How long "was" a day on Earth?

UBIAS Intercontinental Academia Nagoya Workshop, March 9, 2016
How Long “Was” a Day on Earth?
Takanori Sasaki
Department of Astronomy, Kyoto University

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

“Moon is getting further away from Earth?”
Yes, it is!
(c) BBC

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?

Measuring Earth-Moon distance
light: 3×108 m/s
Measuring the time → Deriving the distance

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

Moon was much closer to Earth.
(c) YouTube

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.

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.

How long was a month?
[Kahn & Pompea, Nature, 1978]
30 days @present
9 days @420 Myr ago

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!

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.

Giant Impact Hypothesis
[Hartman & Davis, Icarus, 1975; Cameron & Ward, LPI Conf., 1976]
(c) Wikipedia

Giant Impact Simulation (SPH)
Giant impact between Earth and
Mars-sized body produced Moon
forming disk. [Canup & Asphaug, Nature, 2001]

Formation of the Moon (N-body)

Roche limit
Roche limit
= 3 times Earth’s radius
*Present Moon locates at 60 times Earth’s radius

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]

Earth
Moon
(1) Tidal bulges are raised in the ocean

Earth
Moon
(2) Earth’s rotation displaces
tidal bulge

Earth
Moon
tidal bulge
(3) Moon attracts tidal bulge;
Earth slows down

Earth
Moon
tidal bulge
(3) Moon attracts tidal bulge;
Earth slows down
(4) Tidal bulge attracts Moon;
Moon speeds up
and moves outward

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 →・・・→・・・→ 206Pb
τ (half-life) = 4.5 billion years

The age of Earth and Moon
Hf-W chronometer: 182Hf → 182W (half-life = 9Myr)
Hf: lithophile element → mantle
W: 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.

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 182
W/184
W reported for 79155 is therefore pre-
sumably due mainly to cosmogenic 182
W. Enhanced 182
W/184
W 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 e183
W e182
Wmeas e182
Wcorr
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
e18i
W 5 104
3 [(18i
W/184
W)sample/(18i
W/184
W)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

0
Earth-Moon distance [Earth’s radius]
20
Length
of
a
day
[hr]
24
12
0
18
6
40 60 80
∼
∼
4hr@0yr
6hr@3×104yr
10hr@6×107yr
24hr@4.5×109yr
(present)
47day@5×1010yr
How long was a Day on Earth?

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

Our ancestors lived on Earth
a day of which was shorter than today!
(c) BBC

How long "was" a day on Earth?

Recommended

Recommended

More Related Content

Similar to How long "was" a day on Earth?

Similar to How long "was" a day on Earth? (20)

Recently uploaded

Recently uploaded (20)

How long "was" a day on Earth?