UBIAS Workshop

UBIAS Intercontinental Academia Nagoya Workshop での講演資料です。

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1. UBIAS Intercontinental Academia Nagoya Workshop, March 9, 2016 How Long “Was” a Day on Earth? Takanori Sasaki Department of Astronomy, Kyoto University
2. Takanori Sasaki Assistant Professor Department of Astronomy Kyoto University Ph.D. (Science) the University of Tokyo (2008) Research Interests: Origin and evolution of planetary systems Formation of habitable planets Early evolution of the Earth HP: http://sasakitakanori.com/en
3. “Moon is getting further away from Earth?” Yes, it is! (c) BBC
4. Contents ✤ How long was a month? ✤ How to make the Moon? ✤ Why Moon is moving away from Earth? ✤ How old are Earth and Moon? ✤ How long was a Day on Earth?
5. Contents ✤ How long was a month? ✤ How to make the Moon? ✤ Why Moon is moving away from Earth? ✤ How old are Earth and Moon? ✤ How long was a Day on Earth?
6. Measuring Earth-Moon distance light: 3×108 m/s Measuring the time → Deriving the distance
7. Lunar Laser Ranging Experiment (c) NASA (c) NASA Moon is moving away from Earth at a rate of 3.8 cm per year! [Chapront et al., A&A, 2002] Analysis of LLR experiments from Jan. 1992 until Apr. 2001 to measure the Earth-Moon distance at each time ⇓ 384,400 km
8. Moon was much closer to Earth. (c) YouTube
9. Kepler’s third law (c) YouTube The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. P2 a3 = constant The closer, the faster.
 The further, the slower.
10. How long was a month? [Kahn & Pompea, Nature, 1978] Daily growth lines and lunar monthly sept are formed in Nautilus pompilius Linnaeus shells. The number of days per lunar month can be determined using the fossil shells. The number of growth lines per chamber length (between arrows) can be counted using a scanning electron microscope.
11. How long was a month? [Kahn & Pompea, Nature, 1978] 30 days @present 9 days @420 Myr ago
12. Conclusion ✤ Moon was much closer to Earth and revolved faster. ✤ Moon was formed nearby Earth by the giant impact. ✤ Moon is moving away by gaining angular momentum. ✤ Earth and Moon were born at 4.5 billion years ago. ✤ A day on Earth was much shorter than today!
13. Contents ✤ How long was a month? ✤ How to make the Moon? ✤ Why Moon is moving away from Earth? ✤ How old are Earth and Moon? ✤ How long was a Day on Earth?
14. Proposed hypotheses (~1970s) (c) JAXA Fission: Ancient spinning Earth expelled a piece of its mass. This cannot account for the angular momentum of the Earth-Moon system. Capture: Moon was captured by Earth. Co-Accretion: Earth and Moon formed together. This cannot explain why Moon has a relatively small iron core compared to Earth. A close encounter with Earth typically results in either collision or altered trajectories.
15. Giant Impact Hypothesis [Hartman & Davis, Icarus, 1975; Cameron & Ward, LPI Conf., 1976] (c) Wikipedia
16. Giant Impact Simulation (SPH) Giant impact between Earth and Mars-sized body produced Moon forming disk. [Canup & Asphaug, Nature, 2001]
17. Formation of the Moon (N-body)
18. Roche limit Roche limit ɹ= 3 times Earth’s radius *Present Moon locates at 60 times Earth’s radius
20. Conclusion ✤ Moon was much closer to Earth and revolved faster. ✤ Moon was formed nearby Earth by the giant impact. ✤ Moon is moving away by gaining angular momentum. ✤ Earth and Moon were born at 4.5 billion years ago. ✤ A day on Earth was much shorter than today!
21. Contents ✤ How long was a month? ✤ How to make the Moon? ✤ Why Moon is moving away from Earth? ✤ How old are Earth and Moon? ✤ How long was a Day on Earth?
22. Exchange of angular momentum “It is highly likely that the orbit of the Moon and the spin of the Earth have changed considerably over the age of the solar system due, in particular, to the action of the semidiurnal tide raised by the Moon on the Earth” [Murray & Dermott, 1999]
23. Earth Moon
24. Earth Moon (1) Tidal bulges are raised in the ocean
25. Earth Moon (2) Earth’s rotation displaces tidal bulge (1) Tidal bulges are raised in the ocean
26. Earth Moon (2) Earth’s rotation displaces tidal bulge (3) Moon attracts tidal bulge; Earth slows down (1) Tidal bulges are raised in the ocean
27. Earth Moon (2) Earth’s rotation displaces tidal bulge (3) Moon attracts tidal bulge; Earth slows down (4) Tidal bulge attracts Moon; Moon speeds up and moves outward (1) Tidal bulges are raised in the ocean
28. Conclusion ✤ Moon was much closer to Earth and revolved faster. ✤ Moon was formed nearby Earth by the giant impact. ✤ Moon is moving away by gaining angular momentum. ✤ Earth and Moon were born at 4.5 billion years ago. ✤ A day on Earth was much shorter than today!
29. Contents ✤ How long was a month? ✤ How to make the Moon? ✤ Why Moon is moving away from Earth? ✤ How old are Earth and Moon? ✤ How long was a Day on Earth?
30. Radioactive dating (c) Berkeley Univ. U U U U U U U U 0 yr U U U U Pb Pb Pb Pb τ yr U Pb Pb Pb Pb Pb Pb Pb 3×τ yr U U Pb Pb Pb Pb Pb Pb 2×τ yr 238U →ɾɾɾ→ɾɾɾ→ 206Pb τ (half-life) = 4.5 billion years
31. The age of Earth and Moon Hf-W chronometer: 182Hf → 182W (half-life = 9Myr) ɹHf: lithophile element → mantle ɹW: siderophile element → core Ideal chronometer for metal/silicate segregation ⇓ A giant impact can produce a global magma ocean on a porto-Earth, which seems to lead to considerable metal/silicate segregation. So, Hf-W age would be the age of the last giant impact, i.e., the age of Earth and Moon.
32. The age of Earth and Moon Earth and Moon was born at 62 Myr after formation of Solar system. [Touboul et al., Nature, 2007] e units; the elevated 182W/184W reported for 79155 is therefore pre- sumably due mainly to cosmogenic 182W. Enhanced 182W/184W in time constraint this is no longer required and the aforementioned Sm–Nd ages could possibly date processes associated with the LMO. Table 1 | Hf–W data for lunar metals from KREEP-rich samples, low-Ti and high-Ti mare basalts Sample W (p.p.m.) Hf (p.p.m.) Hf/W e183W e182Wmeas e182Wcorr KREEP-rich samples 68115 23.9 0.407 0.02 0.00 6 0.10 0.33 6 0.14 0.33 6 0.14 20.01 6 0.10 0.18 6 0.12 0.18 6 0.12 0.01 6 0.09 0.18 6 0.12 0.18 6 0.12 0.00 6 0.11 0.14 6 0.15 0.14 6 0.15 Mean (62s) 0.00 6 0.02 0.21 6 0.17 0.21 6 0.17 68815 27.5 0.725 0.03 0.04 6 0.11 0.02 6 0.18 0.02 6 0.18 20.02 6 0.10 0.26 6 0.18 0.26 6 0.18 0.03 6 0.13 0.25 6 0.15 0.25 6 0.15 20.01 6 0.13 0.22 6 0.17 0.22 6 0.17 Mean ( 6 2s) 0.01 6 0.06 0.18 6 0.23 0.19 6 0.23 Weighted average* (62s; n 5 6) 0.00 6 0.03 0.11 6 0.21 0.11 6 0.21 Low-Ti mare basalts 12004 48.7 0.539 0.11 0.04 6 0.21 0.00 6 0.36 0.05 6 0.36 15058 11.3 0.113 0.01 20.10 6 0.15 20.11 6 0.19 0.01 6 0.20 15499 7.64 0.911 0.12 0.03 6 0.22 0.06 6 0.31 0.16 6 0.31 15556 21.6 0.477 0.02 0.02 6 0.21 20.14 6 0.29 0.30 6 0.36 Weighted average (62s; n 5 4) 20.02 6 0.09 20.07 6 0.13 0.09 6 0.14 High-Ti mare basalts 70017 11.6 2.18 0.19 20.13 6 0.14 0.20 6 0.14 0.38 6 0.16 70035 10.1 5.09 0.50 0.08 6 0.13 0.05 6 0.18 0.14 6 0.18 74255 1.32 1.30 1.0 20.11 6 0.14 0.09 6 0.17 0.11 6 0.16 74275 8.92 2.24 0.25 20.16 6 0.18 20.25 6 0.25 20.24 6 0.25 75035 4.65 25.1 5.4 0.07 6 0.15 0.22 6 0.18 0.18 6 0.18 Weighted average (62s; n 5 5) 20.04 6 0.14 0.11 6 0.19 0.16 6 0.24 Bulk lunar mantle* (2 s.e.m., n 5 15) 0.00 6 0.02 0.02 6 0.09 0.09 6 0.10 e18iW 5 104 3 [(18iW/184W)sample /(18iW/184W)standard 2 1]. Replicates for KREEP-rich samples are repeated measurements of the same solution. Mean values are weighted averages calculated with Isoplot (n 5 number of samples). Errors are 62s unless indicated otherwise. * Averages are calculated including data for KREEP-rich samples from ref. 3. NATURE|Vol 450|20/27 December 2007 LETTERS
33. Conclusion ✤ Moon was much closer to Earth and revolved faster. ✤ Moon was formed nearby Earth by the giant impact. ✤ Moon is moving away by gaining angular momentum. ✤ Earth and Moon were born at 4.5 billion years ago. ✤ A day on Earth was much shorter than today!
34. Contents ✤ How long was a month? ✤ How to make the Moon? ✤ Why Moon is moving away from Earth? ✤ How old are Earth and Moon? ✤ How long was a Day on Earth?
35. 0 Earth-Moon distance [Earth’s radius] 20 Length of a day [hr] 24 12 0 18 6 40 60 80 ʙ ʙ 4hr@0yr 6hr@3×104yr 10hr@6×107yr 24hr@4.5×109yr (present) 47day@5×1010yr How long was a Day on Earth?
36. 0 Time [Myr] 2000 Length of a day [hr] 24 12 0 18 6 4000 3000 4560 History of Life on Earth 1000 Earliest evidence of life Photosynthesis Eukaryotes Multicellular life (present) Humans
37. Our ancestors lived on Earth a day of which was shorter than today! (c) BBC
38. Conclusion ✤ Moon was much closer to Earth and revolved faster. ✤ Moon was formed nearby Earth by the giant impact. ✤ Moon is moving away by gaining angular momentum. ✤ Earth and Moon were born at 4.5 billion years ago. ✤ A day on Earth was much shorter than today!