Prospects for Measuring Planetary Spin and Frame-Dragging in Spacecraft Timing Signals

Satellite tracking involves sending electromagnetic signals to Earth. Both the orbit of the spacecraft and the electromagnetic signals themselves are affected by the curvature of spacetime. The arrival time of the pulses is compared to the ticks of local clocks to reconstruct the orbital path of the satellite to high accuracy, and to implicitly measure general relativistic effects. In particular, Schwarzschild space curvature (static) and frame-dragging (stationary) due to the planet's spin affect the satellite's orbit. The dominant relativistic effect on the path of the signal photons is Shapiro delay due to static space curvature. We compute these effects for some current and proposed space missions, using a Hamiltonian formulation in four dimensions. For highly eccentric orbits, such as in the Juno mission and in the Cassini Grand Finale, the relativistic effects have a kick-like nature, which could be advantageous for detecting them if their signatures are properly modeled as functions of time. Frame-dragging appears, in principle, measurable by Juno and Cassini, though not by Galileo 5 and 6. Practical measurement would require disentangling frame-dragging from the Newtonian 'foreground' such as the gravitational quadrupole which has an impact on both the spacecraft's orbit and the signal propagation. The foreground problem remains to be solved.Comment: 10 pages, 6 figures, provisionally accepted for publication in Frontiers in Astronomy and Space Sciences, section Fundamental Astronom

Atomic clocks as a tool to monitor vertical surface motion

Atomic clock technology is advancing rapidly, now reaching stabilities of $\Delta f/f \sim 10^{-18}$, which corresponds to resolving $1$ cm in equivalent geoid height over an integration timescale of about 7 hours. At this level of performance, ground-based atomic clock networks emerge as a tool for monitoring a variety of geophysical processes by directly measuring changes in the gravitational potential. Vertical changes of the clock's position due to magmatic, volcanic, post-seismic or tidal deformations can result in measurable variations in the clock tick rate. As an example, we discuss the geopotential change arising due to an inflating point source (Mogi model), and apply it to the Etna volcano. Its effect on an observer on the Earth's surface can be divided into two different terms: one purely due to uplift and one due to the redistribution of matter. Thus, with the centimetre-level precision of current clocks it is already possible to monitor volcanoes. The matter redistribution term is estimated to be 2-3 orders of magnitude smaller than the uplift term, and should be resolvable when clocks improve their stability to the sub-millimetre level. Additionally, clocks can be compared over distances of thousands of kilometres on a short-term basis (e.g. hourly). These clock networks will improve our ability to monitor periodic effects with long-wavelength like the solid Earth tide.Comment: 11 pages, 5 figures, accepted as express letter in the Geophysical Journal Internationa

Gegen den Feuerbrand mit intensiver Forschung

Zusätzlich zur Beseitigung von Infektionsherden erhalten Hygiene und Sortenwahl sowie die direkte Bekämpfung mit Pflanzenschutzmitteln Bedeutung

Testing scalar-tensor theories and PPN parameters in Earth orbit

We compute the PPN parameters $\gamma$ and $\beta$ for general scalar-tensor theories in the Einstein frame, which we compare to the existing PPN formulation in the Jordan frame for alternative theories of gravity. This computation is important for scalar-tensor theories that are expressed in the Einstein frame, such as chameleon and symmetron theories, which can incorporate hiding mechanisms that predict environment-dependent PPN parameters. We introduce a general formalism for scalar-tensor theories and constrain it using the limit on $\gamma$ given by the Cassini experiment. In particular we discuss massive Brans-Dicke scalar fields for extended sources. Next, using a recently proposed Earth satellite experiment, in which atomic clocks are used for spacecraft tracking, we compute the observable perturbations in the redshift induced by PPN parameters deviating from their general relativistic values. Our estimates suggest that $|\gamma - 1| \sim |\beta -1| \sim 10^{-6}$ may be detectable by a satellite that carries a clock with fractional frequency uncertainty $\Delta f/f \sim 10^{-16}$ in an eccentric orbit around the Earth. Such space experiments are within reach of existing atomic clock technology. We discuss further the requirements necessary for such a mission to detect deviations from Einstein relativity.Comment: 17 pages, 6 figures, accepted for publication in Phys. Rev.

Testing General Relativity and Alternative Theories of Gravity with Space-based Atomic Clocks and Atom Interferometers

The successful miniaturisation of extremely accurate atomic clocks and atom interferometers invites prospects for satellite missions to perform precision experiments. We discuss the effects predicted by general relativity and alternative theories of gravity that can be detected by a clock, which orbits the Earth. Our experiment relies on the precise tracking of the spacecraft using its observed tick-rate. The spacecraft's reconstructed four-dimensional trajectory will reveal the nature of gravitational perturbations in Earth's gravitational field, potentially differentiating between different theories of gravity. This mission can measure multiple relativistic effects all during the course of a single experiment, and constrain the Parametrized Post-Newtonian Parameters around the Earth. A satellite carrying a clock of fractional timing inaccuracy of $\Delta f/f \sim 10^{-16}$ in an elliptic orbit around the Earth would constrain the PPN parameters $|\beta -1|, |\gamma-1| \lesssim 10^{-6}$. We also briefly review potential constraints by atom interferometers on scalar tensor theories and in particular on Chameleon and dilaton models.Comment: 12 pages, 4 figures, 2 tables. Proceeding for ICNFP 201

Ground-based optical atomic clocks as a tool to monitor vertical surface motion

According to general relativity, a clock experiencing a shift in the gravitational potential ΔU will measure a frequency change given by Δf/f≈ΔU/c2. The best clocks are optical clocks. After about 7 hr of integration they reach stabilities of Δf/f∼10−18 and can be used to detect changes in the gravitational potential that correspond to vertical displacements of the centimetre level. At this level of performance, ground-based atomic clock networks emerge as a tool that is complementary to existing technology for monitoring a wide range of geophysical processes by directly measuring changes in the gravitational potential. Vertical changes of the clock's position due to magmatic, post-seismic or tidal deformations can result in measurable variations in the clock tick rate. We illustrate the geopotential change arising due to an inflating magma chamber using the Mogi model and apply it to the Etna volcano. Its effect on an observer on the Earth's surface can be divided into two different terms: one purely due to uplift (free-air gradient) and one due to the redistribution of matter. Thus, with the centimetre-level precision of current clocks it is already possible to monitor volcanoes. The matter redistribution term is estimated to be 3 orders of magnitude smaller than the uplift term. Additionally, clocks can be compared over distances of thousands of kilometres over short periods of time, which improves our ability to monitor periodic effects with long wavelength like the solid Earth tid

Die kombinierte Wirkung von spezialisierten wurzelbohrenden Insekten und Pflanzenkonkurrenz reduziert das Wachstum von Rumex obtusifolius

Die kombinierte Wirkungen von wurzelbohrenden Larven des europäische Schmetterling Pyropteron chrysidiforme (Massenausbringung) auf dem Stumpfblättrigen Ampfer wurden für zwei Gruppen von anfänglich kleinen und großen Pflanzen mit oder ohne Konkurrenz von dem Englischen Raygras bewertet

Anthropogenic disturbance as a driver of microspatial and microhabitat segregation of cytotypes of Centaurea stoebe and cytotype interactions in secondary contact zones

Background and Aims In a mixed-ploidy population, strong frequency-dependent mating will lead to the elimination of the less common cytotype, unless prezygotic barriers enhance assortative mating. However, such barriers favouring cytotype coexistence have only rarely been explored. Here, an assessment is made of the mechanisms involved in formation of mixed-ploidy populations and coexistence of diploid plants and their closely related allotetraploid derivates from the Centaurea stoebe complex (Asteraceae). Methods An investigation was made of microspatial and microhabitat distribution, life-history and fitness traits, flowering phenology, genetic relatedness of cytotypes and intercytotype gene flow (cpDNA and microsatellites) in six mixed-ploidy populations in Central Europe. Key Results Diploids and tetraploids were genetically differentiated, thus corroborating the secondary origin of contact zones. The cytotypes were spatially segregated at all sites studied, with tetraploids colonizing preferentially drier and open microhabitats created by human-induced disturbances. Conversely, they were rare in more natural microsites and microsites with denser vegetation despite their superior persistence ability (polycarpic life cycle). The seed set of tetraploid plants was strongly influenced by their frequency in mixed-ploidy populations. Triploid hybrids originated from bidirectional hybridizations were extremely rare and almost completely sterile, indicating a strong postzygotic barrier between cytotypes. Conclusions The findings suggest that tetraploids are later immigrants into already established diploid populations and that anthropogenic activities creating open niches favouring propagule introductions were the major factor shaping the non-random distribution and habitat segregation of cytotypes at fine spatial scale. Establishment and spread of tetraploids was further facilitated by their superior persistence through the perennial life cycle. The results highlight the importance of non-adaptive spatio-temporal processes in explaining microhabitat and microspatial segregation of cytotype