Apparent Position Research Articles

Determining the orbit from five relative apparent positions

The article describes a new method for determining the orbit of a satellite of a distant body by five measured apparent relative positions. Objects can be components of a visual binary star. The method is based on old ideas proposed back in the 19th century. In 1883, T.N. Thiele theoretically deduced and proposed an interesting method for determining an orbit from three apparent relative positions for a given sector (areal) velocity of the body in apparent orbit. In this paper, this method is supplemented with analytical formulas for determining the sectoral velocity of a satellite of a star or planet in apparent orbit in five positions. Five relative positions are needed to accurately determine the sector velocity of a body in a visible orbit. Further, the parameters of the spatial orbit are determined by three positions. The semi-major axis of the orbit and the mean motion are determined independently. This makes it possible to determine the total mass of the system under study. The proposed method is first tested on a model example, and then its adequacy is shown for the problem of determining the orbit of a visual binary star ZZ Tau based on real observations. In this example, the method is tested, its adequacy is shown. We also consider the application of the method for determining the preliminary orbit of an asteroid satellite with the aim of subsequent refinement of the orbit based on collection of observations over a large time interval. The reliability of the method has yet to be tested on specific problems. For convenience, an online service has been developed on the Internet allowing to calculate the orbit from the reader’s observations.

Remarks on the black hole shadows in Kerr-de Sitter space times

This work is geared towards analysis of shadows cast by Kerr-de Sitter (KdS) and Kerr-de Sitter Revisited (RKdS) black holes. Considering observers in the vicinity of the static radius, we derive the impact parameters defining the apparent positions of the shadows. Such observers are of interest to our work because embedding diagrams have shown that de Sitter space-time is analogous to an asymptotically flat one in the vicinity of the static radius. We also perform a comparative analysis between our result with that in Ref. [1]. Furthermore, we numerically obtain the radii of curvature, vertical diameters and horizontal diameters of the shadows. We find that for Lambda =1.11times 10^{-52} ,, m^{-2}, M87* observations cannot distinguish a RKdS black hole shadow from that of a Kerr black hole. Additionally, for the same value of Lambda , KdS and RKdS black hole shadows are, in practise, indistinguishable. Previously, it has also been shown that when Lambda =1.11times 10^{-52} ,, {text {m}}^{-2}, KdS and Kerr black hole shadows are indistinguishable. Utilizing the 2017 EHT observations of M87* on the allowed range of the characteristic radius of the shadow, we obtain constraints on both black holes. When, a/M>0.812311, we observe that large angles of inclination (theta >30.5107^{circ }) do not pass the constraints for both KdS and RKdS black holes.

FINDING THE PHYSIOLOGICAL RELATIONSHIP BETWEEN JAWS AND INTERALVEOLAR HEIGHT IN PATIENTS WITH OCCLUSIVE DISORDERS ASSOCIATED WITH PRIMARY DEEP OCCLUSION, WHICH RESULTED FROM IMPROPER DENTAL INTERVENTIONS

Recent studies have documented that regaining inter-alveolar height is one of the most difficult tasks during the prosthetics remanufacturing process. Often, during prosthetics remanufacturing process, misunderstanding between a patient and a doctor may occur. It is related to the removal of expensive structures, manufacturing new ones and performing orthodontic treatment that requires additional expenses. According to our observations, even apparent comfortable positioning of the occlusive splint that eliminates the pain sensation could be misleading. Thus, the touchstone for achieving optimal functional and aesthetic results is not only the repositioning of the mandible that eliminates pain sensation in temporomandibular joint, but is also regaining of inter-alveolar height needed for prosthesis remanufacturing.
 Therefore, knowing the treatment outcome, the doctor is able to minimize the risk of errors in prosthesis remanufacturing process and improve the doctor-patient relationship. These steps contribute to the improvement of life quality of the patients. Our study enables us to predict the range of bite correction required. Out study has shown significant functional adaptation of the maxillofacial region. All patients have different adaptive capability to occlusal disorders, which are perceived by the body as a stressful situation. Some patients demonstrate quick adaptation to significant changes in occlusal relationship; others may present a wide range of symptoms even with minor changes in occlusal contacts. Our treatment regimen helps to choose the most appropriate individual algorithm for managing patients. Restorative dental procedures can be attributed to stress factors. Vegetative imbalance can lead to the deterioration of the emotional and behavioural aspects of the personality. The neurotic state of patients that results from this imbalance can misleads prothodontists as to the primary etiological factors of the symptoms present. Our treatment algorithm enables to clearly distinguish between patients’ feelings and the objective problems. Thus, we can find the prime cause of the symptoms. We can also resolve the issue of consulting other specialists in a timely manner. This allows us to improve the relationship between patients and doctors who performed previous prosthetic treatment. We can draw a conclusion about the dominant causative factor, and its interdependence between the treatment course duration and the volume of restorative procedures. This brings patients back to a normal rhythm of life and, as a result, improves their quality of life.

Method for assessment of the apparent detector stack position in a whisk-broom sensor

In a whisk-broom sensor, such as the Advanced Baseline Imager (ABI) onboard the Geostationary Operational Environmental Satellite (GOES)-R series of geostationary satellites, the sensor optics projects the observed scene onto the sensor focal plane arrays (FPA), with the detectors arranged in a column perpendicular to the scan direction. An assessment system compares the images made by the sensor with known landmarks and calculates the image deviations from the landmark positions. These deviations are called navigation residuals, and in this work they are interpreted in a broad sense as deviations of the actual from the ideal optical paths. The deviations can be caused by several issues, such as a sensor pointing error, deficiency in sensor optics, and inaccuracy of detector locations on FPA. As the ABI sensor scans the Earth to make a full-disk image in 22 parallel swaths, we refer the landmark residuals from all swaths to the observing detector positions in the ABI detector column. This interpretation inverts the retrieval of navigation residuals and gives deviations of the image from the expected ideal position on an ideal FPA. As the errors of pointing and sensor optics can be assessed independently, the remaining deviations can be interpreted as these with respect to the ideal detector position map (in other words, to the pre-launch assessment). We call these deviations the apparent detector positions. Knowledge of these deviations will greatly simplify the navigation commissioning for future ABI sensors and similar devices. Using our archive of ABI image navigation data for ABI sensor on the GOES-16 satellite, we show the wealth of additional information about the sensor on-orbit condition that may be extracted with the proposed method. This algorithm can use any image navigation system that is sufficiently precise.

Exploring the Common Mechanisms of Motion-Based Visual Prediction

Human vision supports prediction for moving stimuli. Here we take an individual differences approach to investigate whether there could be a common processing rate for motion-based visual prediction across diverse motion phenomena. Motion Induced Spatial Conflict (MISC) refers to an incongruity arising from two edges of a combined stimulus, moving rigidly, but with different apparent speeds. This discrepancy induces an illusory jitter that has been attributed to conflict within a motion prediction mechanism. Its apparent frequency has been shown to correlate with the frequency of alpha oscillations in the brain. We asked what other psychophysical measures might correlate positively with MISC frequency. We measured the correlation between MISC jitter frequency and another three measures that might be linked to motion-based spatial prediction. We demonstrate that the illusory jitter frequency in MISC correlates significantly with the accrual rate of the Motion Induced Position Shift (MIPS) effect - the well-established observation that a carrier movement in a static envelope of a Gabor target leads to an apparent position shift of the envelope in the direction of motion. We did not observe significant correlations with the other two measures – the Adaptation Induced Spatial Shift accrual rate (AISS) and the Smooth Motion Threshold (SMT). These results suggest a shared perceptual rate between MISC and MIPS, implying a common periodic mechanism for motion-based visual prediction.

Testing the non-circularity of the spacetime around Sagittarius A* with orbiting pulsars

Abstract A disformal Kerr black hole solution is a rotating black hole solution in a modified gravity theory which breaks the circular condition of spacetime differently from the case of the Kerr spacetime. In this paper, assuming that Sagittarius A* (Sgr A*) is a disformal Kerr black hole, we examine the potential to test the spacetime geometry with a hypothetical pulsar whose orbital elements are similar to those of the S2/S0-2 star. By numerically solving the equations of motion for the pulsar and photons emitted from it, we calculate the apparent position of the pulsar and the time of arrival (TOA) of the emitted pulse signals. Our analysis shows that the magnitude of the difference in the TOAs reaches the order of 10 ms if the deviation from the Kerr spacetime is significant. The time difference is mainly caused by the non-circularity of the spacetime at the 1.5 post-Newtonian order. The accuracy of the TOA measurement by a future radio telescope named the Square Kilometer Array (SKA) is between about 0.1 ms and 10 ms for a normal pulsar. Thus, we expect that the SKA can distinguish a disformal Kerr black hole from a Kerr black hole through the non-circularity of the spacetime around Sgr A*.

The human primary visual cortex (V1) encodes the perceived position of static but not moving objects

Brain activity in retinotopic cortex reflects illusory changes in stimulus position. Is this neural signature a general code for apparent position? Here we show that responses in primary visual cortex (V1) are consistent with perception of the Muller-Lyer illusion; however, we found no such signature for another striking illusion, the curveball effect. This demonstrates that V1 does not encode apparent position per se.

Evaluation of the ICRF stability from a position time series analysis

Context. The celestial reference frame is established on the basis of the absolute positions of extragalactic sources that are assumed to be fixed in space. The fixing of the axes is one of the crucial points for the concept behind the International Celestial Reference System (ICRS). However, due to various effects such as its intrinsic activity, the apparent position of the extragalactic sources may vary with time, resulting in a time-dependent deviation of the frame axes that are defined by the positions of these sources. Aims. We aim to evaluate the axis stability of the third realization of the International Celestial Reference Frame (ICRF3). Methods. We first derived the extragalactic source position time series from observations of very long baseline interferometry (VLBI) at the dual S∕X-band (2.3/8.4 GHz) between August 1979 and December 2020. We measured the stability of the ICRF3 axes in terms of the drift and scatter around the mean: (i) we estimated the global spin of the ICRF3 axes based on the apparent proper motion (slope of the position time series) of the defining sources of the ICRF3; (ii) we also constructed the yearly representations of the ICRF3 through annually averaged positions of the defining sources of the ICRF3 and estimated the dispersion in the axes orientation of these yearly frames. Results. The global spin is no higher than 0.8 μas yr-1 for each ICRF3 axis with an uncertainty of 0.3 μas yr-1, corresponding to an accumulated deformation smaller than 30 μas for the celestial frame axes during 1979.6–2021.0. The axes orientation of the yearly celestial frame becomes more stable as time elapses, with a standard deviation of 10 μas–20 μas for each axis. Conclusions. The axes of the ICRF3 are stable at approximately 10 μas–20 μas from 1979.6–2021.0 and the axes stability does not degrade after the adoption of the ICRF3.

Implementation of apertures in a proton pencil-beam dose algorithm

The use of field-specific apertures, routine in scattered or uniform-scanned proton fields, are still a necessity in pencil-beam scanned (PBS) fields to sharpen the penumbral edge at low energies and in high fraction dose application beyond that achievable with small spot size. We describe a model implemented in our clinical pencil-beam algorithm that models the insertion of a shaped aperture, including shapes adapted per energy layer such as may be achieved with a multi-leaf collimator. The model decomposes the spot transport into discrete steps. The first step transport a uniform intensity field of high-resolution sub-pencil-beams at the layer energy through the medium. This transport only considers primary scattering in both the patient and an optional range-shifter. The second step models the aperture areas and edge penumbral transition as a modulation of the uniform intensity. The third step convolves individual steps over the uniform-transported field including the aperture-modified intensities. We also introduce an efficient model based on a Clarkson sector integration for nuclear scattered halo protons. This avoids the explicit modeling of long range halo protons to the detriment of computational efficiency in calculation and optimization. We demonstrate that the aperture effect is primarily due to in-patient and shifter scattering with a small contribution from the apparent beam source position. The model provides insight into the primary physics contributions to the penumbra and the nuclear halo. The model allowed us to fully deploy our PBS capacity at our two-gantry center without which PBS treatments would have been inferior compared to scattered fields with apertures. Finally, Monte Carlo calculations have (nearly) replaced phenomenological pencil-beam models for collimated fields. Phenomenological models do, however, allow exposition of underlying clinical phenomena and closer connection to representative clinical observables.

Improving prediction of temperature profiles of packaged food during retort processing

A one-dimensional (1D) apparent position (AP) numerical solution (APNS) method was previously proposed to predict the evolution of temperature at the slowest heating point (SHP) of canned food in any shaped container during retort processing. In this study, the APNS method was implemented in a two-dimensional (2D) computational domain in a conductive cylinder that provides a contour of AP for the SHP instead of a single AP in the existing 1D method, enabling the selection of the optimal AP that could substantially improve the prediction accuracy of the APNS method. The 2D method was implemented in a web-based software tool. This tool provided a perfect prediction of a simulated product temperature profile of a conductive canned food in a truncated cone-shaped container, and reasonably good predictions of experimentally measured product temperature profiles of canned food in different shaped containers subjected to natural convection or mixed convection/conduction at non-constant heating temperature. • A 1D APNS method has been used to predict temperature profiles of canned food. • A 2D APNS method was developed in this study to improve the prediction accuracy. • The 2D method was validated using data for conductive and convective canned food. • The 2D method was implemented in a web-based software tool.

Multiprobe Radiation Simulation Method for Phased Array Radar Performance Evaluation

The phased array radar exhibits improved tracking accuracy and anti-jamming performance with multi-beam tracking, beam agility, and adaptive beam-forming capabilities. The performance evaluation of the phased array radar is essential for the product designing and development stage. However, the conventional injection simulation and triad radiation simulation methods are not suitable for phased array radars. Therefore, new methods for radiation simulation are required on an urgent basis for the performance evaluation of phased array radars in a reliable, reliable, and repeatable way. This paper focuses on designing a practical anechoic chamber system of multi-probe radiation suitable for phased array radars. The appropriate test distance, the physical size of the anechoic chamber, the multi-probe radiation signal model, and the number of probes required were discussed. Furthermore, an inversion method based on least squares was proposed to solve the complex weights of the probes, thereby simulating the desired apparent center position. The simulation results demonstrated the effectiveness of the proposed method.

Teorijski model solarnog upadnog ugla za proizvoljno orijentisanu fiksnu, ravnu površinu

The apparent position of the Sun in relation to any surface is defined by the solar incident angle. The solar incident angle forms the vector of the position of the Sun and the vector of normal to the observed surface. The spatial position of the aforementioned vectors is determined by solar coordinates, which include: declination, latitude, hour angle, longitude, solar elevation angle, solar azimuth angle, azimuth angle of the observed surface, angle of inclination of the observed surface in the north-south direction and angle of inclination of the observed surface in the east-west direction. This article describes in detail the theoretical model for determining the solar incident angle for an arbitrarily placed fixed, flat surface using vector algebra and analytical geometry, as well as solar coordinates. The study model, which was developed by combining, modifying, and supplementing existing models, can be used to determine the thermal performance of solar devices such as: solar collectors, PV panels, and hybrid solar systems.

Signal preservation of exomoon transits during light curve folding

In the search for moons around extrasolar planets (exomoons), astronomers are confronted with a stunning observation. Although 3400 of the 4500 exoplanets were discovered with the transit method and although there are well over 25 times as many moons than planets known in the Solar System (two of which are larger than Mercury), no exomoon has been discovered to date. In the search for exoplanet transits, stellar light curves are usually phase-folded over a range of trial epochs and periods. This approach, however, is not applicable in a straightforward manner to exomoons. Planet-moon transits either have to be modeled in great detail (including their orbital dynamics, mutual eclipses, etc.), which is computationally expensive, or key simplifications have to be assumed in the modeling. One such simplification is to search for moon transits outside of the planetary transits. The question we address in this report is how much in-transit data of an exomoon remains uncontaminated by the near-simultaneous transits of its host planet. We develop an analytical framework based on the probability density of the sky-projected apparent position of an exomoon relative to its planet and test our results with a numerical planet-moon transit simulator. For exomoons with planet-moon orbital separations similar to the Galilean moons, we find that only a small fraction of their in-transit data is uncontaminated by planetary transits: 14% for Io, 20% for Europa, 42% for Ganymede, and 73% for Callisto. The signal-to-noise ratio (S/N) of an out-of-planetary-transit folding technique is reduced compared to a full photodynamical model to about 38% (Io), 45% (Europa), 65% (Ganymede), and 85% (Callisto), respectively. For the Earth’s Moon, we find an uncontaminated data fraction of typically just 18% and a resulting S/N reduction to 42%. These values are astonishingly small and suggest that the gain in speed for any exomoon transit search algorithm that ignores the planetary in-transit data comes at the heavy price of losing a substantial fraction of what is supposedly a tiny signal in the first place. We conclude that photodynamical modeling of the entire light curve has substantial, and possibly essential, advantages over folding techniques of exomoon transits outside the planetary transits, in particular for small exomoons comparable to those of the Solar System.

Effects of the 12 May 2021 Geomagnetic Storm on Georeferencing Precision

In this work, we present the positioning error analysis of the 12 May 2021 moderate geomagnetic storm. The storm happened during spring in the northern hemisphere (fall in the south). We selected 868 GNSS stations around the globe to study the ionospheric and the apparent position variations. We compared the day of the storm with the three previous days. The analysis shows the global impact of the storm. In the quiet days, 93% of the stations had 3D errors less than 10 cm, while during the storm, only 41% kept this level of accuracy. The higher impact was over the Up component. Although the stations have algorithms to correct ionospheric disturbances, the inaccuracies lasted for nine hours. The most severe effects on the positioning errors were noticed in the South American sector. More than 60% of the perturbed stations were located in this region. We also studied the effects produced by two other similar geomagnetic storms that occurred on 27 March 2017 and on 5 August 2019. The comparison of the storms shows that the effects on position inaccuracies are not directly deductible neither from the characteristics of geomagnetic storms nor from enhancement and/or variations of the ionospheric plasma.

Detecting dark matter subhalos with the Nancy Grace Roman Space Telescope

The dark matter subhalo mass function is a promising way of distinguishing between dark matter models. While cold dark matter predicts halos down to Earth-sized masses, other dark matter models typically predict a cut-off in the subhalo mass function. Thus a definitive detection or limits on the existence of subhalos at small masses can give us insight into the nature of dark matter. If these subhalos exist in the Milky Way, they would produce weak lensing signatures, such as modified apparent positions, on background stars. These signatures would generate correlations in the apparent velocities and accelerations of these stars, which could be observable given sufficient astrometric resolution and cadence. The Nancy Grace Roman Space Telescope's Exoplanet Microlensing Survey will be perfectly suited to measuring the acceleration signatures of these halos. Here we forward model these acceleration signatures and explore the Roman Space Telescope's future constraints on lens profiles and populations. We find that the Roman Space Telescope could place competitive bounds on point source, Gaussian, and Navarro-Frenk-White (NFW) profile lenses that are complementary to other proposed methods. In particular, it could place 95% upper limits on the NFW concentration, $c_{200} < 10^{2.5}$. We discuss possible systematic effects that could hinder these efforts, but argue they should not prevent the Roman Space Telescope from placing strong limits. We also discuss further analysis methods for improving these constraints.

Influence of second-order wave force and focusing position on dynamic responses of tension leg platform under a freak wave

As a semicompliant and semirigid column group structure, both second-order sum-frequency and diff-frequency wave forces and focusing positions are important for tension leg platforms (TLPs) under freak waves. The double-wave train superposition model is widely used to generate freak waves; however, multiple trials are inevitable for freak wave generation owing to the uncertainty in parameter selection, which may decrease the simulation efficiency. In this study, the effects of the energy ratio of the focused wave train, number of constituent waves, and parameters of the JONSWAP wave spectrum on the generation probability of freak waves are studied, and the generation probability of the freak wave is fitted by a Γ cumulative probability density function. The advantage of the fitted formula is that the generation probability of a freak wave is quantified, and an appropriate number of constituent waves can be determined for a given energy ratio of the focused wave to increase the simulation efficiency. Furthermore, the dynamic responses of a TLP in a freak wave considering the influences of second-order wave forces and focusing positions are simulated and discussed. Two main findings are that the second-order diff-frequency wave force may cause large-amplitude low-frequency motion in the surge direction and set-down motion in the heave direction, which are 3.71 and 4.08 times the first-order surge and heave responses, respectively, whereas the second-order sum-frequency wave force may cause high-frequency oscillation in the pitch direction, the amplitude of which is 3.9 times the amplitude of the first-order pitch response. The response of the TLP is significantly increased under the freak wave, especially when the second-order wave force is considered. The apparent focusing position of the maximum response changes with the spectral peak period owing to the nonrepeatability of the freak wave and phase difference of the columns. The maximum predicted errors of surge, heave, and pitch motion reached 42.0%, 41.1%, and 98.9%, respectively, when the freak wave acts on the front column, center of the platform, and back column, which may significantly underestimate the dynamic response. Therefore, the effects of the focusing position should be considered when calculating the response of a TLP under a freak wave.

Completeness of the Gaia verse – V. Astrometry and radial velocity sample selection functions in Gaia EDR3

ABSTRACT We risk reaching false scientific conclusions if we test our physical theories against subsets of the Gaia catalogue without correcting for the biased process by which stars make it into our sample. In this paper, we produce selection functions for three Gaia science samples to enable the community to correct for this bias. We estimate the probability that a source in Gaia EDR3 will have (i) a reported parallax and proper motion, (ii) an astrometric renormalized unit weight error below 1.4, or (iii) a reported radial velocity. These selectionfunctions are estimated as a function of G-band apparent magnitude and position on the sky, with the latter two also being dependent on G − GRP colour. The inferred selection functions have a non-trivial dependence on these observable parameters, demonstrating the importance of empirically estimating selection functions. We also produce a simple estimate for the selection function of the full Gaia EDR3 source catalogue to be used with the subset selection functions. We make all of our selection functions easily accessible through the GitHub repository selectionfunctions.

Effects of Symmetry and Apparent Distance in a Parasagittal-Mirror Variant of the Rubber Hand Illusion Paradigm.

When I see my face in a mirror, its apparent position (behind the glass) is not one that my own face could be in. I accept the face I see as my own because I have an implicit understanding of how mirrors work. The situation is different if I look at the reflection of my right hand in a parasagittal mirror (parallel to body midline) when my left hand is hidden behind the mirror. It is as if I were looking through a window at my own left hand. The experience of body ownership has been investigated using rubber hand illusion (RHI) paradigms, and several studies have demonstrated ownership of a rubber hand viewed in a frontal mirror. Our “proof of concept” study was the first to combine use of a parasagittal mirror and synchronous stroking of both a prosthetic hand (viewed in the mirror) and the participant’s hand, with a manipulation of distance between the hands. The strength of the RHI elicited by our parasagittal-mirror paradigm depended not on physical distance between the hands (30, 45, or 60 cm) but on apparent distance between the prosthetic hand (viewed in the mirror) and the participant’s hand. This apparent distance was reduced to zero when the prosthetic hand and participant’s hand were arranged symmetrically (e.g., 30 cm in front of and behind the mirror). Thus, the parasagittal-mirror paradigm may provide a distinctive way to assess whether competition for ownership depends on spatial separation between the prosthetic hand and the participant’s hand.

Analysis of shape uses local apparent position rather than physical position.

Objects are often identified by the shapes of their boundaries. Here, by measuring threshold amplitudes for detection of sinusoidal modulation of local position, orientation and centrifugal speed in a closed path of Gabor patches, we show that the positions of such boundaries are misperceived to accommodate local illusions of orientation context and motion induced positional bias. These two types of illusion are shown to occur independently, but the misperception of position is additive. We conclude that, in the analysis of shape, the visual system uses the apparent rather than the veridical boundary conformation.

Kepler’s derivation of the bisection of the earth’s orbit in Astronomia Nova

Chapter 22 of Astronomia Nova is focused on the calculation of the Earth’s eccentricity. This is carried out by observing the effect of the Earth’s motion on the apparent position of Mars. Kepler’s method to derive the exact eccentricity, however, requires as data a set of longitudes of Mars while that planet and the Earth are in a very particular and restricted number of possible configurations. This paper explains how Kepler understood and tackled the Earth problem in theoretical terms, and also how he drew information from Tycho’s observational registers in a methodical way in order to obtain the necessary data to calculate the desired parameter, i.e. the eccentricity of the Earth’s orbit. In doing so, I will analyze not only Astronomia Nova’s relevant passages, but also Kepler’s preliminary annotations, as published in the Gesammelte Werke.