The Motion of the Planets

1. The Motion of the Planets The planets are orbiting the sun almost exactly in the plane of the Ecliptic. Jupiter Venus Mars Earth Mercury Saturn The Moon is orbiting Earth in almost the same plane (Ecliptic).

2. Inferior planets are visible only at small angular distances from the Sun

3. The Motion of the Planets Mercury appears at most ~28° from the sun. It can occasionally be seen shortly after sunset in the west or before sunrise in the east. Venus appears at most ~46° from the sun. It can occasionally be seen for at most a few hours after sunset in the west or before sunrise in the east.

4. The Cycles of the Moon Chapter 3

5. Outline I. The Changeable Moon A. The Motion of the Moon B. The Cycle of Phases II. The Tides A. The Cause of the Tides B. Tidal Effects III. Lunar Eclipses A. Earth's Shadow B. Total Lunar Eclipses C. Partial and Penumbral Lunar Eclipses

6. Outline (continued) IV. Solar Eclipses A. The Angular Diameter of the Sun and Moon B. The Moon's Shadow C. Total Solar Eclipses V. Predicting Eclipses A. Conditions for an Eclipse B. The View From Space C. The Saros Cycle

7. The Phases of the Moon (1) From Earth, we see different portions of the Moon’s surface lit by the sun, causing the phases of the Moon.

8. Lunar Phases

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

10. 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 29.53 days (~ 1 month). Synodic period defines the cycle of lunar phases

11. Tides Newton’s law of gravitation

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

13. The Tides Caused by the difference of the Moon’s gravitational attraction on the water on Earth Excess gravity pulls water towards the moon on the near side Forces are balanced at the center of the Earth Excess centrifugal force pushes water away from the moon on the far side  2 tidal maxima  12-hour cycle

14. 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

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

16. 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.

17. Acceleration of the Moon’s Orbital Motion Earth’s tidal bulges are slightly tilted in the direction of Earth’s rotation. Gravitational force pulls the moon slightly forward along its orbit.

18. 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).

19. Tides - reality Modulated by ellipticity of the Earth’s and Moon’s orbits

20. Eclipses p. 28

21. Why not every new and full moon??

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

23. 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 Fig. 3-15, p. 36

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

25. Lunar Eclipses Earth’s shadow consists of a zone of partial shadow, the Penumbra, and a zone of full shadow, the Umbra. If the moon passes through Earth’s full shadow (Umbra), we see a lunar eclipse. If the entire surface of the moon enters the Umbra, the lunar eclipse is total.

27. A Total Lunar Eclipse (1) Note a circular shadow: from this observation Aristotle concluded that Earth is a sphere!

28. Lunar Eclipses: 2002-2012 Typically, 1 or 2 lunar eclipses per year.

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

30. Linear diameter (rad) = L/D Angular diameter (rad) = Distance (deg) = (rad)180/ 180 degrees =  radian

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

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

33. Small Angle Formula (SLIDESHOW MODE ONLY)

34. 3476 km Moon:  = = 0.0091 rad = 0.5 deg 384000 km 1.4106 km Sun:  = = 0.0093 rad = 0.5 deg 1.5108 km Very close!

35. 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.

36. Umbra is below 270 km in diameter It moves at 1600 km/hr Total eclipse lasts for not more than 7.5 min

37. Total Solar Eclipse Chromosphere and Corona Prominences

38. Solar Atmosphere Revealed

39. Diamond Ring Effect

40. Moon’s orbit is elliptical -> when the moon is in apogee, umbra does not reach the earth -> annular eclipse

41. 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

42. Solar Eclipses: 2002-2012 Approximately 1 total solar eclipse per year

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