We establish a fine expansion for the geometric part of the Arthur-Selberg trace formula (as it was conjectured by Werner Hoffmann). For the general linear group, we deduce an expression for the ...contributions of regular by blocks unipotent orbits (orbits with one Jordan block with multiplicity). As a consequence, we find formulas for Arthur's global coefficients attached to such orbits.
We prove a useful relation between the Conley–Zehnder indices of the Reeb vector flow action along periodic orbits in prequantization bundles and the orbifold Chern class of the base symplectic ...orbifolds motivated by the well-known case of manifolds. We also apply this method to primary examples.
With the fast development of Low Earth Orbit enhanced Global Navigation Satellite System (LeGNSS), there is huge demand in LEO real-time Precise Orbit Determination (POD). Real-time Service (RTS) ...from International GNSS Service (IGS) provides the real-time precise GNSS orbit and clock products, which gives an opportunity to make use of kinematic precise point positioning (PPP) method for LEO POD. However, real-time precise GNSS products and onboard GNSS observations interrupt inevitably or even frequently (especially for real-time clock products), resulting in PPP reconvergence as well as large orbit errors in LEO orbit solutions. A new method is put forward to reduce such influence of two types of data interruptions. For interruption of clock products, the Chebyshev extrapolation is used to maintain the continuity of real-time GNSS clock products. For the onboard observation interruption, the predicted dynamic orbits are employed as constraints to overcome the PPP reconvergence. Results show that zero-reconvergence PPP can be realized with our new method, which means there is almost no reconvergence time after data interruption. Moreover, clock prediction can reduce the root mean square errors (RMSE) for real-time LEO orbit from 5.40, 4.70, and 7.33 cm to 5.18, 4.55, and 5.99 cm in along-track, cross-track, and radial directions, respectively, while the predicted dynamic orbit constraints reduce the orbit RMSE by 20-30% in cross-track component and 60-80% in other two components.
With numerous ongoing deployments owned by private companies and startups, dense satellite constellations deployed in low Earth orbit (LEO) will play a major role in the near future of wireless ...communications. In addition, the 3rd Generation Partnership Project (3GPP) has ongoing efforts to integrate satellites into 5G and beyond-5G networks. Nevertheless, numerous challenges must be overcome to fully exploit the connectivity capabilities of satellite constellations. These challenges are mainly a consequence of the low capabilities of individual small satellites, along with their high orbital speeds and small coverage due to the low altitude of deployment. In particular, inter-plane inter-satellite links (ISLs), which connect satellites from different orbital planes, are greatly dynamic and may be considerably affected by the Doppler shift. In this paper, we present a framework and the corresponding algorithms for the dynamic establishment of the inter-plane ISLs in LEO constellations. Our results show that the proposed algorithms increase the sum of rates in the constellation 1) by up to 115% with respect to the state-of-the-art benchmark schemes in an interference-free environment and 2) by up to 71% when compared to random resource allocation in a worst-case scenario for interference.
We compute the proper time Lyapunov exponent for the charged Myers-Perry black hole spacetime and investigate the instability of the equatorial circular geodesics (both time-like and null) via this ...exponent. We also show that for more than four spacetime dimensions (N greater than or equal to 3), there are no Innermost Stable Circular Orbits (ISCOs) in the charged Myers-Perry black hole spacetime. We further show that among all possible circular orbits, time-like circular orbits have longer orbital periods than null circular orbits (photon spheres) as measured by asymptotic observers. Thus, time-like circular orbits provide the slowest way to orbit around the charged Myers-Perry black hole.
China's BeiDou navigation system (BDS) has evolved from the demonstration navigation satellite system (BDS‐1) to the regional navigation satellite system (BDS‐2). Now, the global BeiDou navigation ...system (BDS‐3) is in construction and is proceeding well. The design and functions of BDS‐3 are quite different from those of both BDS‐1 and BDS‐2. In this paper, the general design, the coordinate reference system, and the system time basis of BDS‐3 are introduced. Several new payloads designed to accomplish different objectives are described as well as the platforms on which they are hosted. Since BDS‐3 consists of several different constellations, the general service capabilities and special service functions provided by these different constellations are described. The performances of the initial BDS‐3 platforms are evaluated based on the available eight‐medium Earth orbit (MEO) satellite configuration. The results of satellite orbit determination and prediction with and without the BDS‐3 inter‐satellite links (ISL) are compared and analyzed.
Accretion disc around black hole in Einstein-SU Abbas, G; Rehman, Hamza; Usama, M ...
The European physical journal. C, Particles and fields,
05/2023, Letnik:
83, Številka:
5
Journal Article
Abstract
Even though tens of directly imaged companions have been discovered in the past decades, the number of directly confirmed multiplanet systems is still small. Dynamical analysis of these ...systems imposes important constraints on formation mechanisms of these wide-orbit companions. As part of the Young Suns Exoplanet Survey we report the detection of a second planetary-mass companion around the 17 Myr-old, solar-type star TYC 8998-760-1 that is located in the Lower Centaurus Crux subgroup of the Scorpius–Centaurus association. The companion has a projected physical separation of 320 au and several individual photometric measurements from 1.1 to 3.8 microns constrain a companion mass of 6 ± 1
M
Jup
, which is equivalent to a mass ratio of
q
= 0.57 ± 0.10% with respect to the primary. With the previously detected 14 ± 3
M
Jup
companion that is orbiting the primary at 160 au, TYC 8998-760-1 is the first directly imaged multiplanet system that is detected around a young, solar analog. We show that circular orbits are stable, but that mildly eccentric orbits for either/both components (
e
> 0.1) are chaotic on gigayear timescales, implying in situ formation or a very specific ejection by an unseen third companion. Due to the wide separations of the companions TYC 8998-760-1 is an excellent system for spectroscopic and photometric follow-up with space-based observatories such as the James Webb Space Telescope.
While leading companies will soon have launched their low Earth orbit (LEO) constellations with different orbital characteristics, e.g., altitude and inclination, the analytical understanding of ...these networks with satellites flying on varying altitudes is only limited to specific network setups, e.g., polar orbits. In this letter, we derive the coverage probability of a generic multi-altitude LEO network with the satellites being distributed uniformly on inclined circular orbits at varying altitudes. To maintain tractability of our derivations, we firstly model the satellites as a binomial point process assuming their altitude to be an arbitrarily distributed random variable. Secondly, we take into account the latitude-dependent distribution of satellites over the orbits through finding the effective number of satellites. The coverage probabilities of four multi-altitude benchmark constellations are evaluated in terms of different constellation parameters as well as the user's latitude. The numerical results reveal that after a certain limit, the coverage probability improves only slightly with increasing the constellation size; therefore, the costly over-sizing of LEO networks is not always recommendable.
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