Journal of Geodesy

, Volume 88, Issue 2, pp 113–126 | Cite as

Optimal orbits for temporal gravity recovery regarding temporal aliasing

  • Michael MurböckEmail author
  • Roland Pail
  • Ilias Daras
  • Thomas Gruber
Original Article


The temporal changes of the Earth’s gravity field can be observed on a global scale with low–low satellite-to-satellite tracking (SST) missions. One of the largest restrictions of the quality of low–low SST gravity fields is temporal aliasing. This study investigates the design of optimal satellite orbits for temporal gravity retrieval regarding temporal aliasing. We present a method with which optimal altitudes for the orbit of a gravity satellite mission with the goal of temporal gravity retrieval can be identified. The two basic orbit frequencies, the rates of the argument of the latitude and the ascending node, determine the mapping of the signal measured along the orbit onto the spherical harmonic (SH) spectrum. The main spectral characteristics of temporal aliasing are maxima at specific SH orders. The magnitude of the effects depends on the basic frequencies. This is analyzed with numerical low–low SST closed-loop simulations including both tidal and non-tidal background models and GRACE-like observation noise. Analyses of actual monthly GRACE solutions show that these characteristics do not depend on the low–low SST processing method. Optimal orbits are found in specific altitude bands. The best altitude bands regarding temporal aliasing for polar low Earth orbiters (LEOs) are around 301, 365, 421 and 487 km. In these bands, major aliasing effects do not occur for SH degrees and orders below 70. This study gives unique and in-depth insights into the mechanism of temporal aliasing. As it provides an important orbit design approach, it is independent of any (post-) processing method to reduce temporal aliasing.


Temporal gravity retrieval  Low–low satellite-to-satellite tracking Temporal aliasing  Basic frequencies Spherical harmonic resonance orders Optimal orbits 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael Murböck
    • 1
    Email author
  • Roland Pail
    • 1
  • Ilias Daras
    • 1
  • Thomas Gruber
    • 1
  1. 1.Institut für Astronomische und Physikalische Geodäsie (IAPG)Technische Universität MünchenMunichGermany

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