gravitational forces of the sun and moon deform the earth...
TRANSCRIPT
• Gravitational forces of the Sun andMoon deform the Earth’s shape ⇒tides in the oceans, atmosphere, andsolid earth
• Tidal effect of the Moon:– Earth and Moon are coupled by
gravitational attraction: each onerotates around the center of mass ofthe pair.
– The rotation of the Earth around thatcenter of mass induces a centrifugalacceleration directed away from theMoon
– The Moon produces a gravitationalattraction on the Earth
– The resulting force (centrifugalacceleration + gravitational attraction)is responsible for the tides
• Tidal effect of the Sun: same principlebut 45% smaller effect because oflarger Earth-Sun distance
Tides
Tides• Earth rotation (24 hr) combined
with Moon revolution (~27 days)=> major tidal component is semi-diurnal (M2 = 12 hr 25 min)
• Ocean tides: effect of oceansurface, amplitude of largestcomponent = several meters
• Solid Earth tides: effect on thesolid Earth surface, amplitude,amplitude of largest component~10-50 cm
• By-product of ocean tides: oceantide loading = elastic deformationof the Earth crust due to variationsof ocean water column: up to 15-20 cm near the coast
The ocean tides for harmonic M2 (period of 12 hours and 25 minutes) . The colorrepresent the amplitude and the contour lines indicate the phase lag of the tides with
a spacing of 60 degrees. (Doc. H.G. Scherneck)
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Day of year, 1999
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Water height variations in Brest (France) measured by a tide gauge (October 1999)
Example: ocean tideloading in Brittany, France
Measuring gravity• XVIIth century: pendulum clocks had to be
tuned when moved from Paris (49N) toCayenne (5N) ⇒ first gravity measurementsmade with a pendulum using:
• Absolute measurements: Acceleration of amass in free fall
• Relative measurements:– Extension of a spring (w.r.t. a reference
position)– Levitation of a metal mass in an
electromagnetic field = supraconductinggravimeters
⇒ Need for reference sites where absolute gravityis known
g
lT !2= T = period
l = wire length
relative measurement
absolute measurement
Relative gravity measurements• Mobile masses attached to springs:
– Stable: Measurement of the extensionof the spring (Scintrex)
– Unstable: Measurement of thedisplacement to apply to the spring tobring it back to an equilibriumposition (LaCoste & Romberg)
• Mechanical properties of springsdepend on temperature ⇒ thermostat
• Perfect leveling necessary• Elasticity of springs vary with age ⇒
instrumental drift– Complex, function of age,
transportation, etc.– ~ linear for spring-based gravimeters– Specific to each gravimeter
• Precision ~ 0.01 mGal
LaCoste & Romberg gravimeter
Absolute gravity measurements• Most common technique:
– Glass prism in free fall– Atomic clock => timing of the fall– G = 8H / (DT2 –Dt2)
• Precision ~1 µGal [~ 3 mm]• Transportable, but not easily portable, unlike
relative gravimeters.
Precision of ground-basedgravity measurements
Satelliteorbitography
• Orbit of artificial satellites are perturbed by variations of thegravity field.
• Therefore, precise measurements of their trajectory ⇒ gravityfield
• “Geodetic” satellites and ground tracking network ⇒estimation of precise orbit ⇒ restitution of gravity field
• Satellite trajectory derived from Satellite Laser Ranging (SLR) SLR at the Goddard Geophysical and Astronomical Observatory. The twolaser beams are coming from the network standard SLR station, MOBLAS-7
(MOBile LASer) and the smaller TLRS-3 (Transportable Laser RangingSystem) during a collocation exercise.Tracking a satellite with a network of SLR stations
Starlette, a geodetic satelliteLaunched in 1975, 48 cm diameter, 47 kg
A global gravity field from space…• Current version of global gravity field = GRIM5 [21 satellites, data since 1971, precision
3 mGals]• Advantage = global coverage
Recent space missions
• Obectives are to improve:– Temporal resolution:
atmospheric mass redistribution, oceancirculation, sea level changes and thevisco-elastic response of the Earth'slithosphere to past and present loads
– Spatial resolution from space• Plus atmospheric research• CHAMP• GRACE
CHAMP• CHAllenging Minisatellite Payload• German (GFZ-Potsdam) small
satellite mission launched in July2000.
• Included instruments:magnetometer, accelerometer, GPSreceiver, laser retro reflector andion drift meter.
• Low altitude, near polar orbit• Continuous GPS satellite-to-
satellite tracking ability• On-board measurements of non-
gravitational orbit perturbations
GRACE
• Gravity Recovery And ClimateExperiment
• Launched in March 2002 byNASA/DLR.
• Two identical spacecrafts flying about220 km apart in a polar orbit 500 kmabove the Earth.
• Included instruments: K-Band rangingsystem, accelerometer, GPS receiver,laser retro-reflector, star camera, coarseEarth and Sun sensor, ultra stableoscillator, and center of mass trimassembly.
• Gravity field found by highly accuratemeasurements of the distance betweenthe 2 satellites using GPS and amicrowave ranging system
Satellite altimetry and the geoid• Direct measurement of the ocean
surface using satellites• Satellite carries radar ⇒ ocean –
satellite range• Ground tracking system ⇒ ellipsoid –
satellite distance• Difference = ocean – ellipsoid
distance = dynamic topography• Contains:
– Oceanographic effects: waves,currents, tides
– Gravimetric effects = the geoid• Precision:
– SEASAT (1979) = 10 cm– TOPEX-POSEIDON (1992) = 5 cm– JASON (launched in 2002) < 5 cm
• Advantages: precision, coverage
Satellite altimetry
Seafloor topography derived from Seasat altimetric measurements
Satellite altimetryand the geoid
• Long wavelength → mantle convection• Short wavelength → ocean floor topography• http://topex.ucsd.edu/marine_grav/mar_grav.html
What have we learned?• The Earth’s gravity is the result of its mass, its rotation,
and its (ellipsoidal) shape.• The Earth’s gravity field is associated with a potential.• The geoid is the particular equipotential surface that best
fits the mean sea level (= the horizontal)• Relationship between geoid and gravity• Gravity and geoid “height” vary:
– As a function of mass distribution (in space and time)– As a function of position (e.g. altitude)
• Direct measurements:– Gravity: up to 1 µGal– Geoid height : up to 5 cm