Institute of Geodesy Research Research Projects
Relativistic effects in satellite constellations (CRC 1128, C02)

Relativistic effects in satellite constellations (CRC 1128, C02)

Led by:  Dr.-Ing. habil. Enrico Mai, Dr. Eva Hackmann (ZARM), Prof. Dr. Claus Lämmerzahl (ZARM)
Team:  Dr.-Ing. Liliane Biskupek, PD Dr. Volker Perlick (ZARM), Dennis Philipp (ZARM)
Year:  2014
Funding:  DFG
Is Finished:  yes
Further information

For space based geodesy the relative orbits of satellites have to be tracked with very high precision. In the next years, the necessary experimental capabilities will increase dramatically by the use of laser technology and high precision space clock projects.

  • Inter-satellite laser ranging enables to measure the distance between two or more spacecraft to an accuracy of up to 10 nm. At this level general relativistic effects in the determination of the orbit have to be taken into account. This also includes the relativistic effects of the multipoles of the gravitating body on the orbit.
  • On this level of accuracy also general relativistic effects on the signal propagation have to be considered.
  • With the development of ACES, stable clocks in space will be established with inaccuracies of only a few parts in 1016. Such accurate time measurements can only be interpreted correctly if the full framework of general relativistic effects is taken into account.

technological level for space based geodesy

As a consequence, at the present technological level for space based geodesy it has to be critically analyzed whether the usual post-Newtonian approximations are sufficient to fully exploit the experimental capabilities. The huge technological improvements in the next years and decades can only lead to equally huge improvements in geodesy and related science if a consistent fully general relativistic formulation of geodetic quantities and observables is provided. On the one hand this is needed to judge the accuracy and to derive better relativistic approximations, and on the other hand to provide a complete picture of relativistic effects to be considered in future geodesy missions. Therefore, the crucial aim is to provide fully relativistic descriptions

  • of clocks in space, satellite orbits, and signal propagation (to S/C and ground stations) to an accuracy which allows to fully exploit the experimental capabilities, in particular
  • of the motion of satellites in the gravitational field of the Earth taking into account its relativistic mass multipole moments. Related to this is the definition of general relativistic analogies of concepts commonly used in geodesy, e.g. the geoid and gravity anomalies.


In addition, we will suggest new experimental and theoretical concepts for geodesy in space, which will significantly improve the evaluation and interpretation of gravity measurements and which will provide new approaches for future geodesy missions. This comprises

  • the development of an improved semi-analytical orbital theory, based on the Lie series approach, focusing on relativistic effects, and
  • the investigation of new concepts which are more powerful and effective for gravity measurements based on swarms of satellites.

As an add-on we would like to analyze whether these high precision measurements in the gravitational field of the Earth can be used for improved tests of Special and General Relativity, e.g. for an improved test of the Lense-Thirring precession or a first measurement of the gravitomagnetic clock effect. 

Corresponding Scientists

Dr.-Ing. Liliane Biskupek (IfE)
Dennis Phiipp (ZARM)