Free Association well, Cheap Association. 1 Potpourri

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 Potpourri 2

Expanding Earth Considered plausible by Darwin Advocated by Montovani ( ) Used to explain continental separation Potpourri 3

Expanding Earth Mechanisms thermal expansion mass increase dG/dt (Dirac) Plate tectonics assumes (but does not require) dr/dt = 0 Potpourri 4

Current Geodetic Measurements Potpourri 5

II Modern Geodesy lunar laser ranging satellite laser ranging very-long baseline interferometry global positioning system gravity field measurements Potpourri 6

III Lunar Laser Ranging Five reflectors on the Moon’s surface from US and Soviet missions Potpourri 7

Examples of Retroreflectors Potpourri 8

Corner Retroreflector Potpourri 9

LLR Measurement Potpourri 10

LLR Measurement Details Potpourri 11

Sample Data Potpourri 12

Some Results of LLR Potpourri 13

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. Potpourri 14

IV Photon Pressure Potpourri 15

So one photon of green light Potpourri 16

Effect on the Moon Potpourri 17

Moving the Moon Potpourri 18

V Measuring Gravity Nevil Maskelyne (1775) Superconducting gravimeter Falling corner-cube (1970s) (amazing) GRACE (2002) Potpourri 19

1775: The Royal Society Test Newton’s theory of gravitation Estimate of mass ( or density) of Earth would lead to estimates of planetary masses Potpourri 20

Gravity in 1775 Potpourri 21 true difference: 42.94” apparent difference: 54.6”  deflection: 11.6”

Schiehallion (Scotland) Potpourri 22

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 Potpourri 23

1775 Details (cont.) sustained weather problems mountain survey took a year invented contour lines processing survey results took Hutton two years Potpourri 24

1778 Results (Hutton) density of Earth is 9/5 ths density of mountain estimated (1778) Schiehallion ~ 2.5 Earth ~ 4.5. correct Earth (20% error) modern reprocessing (2007): Potpourri 25

Superconducting Gravimeter developed by John Goodkind (et al.) in the 1970s best relative gravimeter in existence Potpourri 26

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Superconducting Gravimeter (cont.) operates at nanogal level equivalent to mm height change outstanding long-term stability Needs liquid helium (LHe) to operate Potpourri 29

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 Potpourri 30

Basic Operation Potpourri 31

Signal Recorded During Fall Potpourri 32

Details Potpourri 33

Estimating G 500 kg tungsten mass moved 35 cm vertically Potpourri 34

Data for Estimating G Potpourri 35

Results for G Potpourri 36

GRACE (2002) Gravity Recovery And Climate Experiment Potpourri 37

Grace (2002) two satellites 220 km apart 500 km altitude precision orbit determination (gps) ultra-precise separation: 10  m Potpourri 38

Two Identical Satellites Potpourri 39

Grace Entrails Potpourri 40

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 Potpourri 41

Monthly On-shore Gravity Anomalies Potpourri 42

Mississippi Storage Simulation Potpourri 43

Antarctic Impact Potpourri 44

Wilkes-Land Gravity Anomaly Potpourri 45

Wilkes-Land Crater Presuming it’s a crater 5X Chicxulub May be associated with the Permian- Triassic extinction 250 mya largest since multicellular life Potpourri 46

Potpourri 47 The End