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Satellite geophysics. Basic concepts. I1.1a

This document provides a comprehensive overview of geophysical concepts including satellite geophysics, coordinate systems, and the relationship between geocentric and geodetic latitude. It addresses the geoid, mean sea level, and gravity potential, outlining key principles like flattening, orthometric height, and height anomalies. The paper also discusses the effects of non-inertial systems, polar motion, and the implications of the Earth's rotation on gravity measurements. The work of C.C. Tscherning from the University of Copenhagen, published in 2011, serves as a foundation for these concepts.

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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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