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#### The effect of the geocentric gravitational constant on scale

Zhu, S. Y., Massmann, F.-H., Yu, Y. Q., Reigber, C. (2001): The effect of the geocentric gravitational constant on scale, (Scientific Technical Report STR ; 01/12), Potsdam : Deutsches GeoForschungsZentrum GFZ, 17 S. p.

http://gfzpublic.gfz-potsdam.de/pubman/item/escidoc:8530

##### Resources

0112.pdf

(Publisher version), 487KB

##### Abstract

The Effect of the Geocentric Gravitational Constant on Scale:
It is well known that the geocentric gravitational constant (GM) is a scaling factor for the reference frame realized by satellite techniques. One must be aware that its effects on the orbit and on the terrestrial reference frame (station positions) are different. The scale effect on restituted orbits is 1/3* (dGM/GM) (relative error of GM) for all kinds of satellites. But the effect on the terrestrial frame depends on the height of the satellites, on tracking techniques and on the solved for parameters. For ranging techniques such as SLR, the scale variation of the terrestrial frame is 1/3*(dGM/GM)*(rSat) / (rEarth), if the range biases are not solved for. For GPS the GM error is mostly absorbed by the clock estimates (or eliminated by the double differences), only the remaining few percents go into the scale of terrestrial reference frame. For instance if one is using a GM value of 3.986004418 1014 m3/s2 instead of 3.986004415 1014 m3/s2 (relative variation is 7.5 10-10) the scale variation of the terrestrial frame is only about 6 10-11.
Physically, the error in the z-direction of the antenna phase center offsets on board GPS has nothing to do with GM. But its effect on the terrestrial reference frame is practically equivalent to an error in GM. For instance, if all GPS satellites have a 7.1 cm error in dz, the effect on the station position is equivalent to a relative error of 8 10-9 in GM (e.g. changing GM from 3.986004418 to 3.986004386 1014 m3/s2).
Satellite Antenna Phase Center Offsets and Scale Errors in GPS Solutions:
ITRF2000 solutions (see Lareg, 2001) have shown that there are ppb level scale differences between GPS and other techniques and among various GPS Analysis Centers. The trends of the scale differences reach 0.2 ppb per year. The uncertainties of the current available Earth’s gravitational constant could only cause less than 0.1 ppb scale error for GPS technique. On the other hand, the uncertainties in the satellite antenna phase center offsets could produce ppb level scale error. Various BLOCK types of GPS satellites have different phase center errors. The number of BLOCK IIR satellites increases from year to year. This could cause trend-like variations in the scale error.
Beside station positions, satellite antenna phase center errors affect also the clock, Zenith Path Delay, and other solved for parameters perceptibly.