Modeling and analysis of periodic orbits around a contact binary asteroid

The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is represented by a combination of an ellipsoid and a sphere. The gravitational field of this configuration is for the first time expanded into a spherical harmonics model up to degree and order 8. Compared with the exact potential, the truncation at degree and order 4 is found to introduce an error of less than 10 % at the circumscribing sphere and less than 1 % at a distance of the double of the reference radius. The Hamiltonian taking into account harmonics up to degree and order 4 is developed. After double averaging of this Hamiltonian, the model is reduced to include zonal harmonics only and frozen orbits are obtained. The tesseral terms are found to introduce significant variations on the frozen orbits and distort the frozen situation. Applying the method of Poincaré sections, phase space structures of the single-averaged model are generated for different energy levels and rotation rates of the asteroid, from which the dynamics driven by the 4×4 harmonics model is identified and POs are found. It is found that the disturbing effect of the highly irregular gravitational field on orbital motion is weakened around the polar region, and also for an asteroid with a fast rotation rate. Starting with initial conditions from this averaged model, families of exact POs in the original non-averaged system are obtained employing a numerical search method and a continuation technique. Some of these POs are stable and are candidates for future missions

The science case and challenges of space-borne sub-millimeter interferometry

Ultra-high angular resolution in astronomy has always been an important vehicle for making fundamental discoveries. Recent results in direct imaging of the vicinity of the supermassive black hole in the nucleus of the radio galaxy M87 by the millimeter VLBI system Event Horizon Telescope and various pioneering results of the Space VLBI mission RadioAstron provided new momentum in high angular resolution astrophysics. In both mentioned cases, the angular resolution reached the values of about 10–20 microarcseconds (0.05–0.1 nanoradian). Further developments towards at least an order of magnitude “sharper” values, at the level of 1 microarcsecond are dictated by the needs of advanced astrophysical studies. The paper emphasis that these higher values can only be achieved by placing millimeter and submillimeter wavelength interferometric systems in space. A concept of such the system, called Terahertz Exploration and Zooming-in for Astrophysics, has been proposed in the framework of the ESA Call for White Papers for the Voyage 2050 long term plan in 2019. In the current paper we present new science objectives for such the concept based on recent results in studies of active galactic nuclei and supermassive black holes. We also discuss several approaches for addressing technological challenges of creating a millimeter/sub-millimeter wavelength interferometric system in space. In particular, we consider a novel configuration of a space-borne millimeter/sub-millimeter antenna which might resolve several bottlenecks in creating large precise mechanical structures. The paper also presents an overview of prospective space-qualified technologies of low-noise analogue front-end instrumentation for millimeter/sub-millimeter telescopes. Data handling and processing instrumentation is another key technological component of a sub-millimeter Space VLBI system. Requirements and possible implementation options for this instrumentation are described as an extrapolation of the current state-of-the-art Earth-based VLBI data transport and processing instrumentation. The paper also briefly discusses approaches to the interferometric baseline state vector determination and synchronisation and heterodyning system. The technology-oriented sections of the paper do not aim at presenting a complete set of technological solutions for sub-millimeter (terahertz) space-borne interferometers. Rather, in combination with the original ESA Voyage 2050 White Paper, it sharpens the case for the next generation microarcsecond-level imaging instruments and provides starting points for further in-depth technology trade-off studies.</p

An improved sampling rule for mapping geopotential functions of a planet from a near polar orbit

One of the limiting factors in the determination of gravity field solutions is the spatial sampling. Especially during phases, when the satellite repeats its own track after a short time, the spatial resolution will be limited. The Nyquist rule-of-thumb for mapping geopotential functions of a planet, also referred to as the Colombo–Nyquist rule-of-thumb, provides a limit for the maximum achievable degree of a spherical harmonic development for repeat orbits. We show in this paper that this rule is too conservative, and solutions with better spatial resolutions are possible. A new rule is introduced which limits the maximum achievable order (not degree!) to be smaller than the number of revolutions if the difference between the number of revolutions and the number of nodal days is of odd parity and to be smaller than half the number of revolutions if the difference is of even parity. The dependence on the parity is reflected in the eigenvalue spectrum of the normal matrix and becomes especially important in the presence of noise. The rule is based on applying the Nyquist sampling theorem separately in North–South and East–West direction. This is only possible for satellites in highly inclined orbits like champ and grace. Tables for these two satellite missions are also provided which indicate the passed and (in case of grace) expected repeat cycles and possible degradations in the quality of the gravity field solutions

The science case and challenges of spaceborne sub-millimeter interferometry: the study case of TeraHertz Exploration and Zooming-in for Astrophysics (THEZA)

Ultra-high angular resolution in astronomy has always been an important vehicle for making fundamental discoveries. Recent results in direct imaging of the vicinity of the super-massive black hole in the nucleus of the radio galaxy M87 by the millimeter VLBI system Event Horizon Telescope (EHT) and various pioneering results of the Space VLBI mission RadioAstron provided new momentum in high angular resolution astrophysics. In both mentioned cases, the angular resolution reached the values of about 10−20 microrcseconds (0.05−0.1 nanoradian). Angular resolution is proportional to the observing wavelength and inversely proportional to the interferometer baseline length. In the case of Earth-based EHT, the highest angular resolution was achieved by combining the shortest possible wavelength of 1.3 mm with the longest possible baselines, comparable to the Earth’s diameter. For RadioAstron, operational wavelengths were in the range from 92 cm down to 1.3 cm, but the baselines were as long as ∼350,000 km. However, these two highlights of radio astronomy, EHT and RadioAstron do not”saturate” the interest to further increase in angular resolution. Quite opposite: the science case for further increase in angular resolution of astrophysical studies becomes even stronger. A natural and, in fact, the only possible way of moving forward is to enhance mm/sub-mm VLBI by extending baselines to extraterrestrial dimensions, i.e. creating a mm/sub-mm Space VLBI system. The inevitable move toward space-borne mm/sub-mm VLBI is a subject of several concept studies. In this presentation we will focus on one of them called TeraHertz Exploration and Zooming-in for Astrophysics (THEZA), prepared in response to the ESA’s call for its next major science program Voyage 2050 (Gurvits et al. 2021). The THEZA rationale is focused at the physics of spacetime in the vicinity of super-massive black holes as the leading science drive. However, it will also open up a sizable new range of hitherto unreachable parameters of observational radio astrophysics and create a multi-disciplinary scientific facility and offer a high degree of synergy with prospective “single dish” space-borne sub-mm astronomy (e.g., Wiedner et al. 2021) and infrared interferometry (e.g., Linz et al. 2021). As an amalgam of several major trends of modern observational astrophysics, THEZA aims at facilitating a breakthrough in high-resolution high image quality astronomical studies