A VLBI delay model for gravitational deformations of the Onsala 20 m radio telescope and the impact on its global coordinates


Deformations of the reflectors of radio telescopes used in geodetic and astrometric VLBI observations belong to the class of systematic error sources which affect the estimated position of the telescope and which necessitates correction at the observation level. The determination of the gravitationally induced deformations requires some effort and needs specific modeling of the impact on the VLBI delay observables. This has been exercised on the Onsala 20 m radio telescope. In this publication, we present an elevation-dependent model for the contributions of the gravitational deformations to the delay observables for application in VLBI data analysis. New is that thermal expansion in some of the contributing components need to be applied also to the gravitational deformation effects. A further novelty is that we can substantiate the validity of and the need for these corrections. Concerning the validity we show that the empirical model used by astronomical colleagues for deliberately shifting the sub-reflector for gain optimization, exactly (within 0.5 mm RMS) matches the measured gravitationally induced displacement of the sub-reflector plus the change in focal length. The other evidence is the impact on the vertical component of the telescope’s coordinates of − 6.1 mm, which reduces the discrepancy determined in the computations of the ITRF2014 to 1.7 mm.

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Data availability

All data used for developing the model, except of those mentioned in the Acknowledgements, were measured by the authors. These data, especially those of the TLS measurements, are available from the authors on request. The VLBI data of the CONT observing sessions are publicly available on the Internet from the International Service of Geodesy and Astrometry (IVS).


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We are grateful to Jonas Flygare for providing the coefficients of the illumination function, to Anara Kudabayeva for preparing the Monte Carlo simulations, and to Sten Bergstrand for making available his measurement results of the sub-reflector monitoring. Concerning the VLBI data used for the validation, we thank the IVS for providing the VLBI observation data. We also thank Dan MacMillan for checking the manuscript and the three anonymous reviewers for their numerous helpful comments.

Author information




AN developed the VLBI correction model, CH performed and analyzed the TLS measurements, RH carried out the local investigations as well as the VLBI data analysis. All authors contributed to the manuscript and cross-checked the contents.

Corresponding author

Correspondence to A. Nothnagel.

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Nothnagel, A., Holst, C. & Haas, R. A VLBI delay model for gravitational deformations of the Onsala 20 m radio telescope and the impact on its global coordinates. J Geod 93, 2019–2036 (2019). https://doi.org/10.1007/s00190-019-01299-x

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  • VLBI
  • Onsala 20 m radio telescope
  • Group delay
  • Gravitational deformation model
  • Thermal expansion model
  • Impact on ITRF