On the synergy between Ariel and ground-based high-resolution spectroscopy

Since the first discovery of an extra-solar planet around a main-sequence star, in 1995, the number of detected exoplanets has increased enormously. Over the past two decades, observational instruments (both onboard and on ground-based facilities) have revealed an astonishing diversity in planetary physical features (i. e. mass and radius), and orbital parameters (e.g. period, semi-major axis, inclination). Exoplanetary atmospheres provide direct clues to understand the origin of these differences through their observable spectral imprints. In the near future, upcoming ground and space-based telescopes will shift the focus of exoplanetary science from an era of “species discovery” to one of “atmospheric characterization”. In this context, the Atmospheric Remote-sensing Infrared Exoplanet Large (Ariel) survey, will play a key role. As it is designed to observe and characterize a large and diverse sample of exoplanets, Ariel will provide constraints on a wide gamut of atmospheric properties allowing us to extract much more information than has been possible so far (e.g. insights into the planetary formation and evolution processes). The low resolution spectra obtained with Ariel will probe layers different from those observed by ground-based high resolution spectroscopy, therefore the synergy between these two techniques offers a unique opportunity to understanding the physics of planetary atmospheres. In this paper, we set the basis for building up a framework to effectively utilise, at near-infrared wavelengths, high-resolution datasets (analyzed via the cross-correlation technique) with spectral retrieval analyses based on Ariel low-resolution spectroscopy. We show preliminary results, using a benchmark object, namely HD 209458 b, addressing the possibility of providing improved constraints on the temperature structure and molecular/atomic abundances.

Scaling, Mirror Symmetries and Musical Consonances Among the Distances of the Planets of the Solar System

Orbital systems are often self-organized and/or characterized by harmonic relations. Inspired by music theory, we rewrite the Geddes and King-Hele (QJRAS, 24, 10–13, 1983) equations for mirror symmetries among the distances of the planets of the Solar System in an elegant and compact form by using the 2/3rd power of the ratios of the semi-major axis lengths of two neighboring planets (eight pairs, including the belt of the asteroids). This metric suggests that the Solar System could be characterized by a scaling and mirror-like structure relative to the asteroid belt that relates together the terrestrial and Jovian planets. These relations are based on a 9/8 ratio multiplied by powers of 2, which correspond musically to the interval of the Pythagorean epogdoon (a Major Second) and its addition with one or more octaves. Extensions of the same model are discussed and found compatible also with the still hypothetical vulcanoid asteroids versus the transneptunian objects. The found relation also suggests that the planetary self-organization of our system could be generated by the 3:1 and 7:3 resonances of Jupiter, which are already known to have shaped the asteroid belt. The proposed model predicts the main Kirkwood asteroid gaps and the ratio among the planetary orbital parameters with a 99% accuracy, which is three times better than an alternative, recently proposed harmonic-resonance model for the Solar System. Furthermore, the ratios of neighboring planetary pairs correspond to four musical “consonances” having frequency ratios of 5/4 (Major Third), 4/3 (Perfect Fourth), 3/2 (Perfect Fifth) and 8/5 (Minor Sixth); the probability of obtaining this result randomly has a p < 0.001. Musical consonances are “pleasing” tones that harmoniously interrelate when sounded together, which suggests that the orbits of the planets of our Solar System could form some kind of gravitationally optimized and coordinated structure. Physical modeling indicates that energy non-conserving perturbations could drive a planetary system into a self-organized periodic state with characteristics vaguely similar of those found in our Solar System. However, our specific finding suggests that the planetary organization of our Solar System could be rather peculiar and based on more complex and unknown dynamical structures.

Non-zero Yarkovsky acceleration for near-Earth asteroid (99942) Apophis

The leading source of uncertainty to predict the orbital motion of asteroid (99942) Apophis is a non-gravitational acceleration arising from the anisotropic thermal re-emission of absorbed radiation, known as the Yarkovsky effect. Previous attempts to obtain this parameter from astrometry for this object have only yielded marginally small values, without ruling out a pure gravitational interaction. Here we present an independent estimation of the Yarkovsky effect based on optical and radar astrometry which includes observations obtained during 2021. Our numerical approach exploits automatic differentiation techniques. We find a non-zero Yarkovsky parameter, A2 = (−2.899 ± 0.025) × 10−14 au d−2, with induced semi-major axis drift of (−199.0 ± 1.5) m yr−1 for Apophis. Our results provide definite collision probability predictions for the close approaches in 2029, 2036, and 2068.

Subsurface stresses in an elliptical Hertzian contact

The traditional solution for the stresses below an elliptical Hertzian contact expresses the results in terms of incomplete Legendre elliptic integrals, so are necessarily based on the length of the semi-major axis a and the axis ratio k. The result is to produce completely different equations for the stresses in the x and y directions; and although these equations are now well-known, their derivation from the fundamental, symmetric, integrals is far from simple. When instead Carlson elliptic integrals are used, they immediately match the fundamental integrals, allowing the equations for the stresses to treat the two semi-axes equally, and so providing a single equation where two were needed before. The numerical evaluation of the Carlson integrals is simple and rapid, so the result is that more convenient answers are obtained more conveniently. A bonus is that the temptation to record the depth of the critical stresses as a fraction of the length of the semi-major axis is removed. Thomas and Hoersch’s method of finding all the stresses along the axis of symmetry has been extended to determine the full set of stresses in a principal plane. The stress patterns are displayed, and a comparison between the answers for the planes of the major and minor semiaxes is made. The results are unchanged from those found from equations given by Sackfield and Hills, but not previously evaluated. The present equations are simpler, not only in the simpler elliptic integrals, but also for the “tail” of elementary functions.

Detectability of exomoons by examining the signals from a model of transiting exoplanets with moons

Exomoons are natural satellites of exoplanets. Nowadays, none has been confirmed. However, a number of detection techniques have been proposed, including Transit Timing Variations (TTV) and Transit Duration Variations (TDV) techniques. From a recent study, fitting observed transit with the traditional photocentric fitting model shows unique features around the primary and secondary exomoon transits in TDV and transit depth signals, which might reduce the detectability. The aim of this work is to retrieve the variation of TTV, TDV and transit depth signals of exomoon systems with the photocentric fitting model. One year star-planet-moon transit light curves are simulated with LUNA algorithm and fit with TransitFit. The results show that neglecting the TDV and transit depth data with phase around exomoon’s primary and secondary transits improve the exomoon detectability by a factor of ten and the systems with large moon orbital semi-major axis with nearly edge-on orbit around low mass stars can be detected.

Influence of non-gravitational effects on the Centaur upper stage of the Surveyor 2 spacecraft

A small near-Earth asteroid, discovered by the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) on September 17, 2020, turned out to be a part of the Centaur upper stage of the Surveyor 2 spacecraft launched by NASA on September 20, 1966 and subsequently crashed. This object had moved in a heliocentric orbit until it was under the influence of Earth’s gravitational field. As a result, a close approach to the Earth took place at a distance of about 50000 km on December 1, 2020. Despite the fact that the Centaur escaped back into a new orbit around the Sun in March 2021, it is of special interest for research, in particular, to consider the impact of non-gravitational effects on its orbital characteristics. Thus, it was calculated that the maximum displacement of the object trajectory due to the influence of solar radiation pressure over 15 years (the next close approach will take place in 2036) can be about 10.3-13.5 km, depending on the albedo. Estimations of the Yarkovsky effect showed that the magnitude of the expected change in the semi-major axis of Centaur’s orbit is from -8.1 • 10−13 to 1.6 10−13, depending on the angle of its rotation.

Real-Time Deformation Measurements Using Single Image Photogrammetry

Most photogrammetric measurements are currently based on image acquisition in the field and subsequent processing in office environment with certain temporal delay. However, in some cases it is necessary to process the data real-time, or at least in-situ. Bridge load testing is an example of measurement processing directly at the place of imaging, where almost immediate information about the current state or change of the object is required. An algorithm is developed for these purposes, including a camera controlling software and a MATLAB code that identifies and quantifies the shifts of the observed points in the image plane. The observed points are in the shape of black disks on a white background. Using a horizontal camera position individual epochs are captured. Each image is immediately transferred to a computer via Wi-Fi. The MATLAB code then loads the image and binarizes it. Binarization of the image is performed by the Canny edge detector. Using normalized 2-D cross-correlation, the algorithm determines the approximate coordinates based on a target template. A function performs least squares ellipse fitting and determines the center of the target in sub-pixel accuracy, the semi-major axis, the semi-minor axis and the rotation angle of the ellipse. The target detection is executed in a while cycle loop, which compares the point coordinates from each epoch to the initial state, thus quantifying the deformations in pixels. If the next image is not yet available, the loop restarts. The deformations are calculated based on the known scale of each target. This paper presents a detailed description of the development of the algorithm, the results achieved and the proposed improvements going forward.

The Green Bank Northern Celestial Cap Pulsar Survey. VI. Discovery and Timing of PSR J1759+5036: A Double Neutron Star Binary Pulsar

The Green Bank North Celestial Cap survey is a 350 MHz all-sky survey for pulsars and fast radio transients using the Robert C. Byrd Green Bank Telescope. To date, the survey has discovered over 190 pulsars, including 33 millisecond pulsars and 24 rotating radio transients. Several exotic pulsars have been discovered in the survey, including PSR J1759+5036, a binary pulsar with a 176 ms spin period in an orbit with a period of 2.04 days, an eccentricity of 0.3, and a projected semi-major axis of 6.8 light seconds. Using seven years of timing data, we are able to measure one post–Keplerian parameter, advance of periastron, which has allowed us to constrain the total system mass to 2.62 ± 0.03 M ⊙. This constraint, along with the spin period and orbital parameters, suggests that this is a double neutron star system, although we cannot entirely rule out a pulsar-white dwarf binary. This pulsar is only detectable in roughly 45% of observations, most likely due to scintillation. However, additional observations are required to determine whether there may be other contributing effects.

Short-Arc Association and Orbit Determination for New GEO Objects with Space-Based Optical Surveillance

For Geosynchronous Earth Orbit (GEO) objects, space-based optical surveillance has advantages over regional ground surveillance in terms of both the timeliness and space coverage. However, space-based optical surveillance may only collect sparse and short orbit arcs, and thus make the autonomous arc association and orbit determination a challenge for new GEO objects without a priori orbit information. In this paper, a three-step approach tackling these two critical problems is proposed. First, under the near-circular orbit assumption, a multi-point optimal initial orbit determination (IOD) method is developed to improve the IOD convergence rate and the accuracy of the IOD solution with angles-only observations over a short arc. Second, the Lambert equation is applied to associate two independent short arcs in an attempt to improve accuracy of the single-arc IOD semi-major axis (SMA) with the use of virtual ranges between the optical sensor and GEO object. The key idea in the second step is to generate accurate ranges at observation epochs, which, along with the real angle data, are then used to achieve much improved SMA accuracy. The third step is basically the repeated application of the second step to three or more arcs. The high success rate of arc associations and accurate orbit determination using the proposed approach are demonstrated with simulated space-based angle data over short arcs, each being only 3 min. The results show that the proposed approach is able to determine the orbit of a new GEO at a three-dimensional accuracy of about 15 km from about 10 arcs, each having a length of about 3 min, thus achieving reliable cataloguing of uncatalogued GEO objects. The IOD and two-arc association methods are also tested with the real ground-based observations for both GEO and LEO objects of near-circular orbits, further validating the effectiveness of the proposed methods.