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Free Associationwell, Cheap Association.

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I The Size of the Earth

• Earth’s radius has necessarily changed over time.

• Is it now doing so?

•Divergent views through 1970s• Expanding Earth• Shrinking Earth• Static Earth

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Expanding Earth

• Considered plausible by Darwin

• Advocated by Montovani (1854-1933)

•Used to explain continental separation

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Expanding Earth

•Mechanisms• thermal expansion• mass increase• dG/dt (Dirac)

• Plate tectonics assumes (but does not require) dr/dt = 0

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Current Geodetic MeasurementsInternational Terrestrial Reference Frame• constrained by space geodesy measurements (discussed later)

• based on about 25 years of data

• radius change is: 5

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II Modern Geodesy

• lunar laser ranging

• satellite laser ranging

• very-long baseline interferometry

• global positioning system

• gravity field measurements6

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III Lunar Laser Ranging

• Five reflectors on the Moon’s surface from US and Soviet missions

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Examples of Retroreflectors

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Corner Retroreflector

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LLR Measurement

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LLR Measurement Details

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Sample Data

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Some Results of LLR

•Moon is receding at 3.8 cm/yr

• Probably has a liquid core of R/5

• since 1969

•General relativity good to accuracy of measurement 13

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Another Result of LLR

If you believe that the reflectors are on the Moon’s surface, you might agree that the Apollo landings really occurred.

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IV Photon Pressure

• A photon carries momentum determined by it’s frequency:

• is Planck’s constant

• green light has a frequency of about

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So one photon of green light

• has

• the Moon is struck by

• each second that imparts

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Effect on the Moon

• each second that imparts

•Moon’s mass is

• So the velocity change each second is

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Moving the Moon

• So the velocity change each second is

• That’s actually acceleration.• If we kept it up for a billion years we would get

•which would be readily detectable18

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V Measuring Gravity

•Nevil Maskelyne (1775)

•Superconducting gravimeter

•Falling corner-cube (1970s)

• (amazing) GRACE (2002)19

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1775: The Royal Society

• Test Newton’s theory of gravitation

• Estimate of mass ( or density) of Earth would lead to estimates of planetary masses

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Gravity in 1775

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true difference: 42.94”apparent difference: 54.6” deflection: 11.6”

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Schiehallion (Scotland)

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1775 Details

• built observatories on S & N sides of Schiehallion

•bothy for the equipment and observers

• 337 observations on 142 stars• corrected for precession, nutation, aberration

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1775 Details (cont.)

• sustained weather problems

•mountain survey took a year• invented contour lines

• processing survey results took Hutton two years

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1778 Results (Hutton)

• density of Earth is 9/5ths density of mountain

• estimated (1778)• Schiehallion ~ 2.5• Earth ~ 4.5.• correct Earth 5.515 (20% error)

•modern reprocessing (2007): 5.480

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Superconducting Gravimeter

• developed by John Goodkind (et al.) in the 1970s

• best relative gravimeter in existence

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Superconducting Gravimeter (cont.)

• operates at nanogal level• equivalent to 0.003 mm height

change• outstanding long-term stability

•Needs liquid helium (LHe) to operate

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Falling Corner-cube Gravimeter• Absolute measurement of g

• Accurate to 1 gal, about 3 mm of vertical motion

• Based on an optical corner cube falling on a vertical laser beam

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Basic Operation

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Signal Recorded During Fall

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Details

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Estimating G

500 kg tungsten mass moved 35 cm vertically

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Data for Estimating G

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Results for G

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GRACE (2002)

Gravity Recovery And Climate Experiment

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Grace (2002)

• two satellites• 220 km apart• 500 km altitude

• precision orbit determination (gps)• ultra-precise separation: 10m

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Two Identical Satellites

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Grace Entrails

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Grace Uses and Results

•Gravity maps 1000X improved•Many uses in hydrology•Ocean currents• Ice cap changes• Sea-level change• Plate tectonic motions• Core motions and the geodynamo

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Monthly On-shore Gravity Anomalies

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Mississippi Storage Simulation

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Antarctic Impact

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Wilkes-Land Gravity Anomaly

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Wilkes-Land Crater

Presuming it’s a crater

• 5X Chicxulub

•May be associated with the Permian-Triassic extinction• 250 mya• largest since multicellular life 46

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The End