Satellite Geodesy

Variationen des Antennenphasezentrums, Ungenauigkeit der GPS-Bahnen

GPS antennas are omnidirectional, VLBI antennas are directed.

rho = c * delta_t / 2

favorable propagation characteristics of visible light in the atmopshere (water vapor has no influence) // direct distance measurement are performed // satellites with a very long life-time // simple instrumentation on the satellite (nothing but a retro-reflector)

depending on weather conditions (clouds, fog) // expensive infrastructure and instrumentation at the ground station // very heavy equipment (transport)

retro-reflectors // generator of the laser pulses // optical telescope // receiving system: detector and analyzer of the returning pulse (echo) // timing equipment

Nutation (LLR), Polar Motion (both), Length of Day (both), Ocean tide amplitude (SLR), Coord. + Velocities (both), Geocenter (SLR), etc. see Table 2.1

rho = h* - h, with rho = c * delta_t / 2

sea level also possible for bigger lakes and Iceshields. // Geoid over the oceans very accurately and with hight spatial resolution // gravitiy anomalies (computed out of the altimeter geoid) => new earth models // information about the dynamics of the oceans (currents, ocean tides)

A Point where a descending and a ascending groundtrack cross-over eachother

Two corrected measurements have to be equal at a cross-over point. // The differences between those measurements cam be used for the orbit determination/correction // the height of the mean sea level can be corrected and improved

h*: height of the satellite above reference ellipsoid, N: geoidundulation, Zeta_p: permanent part of ocean currents, Zeta_v: variable part of ocean currents, htrp: Delay caused by the tropospheric refration, hion: Delay caused by the ionospheric refraction, hwav: Correction of the wind waves on the sea surface. It is computed based on the “signifant wave height (SWH), that can be reconstructed from the temporal distribution of the reflected pulse (shape of pulse), hsys: instrumental corrections, e: error of the altimeter observation

Satelliten-Altimetrie, Crossover-Points, Modellierungen von Geoid, Strömungen, etc.

Kalibrierung mit GPS-Bojen / SLR-Stationen. Ev mit InSAR?

to reduce systematic errors (due to orbits), following satellite missions are placed on orbits with the same parameters. The measurements can be performed under the same conditions for long time.

Kleine Inklination: grosse Temporale Auflösung, Grosse Inklination: grössere Abdeckung, und vice versa

Cycles = Repeat Period, Weniger Cross-Overs aber hohe Temporale Auflösung wenn kurze Repeat Periode

Viel kleinerer Ionospheren-Effekt, see Page 93.

Wasserdampf in Atmosphäre bestimmen => wet part

plate motion // loading effects of the oceans and the atmosphere // solid earth tides and pole tides // variations of the antenna phase center, deformation of the antenna and similar effects (depending on the observation technique)

pole tides: polar motion -> changing centrifugal forces // solid earth tides: gravitational forces of other massive bodies (e.g. moon, sun) // ocean loading: the water mass at high tide presses down the continental plates // atmospheric loading: pressure

pole tides: 1-2cm // solid earth tides: 50cm // ocean loading: vertical: several centimeters (CH:1cm), horizontal: a few millimeters // atmospheric loading: 2cm (vertical)

Rotation of a rigid plate around its pole of rotation on the surface of a spherical earth

Love and Shida numbers describe the Earth’s response to external forces exerted by celestial bodies due to the elasticity of the Earth // link between the change in the gravitational potential and the resulting change of the station position // Love numbers: for the vertical deformation // Shida numbers: for the horizontal deformation

by parameter estimation algorithms? (least-square procedures, Kalman filters)

Plate motion in East and North direction, altitude changes (postglacial rebound?) with noise (due to loading effects, tides, groundwatereffects, GPS measurements are weaker in altitude (geometry, atmospherical effects)

see page 86, Reyleigh-Equation. In the vaccum or non-dispersive area.

GPS: ~1 GHz (1227 and 1575 MHz) //

VLBI: S-band (f~2 GHz),

X-band (f~8 GHz) //

SLR/LLR: ~5*1014 Hz //

Sat. Altimetry: 13.5 - 13.9 GHz

Different height, air pressure, temperature, dispersion, TEC, water vapour, ...

delay (up to 100m) more important (beding is important for astronomers, 1-2cm)

page 90 ff

50-1000km

Free electron were thrown out of the gas molecules by the x-ray and ultra-violete radiation from the sun.

a) Solar activity: The intensity of the solar radiation varies with time. There is an 11-year solar cycle _ periodic variations of the number of the Sun spots. b) Altitude: Different gases need different energies to be ionized. As the absorption of the solar radiation is taking place at different altitudes depending on the frequency of the radiation, the individual gases are ionized in different altitude bands

… the electron density Ne (= number of free electrons per m3)