Radio Science

Quantum mechanical uncertainty limitations on deep space navigation by Doppler tracking and very long baseline interferometry

Authors

  • W. H. Cannon


Abstract

The ultimate precision with which very long baseline interferometry (VLBI) can determine the angular position of a spacecraft is determined by the quantum mechanical limitations on the performance of the interferometer receivers and the quantum mechanical uncertainty relation ΔNΔΦ ≥ 1. It is shown that for the navigation of a typical deep space mission using present-day techniques, fundamental physics imposes the following limits on the precision of spacecraft navigation: (1) Minimum noise on determination of phase of spacecraft navigation tone, ΔΦmin ≈ 1.9 × 10−5 radians per AU, (2) minimum noise on determination of phase of VLBI navigation fringes, ΔΘmin ≈ 2.6 × 10−5 radians per AU, (3) minimum noise on determination of VLBI navigation fringe frequency, Δfmin ≈ 2.9 × 10−9 Hz per AU, (4) minimum noise on determination of VLBI group delay, Δτgmin ≈ 0.5 ps per AU, and (5) minimum noise on determination of spacecraft angular position, ΔΨmin ≈ 2.9 × 10−11 radians per AU. The above limitations which are a consequence of quantum mechanical uncertainty on the determinations of the phase of a spacecraft tracking signal may be circumvented in principle by the application of squeezed quantum states.

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