1. Test 1 Test covers Chapters 1-3 Part 1: Short questions and problems
Part 2: bonus problems, extra points
Show your work everywhere
Don’t forget to prepare formula sheet
Bring your calculator
Textbook and lecture notes are not allowed

2. How to prepare: Read chapters and lecture notes
Pay extra attention to chapter summary
Answer review questions
Solve homework problems

3. Remember and check UNITS for all terms in the formulas!!!
Indicate units on your formula sheet
Express all terms in correct units before
plugging in the formula
Check your answer for right unit

4. Chapter 1
Scale of different objects: planets, sun, orbits of planets, interstellar distances, Milky Way galaxy, distances between galaxies, Universe
No need to memorize exact numbers, but try to remember the order of magnitude!
It will help you to check whether your answers make sense

5. Distance scale 107 m planets 109 m Sun and stars 1011 m ~ 1 AU
Solar System
1021 m
~ 10 kpc
galaxy
1022 m
~ 1 Mpc
Distance
between
galaxies
1017 m
~ 3 pc
distance
between
stars
1025 m
~ 500 Mpc
Largest
structure
1026 m
~ Gpc
Hubble
radius

6. New units of distance 1 AU = 1.5x1011 m (orbits of planets)
1 light-year (ly) ~ 1016 m ~ 105 AU (interstellar distances)
1 ly = c1 year (the distance the light travels in 1 year)
Velocity of light in vacuum: c = 3 108 m/s
1 parsec (pc)  3.26 ly = 3 1016 m
Kpc, Mpc, Gpc

7. Chapter 2,3

8. Relationship between magnitudes and intensities
Define the magnitude scale so that two stars that differ by
5 magnitudes have an intensity ratio of 100.

9. 90o-L

11. Apparent motion of the sun, moon, stars, and planets

15. Drawn for northern latitudes, these are the paths the sun takes across the sky on the equinoxes and solstices. Can you see that the summer path is longer (and therefore that the summer sun stays in the sky longer)?

16. 90o-L

17. Seasons - summary
Seasons are NOT caused by varying distances from the Earth to the Sun
The primary cause of seasons is the 23.5 degree tilt of the
Earth's rotation axis with respect to the plane of the ecliptic.
The Seasons in the Northern Hemisphere
Note: the Earth is actually closest to the Sun in January 4!
Perihelion: × 106 km; Aphelion: × 106 km

18. Thus, we experience Summer in the Northern Hemisphere when the Earth is on that part of its orbit where the N. Hemisphere is oriented more toward the Sun and therefore:
the Sun rises higher in the sky and is above the horizon longer,
The rays of the Sun strike the ground more directly.
Likewise, in the N. Hemisphere Winter the hemisphere is oriented away from the Sun, the Sun only rises low in the sky, is above the horizon for a shorter period, and the rays of the Sun strike the ground more obliquely.

19. Ice Ages - cause
Atmospheric composition, especially greenhouse gases and dust;
Changes in the Earth’s orbit and inclination;
The motion of tectonic plates resulting in changes in the landmass distribution;
Variations in the solar output;
The impact of large meteorites;
Eruptions of supervolcanoes

20. Cycles of glaciation - cause
Theory: cyclic climate changes due to variations in the Earth’s orbital parameters
Precession (26,000 yr cycle)
Eccentricity (varies from 0.00 to 0.06 with 100,000 and 400,000 yr cycles)
Axis tilt (varies from 24.5o to 22.1o with 41,000 yr cycle
Milutin Milankovitch 1920

22. Varies from 0.00 to 0.06 (currently 0.017)
Periodicity 100,000 and 400,000 yr
Eccentricity cycle modulates the amplitude of the precession cycle

23. 26,000 yr cycle

24. Figure 2.7: Precession. (a) A spinning top precesses in a conical motion around the perpendicular to the floor because its weight tends to make it fall over. (b) Earth precesses around the perpendicular to its orbit because the gravity of the sun and moon tend to twist it upright.

25. An effect called precession causes the Sun's vernal equinox point to slowly shift westward over time, so a star's RA and dec will slowly change by about 1.4 degrees every century (a fact ignored by astrologers), or about 1 minute increase in a star's RA every twenty years. This is caused by the gravitational pulls of the Sun and Moon on the Earth's equatorial bulge (from the Earth's rapid rotation) in an effort to reduce the tilt of the Earth's axis with respect to the ecliptic and the plane of the Moon's orbit around the Earth (that is itself slightly tipped with respect to the ecliptic).

26. Milankovitch theory:
Very good agreement in general, but some findings are still contradictory
The response of the climate system to external variations is highly nonlinear: small external variations can trigger large changes in climate. Example: ice-albedo positive feedback loop.
Figure 3.17: The Milankovitch theory predicts periodic changes in solar heating (shown here as the equivalent summer latitude of the sun). Over the last 400,000 years, these changes seem to have varied in step with ocean temperatures measured from fossils in sediment layers from the seabed. (Adapted from Cesare Emiliani)

27. The Phases of the Moon
From Earth, we see different portions of the Moon’s surface lit by the sun, causing the phases of the Moon.

28. Lunar Phases

29. The Phases of the Moon (2)
The Moon orbits Earth in a sidereal period of days.
27.32 days
Moon
Earth
Fixed direction in space

30. The Phases of the Moon (2)
Fixed direction in space
29.53 days
Earth
Moon
Earth orbits around Sun => Direction toward Sun changes!
The Moon’s synodic period (to reach the same position relative to the sun) is days (~ 1 month).
Synodic period defines the cycle of lunar phases

31. Tides
Integrate over the mass distribution
In the Earth’s body

32. Spring and Neap Tides
The Sun is also producing tidal effects, about half as strong as the Moon.
Near Full and New Moon, those two effects add up to cause spring tides.
Near first and third quarter, the two effects work at a right angle, causing neap tides.
Spring tides
Neap tides

33. Effects of tides Slow down the rotation of earth
Seabed slips under the water bulges
Friction slows down the rotation
The day was 18 hours long 900 million yr ago

34. The Tidally-Locked Orbit of the Moon
The Earth also exerts tidal forces on the moon’s rocky interior that slow down its rotation.
 It is rotating with the same period around its axis as it is orbiting Earth (tidally locked).
 We always see the same side of the moon facing Earth.

35. Effects of tides
1. Synchronization of the rotational and orbital period
2. Tides cause the heating of the interiors of the interacting bodies
3. If the bodies are too close to each other, they can be
disrupted by tides (Roche limit).

36. Why not every new and full moon??
Eclipses
Why not every new and full moon??

37. Moon’s orbit is tilted by 5o from the ecliptic

38. For an eclipse to occur,
The moon should be at one of the nodes – crossing the plane of the earth’s orbit
The line of nodes should point at the sun
Figure 3.15: The moon’s orbit is tipped about 5° to Earth’s orbit. The nodes N and N’ are the points where the moon passes through the plane of Earth’s orbit. If the line of nodes does not point at the sun, the shadows miss, and there are no eclipses at new moon and full moon. At those parts of Earth’s orbit where the line of nodes points toward the sun, eclipses are possible at new moon and full moon.

39. Conditions for Eclipses
The moon’s orbit is inclined against the ecliptic by ~ 50.
A solar eclipse can only occur if the moon passes a node near new moon.
A lunar eclipse can only occur if the moon passes a node near full moon.

40. Solar Eclipses How come that the Moon can eclipse the Earth??
Earth-Moon system to scale
How come that the Moon can eclipse the Earth??
Accidentally, they have almost the same angular sizes!

41. Angular diameter (rad) = (rad) = L/D Distance
Figure 3.7: The three quantities related by the small-angle formula. Angular diameter is given in seconds of arc in the formula. Distance and linear diameter must be expressed in the same units—both in meters, both in light-years, and so on.
Linear diameter
Angular diameter (rad) =
(rad) = L/D
Distance
180 degrees =  radian
(deg) = (rad)180/

42. Small Angle Formula radian = 180 degrees Note units!! L D D L
Convert from radian to arcseconds:
radian = 180 degrees
1 deg = 60 arcmin = 3600 arcsec
Note units!!

43. Exact Formula radian = 180 degrees Note units!! L D D L
Convert from radian to arcseconds:
radian = 180 degrees
1 deg = 60 arcmin = 3600 arcsec
Note units!!

44. Small Angle Formula
(SLIDESHOW MODE ONLY)

45. Moon: Sun: Very close! 3476 km  = = 0.0091 rad = 0.5 deg 384000 km

46. Solar Eclipses
The sun appears approx. as large in the sky (same angular diameter ~ 0.50) as the moon.
 When the moon passes in front of the sun, the moon can cover the sun completely, causing a total solar eclipse.

47. Umbra is below 270 km in diameter It moves at 1600 km/hr
Figure 3.8: (a) The umbral shadow of the moon sweeps over a narrow strip of Earth.
Umbra is below 270 km in diameter
It moves at 1600 km/hr
Total eclipse lasts for not more than 7.5 min

48. Total Solar Eclipse
Chromosphere and Corona
Prominences

49. Solar Atmosphere Revealed

50. Diamond Ring Effect

51. Moon’s orbit is elliptical -> when the moon is in apogee, umbra does not reach the earth -> annular eclipse
Figure 3.11: (b) An annular eclipse occurs when the moon is in the farther part of its orbit and its umbral shadow does not reach Earth. From Earth, we see an annular eclipse because the moon’s angular diameter is smaller than the angular diameter of the sun.

52. Annular Solar Eclipses
When Earth is near perihelion, and the moon is near apogee, we see an annular solar eclipse.
The angular sizes of the moon and the sun vary, depending on their distance from Earth.
Perigee
Apogee
Aphelion
Perihelion
Moon’s orbit is more elliptical than the earth’s orbit

53. Solar Eclipses:
Approximately 1 total solar eclipse per year

54. Saros cycle: 18 years, 11 days, 8 hours
The Saros Cycle
Saros cycle: 18 years, 11 days, 8 hours
Repeats in one place every 3 cycles, or ~ 54 yr 1 month