Mantle plumes topography measured relative to geoid

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Mantle plumes Topography measured relative to geoid Use geoid to convert planetary radius to topography Topography and geoid height are usually correlated Ratio of topography and geoid heights called the admittance
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PYTS 411/511 – Planetary Gravity and Topography 13 Flybys Strength of central field can tell you the planet’s mass Details can get you the J 2 term in the gravity field Figure out the moments of inertia – get a core size! Orbiters Precession of orbit most dependant on H (=(C-A)/C) or J 2 Pro-grade orbiters have retrograde precession and vice versa Useful property for mapping planets, you’re orbit will move for you Gravitational anomalies on the surface Only really addressable with orbiters Surface resolution roughly similar to altitude Anomalies cause along-track acceleration and deceleration Changes in velocity cause doppler shift in tracking signal Convert Earth line-of-sight velocity changes to change in g Downward continue to surface to get surface anomaly Measuring Gravity with Spacecraft ( 29 2 2 MR A C J - =
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PYTS 411/511 – Planetary Gravity and Topography 14 Before we can start interpreting gravity anomalies we need to make sure we’re comparing apples to apples… Corrections to Observations Free-Air correction Assume there’s nothing but vacuum between observer and reference ellipsoid Just a distance correction r gh g h r GM r r r g g FA FA 2 2 - = = = δ δ δ δ Bouguer correction Assume there’s a constant density plate between observer and reference ellipsoid Remove the gravitation attraction due to the mass of the plate If you do a Bouguer correction you must follow up with a free-air correction h G g B ρ π 2 =
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PYTS 411/511 – Planetary Gravity and Topography 15 Terrain correction Not commonly done except in very mountainous regions Divide terrain into radial sectors Use DEM to find h at distance r 1 to r 2 Isostatic correction Effects of isostasy Eötvös correction Vertical component of the coriolis force (for moving observers) Tidal correction Effects of Moons/Sun on local planetary shapes Other corrections Local-geology specific effects of density anomalies e.g. δ g T = G dm r 2 + z 2 cos q ( ) = G r rdrdzdf r 2 + z 2 z r 2 + z 2 D g T = Gr f r 1 2 + h 2 - r 1 ( ) - r 2 2 + h 2 - r 2 ( ) [ ]
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PYTS 411/511 – Planetary Gravity and Topography 16 Start with g obs Do terrain correction first If needed g obs – Δg T Then remove bouguer plate g obs – Δg T – Cg B Then do free-air correction g obs – Δg T – Δg B – Δg FA The remove expected g o g obs – Δg T – Δg B – Δg FA – g o This is the gravity anomaly Often, for spacecraft data, only the free-air correction is made Now we can compare gravity values from place to place
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PYTS 411/511 – Planetary Gravity and Topography 17 Airy Isostasy Compensation achieved by mountains having
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