Scale and Satellite Center of Mass Issues VLBI GPS J.C. Ries Center for Space Research The University of Texas at Austin GGOS GNCWG Meeting San Francisco December 12, 2007 1
Scale Issues Relativistic framework for SLR and VLBI Is it consistent? Impact of Center of Mass (CoM) offset model on estimation of GM All satellite-based techniques for TRF assume apriori value for GM Range bias influence on TRF scale/geocenter GGOS GNCWG Meeting San Francisco December 12, 2007 2
General Relativity and the TRF scale (1) For SLR, we have adopted a terrestrial time coordinate (TT) that differs from geocentric coordinate time (TCG) by the influence of the Earth s gravitational potential on time as measured on the Earth s surface d(tt)/d(tcg) = (1-L G ) where L G = U/c 2 0.7x10-9 (U=GM/R e ) Since the speed of light is a defined quantity, the result is a unit of length that is also scaled by 0.7 ppb relative to TCG-like units For VLBI, the consensus model was adopted to be consistent with the SLR realization of the geocentric frame GGOS GNCWG Meeting San Francisco December 12, 2007 3
General Relativity and the TRF scale (2) To realize the same reference frame as SLR, the potential term excludes the potential due to the Earth, which is multiplied by a factor of 2 VLBI distances are smaller than physical distances by 1.4 ppb; SLR distances are smaller by only 0.7 ppb (IERS 2003 standards) It would appear that they are not defining the same reference frame GGOS GNCWG Meeting San Francisco December 12, 2007 4
General Relativity and the TRF scale (3) To realize the same reference frame as SLR, the potential term excludes the potential due to the Earth, which is multiplied by a factor of 2 VLBI distances are smaller than physical distances by 1.4 ppb; SLR distances are smaller by only 0.7 ppb It would appear that they are not defining the same reference frame Both differ from TCG-like coordinates (which are not physical distances ) by 0.7 ppb..reference frames are consistent (IERS 2003 standards) GGOS GNCWG Meeting San Francisco December 12, 2007 5
Are we missing anything else? Ashby (2003) proposed that, due to the time definition, an additional term (of 0.7 ppb) is required for the light-time correction This correction is intriguing because it appears to reduce the bias between SLR and VLBI GGOS GNCWG Meeting San Francisco December 12, 2007 6
Not a problem Ashby (2003) proposed that, due to the time definition, an additional term (of 0.7 ppb) is required for the light-time correction X Additional term appears to reflect failure to rescale all units consistently to maintain same value for speed of light GGOS GNCWG Meeting San Francisco December 12, 2007 7
Center of mass offset impact ITRF2005 scale issue motivated more careful analysis of impact of CoM model errors on GM, for LAGEOS and other satellites Satellite (A in Earth radii) Starlette (~1) LAGEOS (~2) GPS (~4) CoM Error required for 1 ppb error in GM 1 mm 3 mm ~8 mm (extrapolated) GM from low satellites is very sensitive to CoM errors Laser reflectors on high-altitude satellites, such as future GPS satellites, could provide helpful scale information but the CoM has to be known very well to provide better accuracy GGOS GNCWG Meeting San Francisco December 12, 2007 8
ITRF Performance for Starlette SLR residual RMS for 2000-2005 using 6-day arcs, GGM02C, full network, Mendes/Pavlis refraction model ITRF2000 (75 mm CoM) ITRF2005 (scaled, 75 mm CoM) ITRF2005 (scaled, 80 mm CoM) SLR RMS (mm) 19.7 19.1 18.7 SLR Mean (mm) -3.9-3.7 0.1 Other analyses also indicate CoM should be closer to 80 mm GGOS GNCWG Meeting San Francisco December 12, 2007 9
GM, Scale and Satellite CoM GM and TRF scale implicitly defined by CoM offset used for LAGEOS-1 and 2 (changing CoM linearly scales both) Each 3 mm change in CoM changes TRF by 3 mm and GM by 1 ppb 6 mm change already adopted for one site (RGO) Current CoM for Starlette (and Stella) is 75 mm all sites Recent analysis suggests something larger; ~80 mm Adopting 247 mm for LAGEOS and 80 mm for Starlette resulted in a common TRF scale and GM (398600.4410 km 3 /s 2, ~1 ppb change) However, Starlette is not as good a geodetic target as LAGEOS, and GM recovery is influenced by drag parameterization at ~1 ppb level No apparent problems with consistency of treatment of relativity GGOS GNCWG Meeting San Francisco December 12, 2007 10
Impact of biases on TRF determination Scale factor wrt ITRF 2000 without SLR biases Scale factor wrt ITRF 2000 without SLR biases estimation estimation (close to ITRF 2005 strategy) Coulot, D., P. Berio, D. Féraudy, O. Laurain, and P. Exertier, Different ways of considering biases for Satellite Laser Ranging data processing: consequences on Terrestrial Reference Frame scale factors, submitted to Geophys. Res. Lett., 2007. SLR ranging biases should be routinely estimated (with appropriate care) Scale factor wrt ITRF 2000 with SLR biases Scale factor wrt ITRF 2000 with SLR biases estimation estimation Without a place to go, biases will distort TRF determination GGOS GNCWG Meeting San Francisco December 12, 2007 11
Range bias and TRF Scale Range biases should probably be routinely estimated as part of TRF determination Separable from station heights, although highly correlated Appropriate constraints are required (how big and how often) Some attentuation of interesting signals may occur GGOS GNCWG Meeting San Francisco December 12, 2007 12