1. Tides, Tidal Friction, and Synchronous Rotation

2. Why do tides occur?

3. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon

4. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon But how?

5. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon This is how: The Universal Law of Gravitation The strength of gravity decreases with distance

6. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon So the Moon pulls harder on the nearer side

7. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon So the Moon pulls harder on the nearer side This stretches the Earth out, making two tidal bulges on opposite sides

8. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon So the Moon pulls harder on the nearer side This stretches the Earth out, making two tidal bulges on opposite sides The Moon goes around the Earth slower than the Earth rotates

9. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon So the Moon pulls harder on the nearer side This stretches the Earth out, making two tidal bulges on opposite sides The Moon goes around the Earth slower than the Earth rotates So any point on Earth should have two high tides and two low tides each day

10. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon So the Moon pulls harder on the nearer side This stretches the Earth out, making two tidal bulges on opposite sides The Moon goes around the Earth slower than the Earth rotates So any point on Earth should have two high tides and two low tides each day But they aren’t exactly 12 hours apart

11. Tides, Tidal Friction, and Synchronous Rotation Why do tides occur? They are caused by the gravity of the Moon So the Moon pulls harder on the nearer side This stretches the Earth out, making two tidal bulges on opposite sides The Moon goes around the Earth slower than the Earth rotates So any point on Earth should have two high tides and two low tides each day But they aren’t exactly 12 hours apart Why?

12. Tides, Tidal Friction, and Synchronous Rotation It’s because the Moon orbits around the Earth

13. Tides, Tidal Friction, and Synchronous Rotation It’s because the Moon orbits around the Earth So at a given location, the Earth has to go through more than one sidereal rotation to get back to the same tide

14. Tides, Tidal Friction, and Synchronous Rotation It’s because the Moon orbits around the Earth So at a given location, the Earth has to go through more than one sidereal rotation to get back to the same tide It also depends on the shape of the coast and the shape of the bottom

15. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters

16. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place

17. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high

18. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge

19. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge But elsewhere, the variation can be much greater

20. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge But elsewhere, the variation can be much greater For example, the Bay of Fundy

21. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge But elsewhere, the variation can be much greater For example, the Bay of Fundy This is high tide there

22. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge But elsewhere, the variation can be much greater For example, the Bay of Fundy This is high tide there This is low tide

23. Tides, Tidal Friction, and Synchronous Rotation The tidal bulge in mid-ocean is only about 2 meters But tidal heights vary from place to place Locally, the tide at the beach varies about 4 feet from low to high – much less than the mid-ocean bulge But elsewhere, the variation can be much greater For example, the Bay of Fundy This is high tide there This is low tide The tides can vary by as much as 40 feet!

24. Tides, Tidal Friction, and Synchronous Rotation This is due to the shape of the bay

25. Tides, Tidal Friction, and Synchronous Rotation This is due to the shape of the bay The natural frequency with which waves want to slosh back and forth in the bay

26. Tides, Tidal Friction, and Synchronous Rotation This is due to the shape of the bay The natural frequency with which waves want to slosh back and forth in the bay – like in a bath tub

27. Tides, Tidal Friction, and Synchronous Rotation This is due to the shape of the bay The natural frequency with which waves want to slosh back and forth in the bay – like in a bath tub – matches the time it takes for the tide to roll in

28. Tides, Tidal Friction, and Synchronous Rotation This is due to the shape of the bay The natural frequency with which waves want to slosh back and forth in the bay – like in a bath tub – matches the time it takes for the tide to roll in So the sloshing amplifies the tides and leads to the huge variation in water height between low and high tides

29. Tides, Tidal Friction, and Synchronous Rotation The Sun also affects the tides, but because of its distance only about 1/3 as much as the Moon

30. Tides, Tidal Friction, and Synchronous Rotation The Sun also affects the tides, but because of its distance only about 1/3 as much as the Moon Occasionally the Sun and the Moon work together to produce unusually extreme tides

31. Tides, Tidal Friction, and Synchronous Rotation The Sun also affects the tides, but because of its distance only about 1/3 as much as the Moon Occasionally the Sun and the Moon work together to produce unusually extreme tides When the Sun, Earth, and Moon are in a line there is a “spring tide”

32. Tides, Tidal Friction, and Synchronous Rotation The Sun also affects the tides, but because of its distance only about 1/3 as much as the Moon Occasionally the Sun and the Moon work together to produce unusually extreme tides When the Sun, Earth, and Moon are in a line there is a “spring tide” When they form a right angle there is a “neap tide”

33. Tides, Tidal Friction, and Synchronous Rotation The Sun also affects the tides, but because of its distance only about 1/3 as much as the Moon Occasionally the Sun and the Moon work together to produce unusually extreme tides When the Sun, Earth, and Moon are in a line there is a “spring tide” When they form a right angle there is a “neap tide” When should these occur?

34. Tides, Tidal Friction, and Synchronous Rotation In fact, the tidal bulge is not lined up with the Earth and Moon This is due to “tidal friction” As the Earth rotates through the tidal bulges, it pulls them ahead So they run slightly “ahead” of the Earth-Moon line If the Earth didn’t rotate faster than the Moon orbits, the bulges would be on the Earth-Moon line

35. Tides, Tidal Friction, and Synchronous Rotation This tidal friction slows down Earth's rotation Length of day increases ~2 ms per century (1 s per 50,000 y) It also pulls the Moon ahead in its orbit This increases orbital energy And moves the Moon away from the Earth by ~4 cm per year So the Moon is ~1 m farther away than when Apollo 11 landed

36. Tides, Tidal Friction, and Synchronous Rotation Knowing what you know about conservation of angular momentum, how will this affect the angular momentum of the system consisting of the Earth and the Moon?

37. Tides, Tidal Friction, and Synchronous Rotation Knowing what you know about conservation of angular momentum, how will this affect the angular momentum of the system consisting of the Earth and the Moon? The angular momentum lost by the Earth is gained by the Moon

38. Tides, Tidal Friction, and Synchronous Rotation The Earth’s rotation is slowed ever so slightly by this process

39. Tides, Tidal Friction, and Synchronous Rotation The Earth’s rotation is slowed ever so slightly by this process But the Earth’s tidal force causes a tidal bulge on the Moon, too

40. Tides, Tidal Friction, and Synchronous Rotation The Earth’s rotation is slowed ever so slightly by this process But the Earth’s tidal force causes a tidal bulge on the Moon, too And the Moon’s rotation has been affected much more, because the Moon is much smaller

41. Tides, Tidal Friction, and Synchronous Rotation Over time, the Moon’s rotation has slowed until its rate matches its orbital period

42. Tides, Tidal Friction, and Synchronous Rotation Over time, the Moon’s rotation has slowed until its rate matches its orbital period It is now in “synchronous rotation” with its orbit

43. Tides, Tidal Friction, and Synchronous Rotation Over time, the Moon’s rotation has slowed until its rate matches its orbital period It is now in “synchronous rotation” with its orbit This is why it always shows the same face to us

44. Tides, Tidal Friction, and Synchronous Rotation Over time, the Moon’s rotation has slowed until its rate matches its orbital period It is now in “synchronous rotation” with its orbit This is why it always shows the same face to us Well, almost the same face

45. Tides, Tidal Friction, and Synchronous Rotation Over time, the Moon’s rotation has slowed until its rate matches its orbital period It is now in “synchronous rotation” with its orbit This is why it always shows the same face to us Well, almost the same face…these are called “librations”

46. Tides, Tidal Friction, and Synchronous Rotation There are many other examples of this sort of rotational “locking”

47. Tides, Tidal Friction, and Synchronous Rotation There are many other examples of this sort of rotational “locking” Some are truly synchronous:

48. Tides, Tidal Friction, and Synchronous Rotation There are many other examples of this sort of rotational “locking” Some are truly synchronous: the Moon

49. Tides, Tidal Friction, and Synchronous Rotation There are many other examples of this sort of rotational “locking” Some are truly synchronous: the Moon Pluto and its moon Charon

50. END OF LECTURE 09 JUN 2008

51. Tides, Tidal Friction, and Synchronous Rotation There are many other examples of this sort of rotational “locking” Some are truly synchronous: the Moon Pluto and its moon Charon Others somewhat different:

52. Tides, Tidal Friction, and Synchronous Rotation There are many other examples of this sort of rotational “locking” Some are truly synchronous: the Moon Pluto and its moon Charon Others somewhat different: Mercury’s 2:3::orbital:rotational resonance with the Sun