Chronometric Geodesy: Methods and Applications

Delva, Pacôme; Denker, Heiner; Lion, Guillaume

doi:10.1007/978-3-030-11500-5_2

Cited by 22 publications

(22 citation statements)

References 164 publications

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“…High-performance optical clocks can probably be used to test the fundamental laws of physics (Delva et al 2017), redefine time scales (Lodewyck 2019) and improve global positioning and navigation (Schuldt et al 2018). They can also enable a new measurement concept in geodesy, termed as relativistic geodesy with clocks or chronometric geodesy (Delva et al 2019). The scheme of this measurement concept is illustrated in Fig.…”

Section: Optical Clocksmentioning

confidence: 99%

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Using quantum optical sensors for determining the Earth’s gravity field from space

Müller

2020

J Geod

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Quantum optical technology provides an opportunity to develop new kinds of gravity sensors and to enable novel measurement concepts for gravimetry. Two candidates are considered in this study: the cold atom interferometry (CAI) gradiometer and optical clocks. Both sensors show a high sensitivity and long-term stability. They are assumed on board of a low-orbit satellite like gravity field and steady-state ocean circulation explorer (GOCE) and gravity recovery and climate experiment (GRACE) to determine the Earth's gravity field. Their individual contributions were assessed through closed-loop simulations which rigorously mapped the sensors' sensitivities to the gravity field coefficients. Clocks, which can directly obtain the gravity potential (differences) through frequency comparison, show a high sensitivity to the very long-wavelength gravity field. In the GRACE orbit, clocks with an uncertainty level of 1.0 × 10 −18 are capable to retrieve temporal gravity signals below degree 12, while 1.0 × 10 −17 clocks are useful for detecting the signals of degree 2 only. However, it poses challenges for clocks to achieve such uncertainties in a short time. In space, the CAI gradiometer is expected to have its ultimate sensitivity and a remarkable stability over a long time (measurements are precise down to very low frequencies). The three diagonal gravity gradients can properly be measured by CAI gradiometry with a same noise level of 5.0 mE/ √ Hz. They can potentially lead to a 2-5 times better solution of the static gravity field than that of GOCE above degree and order 50, where the GOCE solution is mainly dominated by the gradient measurements. In the lower degree part, benefits from CAI gradiometry are still visible, but there, solutions from GRACE-like missions are superior.

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Section: Optical Clocksmentioning

confidence: 99%

“…For physical heights, the next step would be achieving a consistent 1 cm accuracy level. Clocks are thus considered as a new powerful measurement tool and are relevant for a variety of geodetic applications (Müller et al 2018;Delva et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Using quantum optical sensors for determining the Earth’s gravity field from space

Müller

2020

J Geod

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“…The most accurate optical atomic clocks operational today have already opened a new field of application, namely chronometric geodesy [76,220]. The underlying principle is that, following Einstein's theory of general relativity, time dilation occurs: a clock in a gravitational potential will slow down with respect to a clock in empty space.…”

Section: Chronometric Geodesymentioning

confidence: 99%

“…With a future generation of optical atomic clocks the precision of navigation may improve up to a point where, for example, small strains of the earth's crust can be measured and applied for earthquake prediction [101,209]. Importantly, however, optical atomic clocks of the highest accuracies have even led to the creation of the novel field of chronometric geodesy [76]. At the achieved accuracies, general relativistic effects enter the game: time dilation caused by the local gravitational field becomes observable.…”

Section: Introductionmentioning

confidence: 99%

The $$^{229}$$Th isomer: prospects for a nuclear optical clock

Wense

2020

Eur. Phys. J. A

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The proposal for the development of a nuclear optical clock has triggered a multitude of experimental and theoretical studies. In particular the prediction of an unprecedented systematic frequency uncertainty of about $$10^{-19}$$ 10 - 19 has rendered a nuclear clock an interesting tool for many applications, potentially even for a re-definition of the second. The focus of the corresponding research is a nuclear transition of the $$^{229}$$ 229 Th nucleus, which possesses a uniquely low nuclear excitation energy of only $$8.12\pm 0.11$$ 8.12 ± 0.11 eV ($$152.7\pm 2.1$$ 152.7 ± 2.1 nm). This energy is sufficiently low to allow for nuclear laser spectroscopy, an inherent requirement for a nuclear clock. Recently, some significant progress toward the development of a nuclear frequency standard has been made and by today there is no doubt that a nuclear clock will become reality, most likely not even in the too far future. Here we present a comprehensive review of the current status of nuclear clock development with the objective of providing a rather complete list of literature related to the topic, which could serve as a reference for future investigations.

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“…On the one hand, high-precision satellite missions such as GRACE/GRACE-FO allow to deduce properties of the Earth's gravity field, its changes on various time scales, and the investigation of underlying phenomena [1][2][3]. On the other hand, Earth-bound clock comparison networks or portable optical atomic clocks are used in the framework of chronometric geodesy [4][5][6][7]. One of the central notions that is to be determined by such geodetic measurements is the Earth's geoid -its mathematical figure as the German mathematician C.F.…”

Section: Introductionmentioning

confidence: 99%

Relativistic geoid: Gravity potential and relativistic effects

et al. 2020

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The Earth's geoid is one of the most important fundamental concepts to provide a gravity fieldrelated height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable. Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential as a generalization of known (post-)Newtonian notions. This potential exists for any stationary configuration and rigidly co-rotating observers. It is the same as realized by local plumb lines. In a second step, we employ the gravity potential to define the relativistic geoid in direct analogy to the Newtonian understanding. In the respective limits, it allows to recover well-known (post-) Newtonian results. For a better illustration and proper interpretation of the general relativistic gravity potential and geoid, we consider some particular examples. Explicit results are derived for exact vacuum solutions to Einstein's field equation as well as a parametrized post-Newtonian model. Comparing the Earth's Newtonian geoid to its relativistic generalization is a very subtle problem. However, an isometric embedding into Euclidean three-dimensional space can solve it and allows a genuinely intrinsic comparison. With this method, the leading-order differences are determined, which are at the mm-level.

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Chronometric Geodesy: Methods and Applications

Abstract: 1 Resolution 1 of the 13th CGPM [7]. 2 This is based on the numbers given in table 1 of [10] and table 1 of [11]: the relative accuracy of the gravitational part of the relativistic shift effect is taken as ( √ 18 2 + 10 2 + 7 2 ns)/(179 ns).

Cited by 22 publications

References 164 publications

Using quantum optical sensors for determining the Earth’s gravity field from space

Using quantum optical sensors for determining the Earth’s gravity field from space

The $$^{229}$$Th isomer: prospects for a nuclear optical clock

Relativistic geoid: Gravity potential and relativistic effects

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