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Satellite geophysics. Basic concepts. I1.1a

Satellite geophysics. Basic concepts. I1.1a. Z. Meridian plane. h. r. = geocentric latitude φ = geodetic latitude r = radial distance, h = ellipsoidal height a = semi-major axis, b = semi-minor axis z = axis of rotation, 1900. flattening = (a-b)/a. b. φ. X-Y. a.

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Satellite geophysics. Basic concepts. I1.1a

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  1. Satellite geophysics. Basic concepts.I1.1a Z Meridian plane h r = geocentric latitude φ = geodetic latitude r = radial distance, h = ellipsoidal height a = semi-major axis, b = semi-minor axis z = axis of rotation, 1900. flattening = (a-b)/a. b φ X-Y a C.C.Tscherning, University of Copenhagen, 2011-10-25 1

  2. Coordinate-systems Example: Frederiksværk φ=560, λ=120, h= 50 m C.C.Tscherning, 2011-10-25.

  3. Geoid and mean sea level Earth surface H Geoid: gravity potential constant h=H+N=Orthometric height + geoid height along plumb-line =HN+ζ=Normal height + height anomaly, along plumb-line of gravity normal field N Ellipsoid C.C.Tscherning, 2011-10-25.

  4. Coordinate-systems and time. Z NON INERTIAL SYSTEM Mean-rotationaxis 1900. Gravity-centre Y- Rotates with the Earth CTS: Conventional Terrestrial System Greenwich X

  5. POLAR MOTION • Approximatively circular • Period 430 days (Chandler period) • Main reason: Axis of Inertia does not co-inside with axis of rotation. • Rigid Earth: 305 days: Euler-period.

  6. POLBEVÆGELSEN • . • http://aiuws.unibe.ch/code/erp_pp.gif

  7. Ch. 3, Transformation CIS - CTS • Precession • Nutation • Rotation+ • Polar movement Sun+Moon

  8. Gravity potential, Kaula Chap. 1. • Attraction (force): • Direction from gravity center of m to M. • With m = 1 (unitless), then acceleration C.C.Tscherning, 2011-10-25.

  9. Gradient of scalar potential, V, C.C.Tscherning, 2011-10-25.

  10. Volume distribution, ρ(x,y,z) • V fulfills Laplace equation C.C.Tscherning, 2011-10-25.

  11. Spherical coordinates • Geocentric latitude • Longitude, λ, r = distance to origin. C.C.Tscherning, 2011-10-25.

  12. Laplace in spherical coordinates C.C.Tscherning, 2011-10-25.

  13. Spherical harmonics • Define: C.C.Tscherning, 2011-10-25.

  14. Orthogonal basis functions • Generalizes Fourier-series from the plane C.C.Tscherning, 2011-10-25.

  15. Centrifugal potential • On the surface of the Earth we also measure the centrifugál acceleration, r C.C.Tscherning, 2011-10-25.

  16. Normal potential, U • Good approximation to potential of ideal Earth • Reference ellipsoid is equipotential surface, U=U0, ideal geoid. • It has correct total mass, M. • It has correct centrifugal potential • Knowledge of the series development of the gravity potential can be used to derive the flattening of the Earth ! C.C.Tscherning, 2011-10-25.

  17. Anomalous potential,T • T=W-U, • same mass and gravity center. • Makes all quantities small,gives base for linearisation. C.C.Tscherning, 2011-10-25.

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