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

Coordinate-systems Example: Frederiksværk φ=56 0, λ=12 0, h= 50 m C.C.Tscherning,

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

4 GEOID

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

6 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.

7 POLBEVÆGELSEN.

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

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

Gradient of scalar potential, V, C.C.Tscherning,

Volume distribution, ρ(x,y,z) V fulfills Laplace equation C.C.Tscherning,

Spherical coordinates Geocentric latitude Longitude, λ, r = distance to origin. C.C.Tscherning,

Laplace in spherical coordinates C.C.Tscherning,

Spherical harmonics Define: C.C.Tscherning,

Orthogonal basis functions Generalizes Fourier-series from the plane C.C.Tscherning,

16 Gravity model database. Spherical harmonic coefficients: CCT, Nov (CCT)

Centrifugal potential On the surface of the Earth we also measure the centrifugál acceleration, C.C.Tscherning, r

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,

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

20 Gravity. Source: DTU-Space. Ole Andersen. CCT, Nov (CCT)