an object by measuring its blackbody radiation 64

65. Summary of Chapter 2, cont.
Spectroscope splits light beam into component frequencies.
Continuous spectrum is emitted by solid, liquid, and dense gas.
Hot gas has characteristic emission spectrum.
Continuous spectrum incident on cool, thin gas gives characteristic absorption spectrum. 65

66. Summary of Chapter 2, cont.
Spectra can be explained using atomic models, with electrons occupying specific orbitals.
Emission and absorption lines result from transitions between orbitals.
Doppler effect can change perceived frequency of radiation.
Doppler effect depends on relative speed of source and observer. 66