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# Lesson3b

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1. Lesson3b Orbital Properties of the Moon

2. Rotation is constant, orbital speed is not.

3. 7 days 14 days 0 days 21 days

4. Same side always faces exactly toward the Earth if the Moon is in a circular orbit.

5. 7 days 14 days 0 days 21 days

6. In 14 days the Moon completes one rotation on its axis. But since the orbit is elliptical, the moon’s orbital speed slows. It is not quite half-way around the orbit in 14 days. This means the Moon has over rotated on its axis and as a result, we see the Moon appear to wobble.

7. Tidal Forces • It is not a coincidence that the Moon rotates once every orbit. • This is due to tidal interactions between the Earth and the Moon. • The tidal interactions allow the transportation of angular momentum between the two bodies.

8. Mt. Saint Michael Normandy, France

9. Angular Momentum • This is the momentum that keeps things spinning. It depends on the mass (M), the radius (R) and the velocity (V). • L = M x V x R • Angular momentum for a system is always conserved. • M, V or R can change, but L has to stay constant.

10. The Earth-Moon System • The total angular momentum of the Earth-Moon system is conserved. • LErotation – Angular momentum from Earth spinning on its axis • LEorbital – Angular momentum of Earth moving in small circle • LMrotation -- Angular momentum from Moon spinning on its axis • LMorbital -- Angular momentum of Moon moving in orbit

11. Total Angular Momentum • Ltotal = LErotation + LEorbital + LMrotation + LMorbital • The total angular momentum is conserved, but the system can exchange angular momentum from one component to the other.

12. Result • Moon pulls back on the Earth, slowing the Earth’s rotation. • But total angular momentum in a system is always conserved. • If the Earth’s rotation slows, then the rotational angular momentum of the Earth decreases. • The Moon has to pick up that angular momentum. It does this by an increase in the Moon’s orbital angular momentum. The Moon speeds up in its orbit.

13. Lunar ranging program shows the Moon is receding from the Earth at 3.8 cm/year.

14. Lunar Ranging

15. Lunar ranging program shows the Moon is receding from the Earth at 3.8 cm/year. • If this rate were constant then over 1 million years (1 x 106 years) the Moon would increase the size of its orbit by 3.8 x 106 cm or 3.8 x 104 meters, or 38 km. • At the same time the Earth’s rotation has slowed by 22 seconds. So 1 million years ago the Earth’s day was 22 seconds shorter.

16. Extrapolating to 4.6 billion years and assuming the rate of transfer of angular momentum was constant (which it wasn’t) the Moon would have been 175,000 km closer. (Current distance is 384,403 km) • The Earth’s rotation at this time was 6.5 hours. • Note: This is complicated. The effect of tides was greater in the past and that means the exchange in angular momentum was not constant throughout the life time of the system.

17. The ground also bulges along a line connecting the Earth and the Moon. The Moon’s surface bulges toward the Earth and away from the Earth, just like the oceans due on the Earth. • Long ago, when the Moon use to rotate on its axis faster than it does today, the Earth tugged on the Moon’s tidal bulge and forced the Moon to slow its rotation until it finally became tidally locked. (synchronous orbit) • This is the lowest energy state for the Moon.

18. Why wouldn’t zero rotation for the Moon be the lowest energy state? If the Moon didn’t rotate on its axis it would have zero rotational angular momentum. Wouldn’t this be a lower energy state for the Moon? • Why isn’t zero rotation the lowest energy state for the Moon?

19. Back to Libration • The Moon isn’t quite in a circular orbit. It wobbles because its orbit is slightly elliptical. • When the Moon is farthest away, it moves more slowly in its orbit. But the rotation around its axis is at a constant rate. • This means the Moon over rotates compared to us on Earth. • Could this be related to some Moon Quakes?

20. Subtle (or not so subtle) effect • The rotation of the Earth causes it to bulge at the equator. The difference in diameter is not huge, but measureable. • Earth Equatorial diameter: 12,756 km • Earth Polar diameter: 12,713 km • Difference: 43 km. • What was this difference like billions of years ago?

21. . • The Earth was flatter (more oblate) because it was spinning faster • The Earth was more spherical because it was more molten • It was the same as today

22. Material moves to poles as rotation slows

23. Material moves to poles as rotation slows

24. If the Earth were not rotating it would be a sphere, not an oblate sphere. • As the Earth’s rotation has slowed, the shape of the Earth has slowly changed from a more flattened sphere to more spherical. • This changing shape forces the lithosphere to move to the polar regions. • This helps to propagate plate tectonics on the Earth. It is not the only effect, but one of them. • RESULT: The Moon has helped to drive plate tectonics on the Earth.

25. Apollo landing sites

26. Do you think the Apollo astronauts really went to the Moon or was it faked?

27. . • Yes, they went to the Moon. • No, it was faked. • I’m not sure but it might have been faked • I’ve never considered this question

28. Lunar Module

29. What was left behind

30. The Lunar Rover

31. Lunar Reconnaissance Orbiter (LRO)

32. Lunar Reconnaissance Orbiter

33. Lunar Reconnaissance Orbiter

34. Regolith is why we can see the tracks

35. Old illustration of the Moon

36. Reality

37. Although the Moon has no atmosphere there is still a form of erosion. • Meteorite impacts. In particular, micro-meteorites which can not make it through the Earth’s atmosphere.

38. Old Young

39. Older craters begin to lose their sharp edges because constant “sand blasting” by micrometeorites break off small pieces. • The resultant small pieces become the Lunar Regolith.

40. The layer of regolith varies in depth from a few meters deep in the youngest maria to over 20 meters deep (~ 60 feet) in the highlands. • Only the top few inches are a fine powder. The rest in compressed by the weight of the overlying regolith. • Regolith is composed of bits of rocks found in that particular area of the Moon.

41. Mare Regolith • Glass beads come from volcanic lava • Impact glass is more distorted, and comes when the heat of impact melts some of the rock into glass • Rock fragments are just little pieces of rock from the surface around the area • Plagioclase feldspar is typically found in crustal material. (sodium, calcium, aluminum, silicon, oxygen) (light elements)

42. Lunar Rocks • Most rocks on the Moon are Breccia. They are composite rocks that are made of differing materials which have been fused together.

43. Mare Breccia rock