Search Results (14)

Contrails, or condensation trails, left by aircraft, significantly contribute to global warming by trapping heat in the Earth’s atmosphere. Despite their critical role in climate dynamics, the environmental impact of contrails remains underexplored. This research addresses this gap by focusing on the use of CubeSats for real-time contrail monitoring, specifically over major air routes such as the Europe–North Atlantic Corridor. The study proposes a 3 × 3 CubeSat constellation in highly eccentric orbits, designed to maximize coverage and data acquisition efficiency. Simulation results indicate that this configuration can provide nearly continuous monitoring with optimized satellite handovers, reducing blackout periods and ensuring robust multi-satellite visibility. A machine learning-based system integrating space-based humidity and temperature data to predict contrail formation and inform flight path adjustments is proposed, thereby mitigating environmental impact. The findings emphasize the potential of CubeSat constellations to revolutionize atmospheric monitoring practices, offering a cost-effective solution that aligns with global sustainability efforts, particularly the United Nations Sustainable Development Goal 13 (Climate Action). This research represents a significant step forward in understanding aviation’s non-CO₂ climate impact and demonstrates the feasibility of real-time contrail mitigation through satellite technology. Full article

Kepler’s discoveries were permitted by his remarkable insight to place the Sun at the focus of an elliptical planetary orbit. This coordinate system reduces a 2-dimensional orbit to a single spatial dimension. We consider an alternative coordinate system centered on the “image focus,” which is the symmetrical (mirror) counterpart of the “real focus” occupied by the Sun. Our analytical approach provides new purely geometric formulae and an exact relationship for the dynamic property of orbital time. In addition, considering the mirror symmetry of the ellipse leads to a simple approximation: the radial hand of an orbital clock rotates counterclockwise at a nearly steady angular velocity 2π/T about the “image focus,” where T is the orbital period. This approximation is a useful pedagogic tool and has good accuracy for orbits with low to moderate eccentricities, since the deviation from the exact result goes as eccentricity squared. Planetary comparisons are made. In particular, the angular speeds of Mercury and Jupiter are highly variable in the geocentric and heliocentric reference frames, but are nearly constant in the image focus reference frame. Our findings resolve whether the image focus is the location for observing uniform motion of an elliptical orbit, and pertain to their stability. Full article

The aim of this work is to investigate the main dominant terms of lunisolar perturbations that affect the orbital eccentricity of a Molniya satellite in the long term. From a practical point of view, these variations are important in the context of space situational awareness—for instance, to model the long-term evolution of artificial debris in a highly elliptical orbit or to design a reentry end-of-life strategy for a satellite in a highly elliptical orbit. The study assumes a doubly averaged model including the Earth’s oblateness effect and the lunisolar perturbations up to the third-order expansion. The work presents three important novelties with respect to the literature. First, the perturbing terms are ranked according to their amplitudes and periods. Second, the perturbing bodies are not assumed to move on circular orbits. Third, the lunisolar effect on the precession of the argument of pericenter is analyzed and discussed. As an example of theoretical a application, we depict the phase space description associated with each dominant term, taken as isolated, and we show which terms can apply to the relevant dynamics in the same region. Full article

As an emerging orbital system with flexibility and brand application prospects, the highly elliptical orbit synthetic aperture radar (HEO SAR) can achieve both a low orbit detailed survey and continuous earth surface observation in high orbit, which could be applied to marine reconnaissance and surveillance. However, due to its large eccentricity, two challenges have been faced in the signal processing of HEO SAR at present. The first challenge is that the traditional equivalent squint range model (ESRM) fails to accurately describe the entire range for the whole orbit period including the perigee, the apogee, and the squint subduction section. The second one is to exploit an efficient HEO SAR imaging algorithm in the squinted case which solves the problem that traditional imaging algorithm fails to achieve the focused imaging processing of HEO SAR during the entire orbit period. In this paper, a novel imaging algorithm for HEO SAR is presented. Firstly, the signal model based on the geometric configuration of the large elliptical orbit is established and the Doppler parameter characteristics of SAR are analyzed. Secondly, due to the particularity of Doppler parameters variation in the whole period of HEO, the equivalent velocity and equivalent squint angle used in MESRM can no longer be applied, a refined fourth-order equivalent squint range model(R4-ESRM) that is suitable for HEO SAR is developed by introducing fourth-order Doppler parameter into Modified ESRM (MESRM), which accurately reconstructs the range history of HEO SAR. Finally, a novel imaging algorithm combining azimuth resampling and time-frequency domain hybrid correlation based on R4-ESRM is derived. Simulation is performed to demonstrate the feasibility and validity of the presented algorithm and range model, showing that it achieves the precise phase compensation and well focusing. Full article

For a scenario of a close flyby of a compact star near a spinning black hole, we provide analytical and numerical estimates for the shift of trajectory periastron due to relativistic (beyond post-Newtonian) effects. More specifically, we derived a generalized expression (not limited to quasi-circular or elliptical orbits) directly linking the periastron shift and the spin of the black hole. The expression permits the estimation of black hole spin based on astronomical tracking of locations of stars traveling along highly eccentric (parabolic and hyperbolic) trajectories in close vicinity of a black hole. We also demonstrate how stars traveling on hyperbolic or parabolic trajectories may be (temporarily) captured onto quasi-circular orbits around black holes, and we quantitatively examine conditions for such scenarios. Full article

Binary systems that host a massive star and a non-accreting pulsar can be powerful non-thermal emitters. The relativistic pulsar wind and the non-relativistic stellar outflows interact along the orbit, producing ultrarelativistic particles that radiate from radio to gamma rays. To properly characterize the physics of these sources, and better understand their emission and impact on the environment, careful modeling of the outflow interactions, spanning a broad range of spatial and temporal scales, is needed. Full three-dimensional approaches are very computationally expensive, but simpler approximate approaches, while still realistic at the semi-quantitative level, are available. We present here the results of calculations done with a quasi three-dimensional scheme to compute the evolution of the interacting flows in a region spanning in size up to a thousand times the size of the binary. In particular, we analyze for the first time the role of different eccentricities in the large scale evolution of the shocked flows. We find that the higher the eccentricity, the closer the flows behave like a one-side outflow, which becomes rather collimated for eccentricity values $\gtrsim$0.75. The simulations also unveil that the pulsar and the stellar winds become fully mixed within the grid for low eccentricity systems, presenting a more stochastic behavior at large scales than in the highly eccentric systems. Full article

Obtaining the inverse of a nonlinear monotonic function $f\left(x\right)$ over a given interval is a common problem in pure and applied mathematics, the most famous example being Kepler’s description of orbital motion in the two-body approximation. In traditional numerical approaches, this problem is reduced to solving the nonlinear equation $f\left(x\right)-y=0$ in each point y of the co-domain. However, modern applications of orbital mechanics for Kepler’s equation, especially in many-body problems, require highly optimized numerical performance. Ongoing efforts continually attempt to improve such performance. Recently, we introduced a novel method for computing the inverse of a one-dimensional function, called the fast switch and spline inversion (FSSI) algorithm. It works by obtaining an accurate interpolation of the inverse function $f^{-1}\left(y\right)$ over an entire interval with a very small generation time. Here, we describe two significant improvements with respect to the performance of the original algorithm. First, the indices of the intervals for building the spline are obtained by k-vector search combined with bisection, thereby making the generation time even smaller. Second, in the case of Kepler’s equation, a multistep method for the optimized calculation of the breakpoints of the spline polynomial was designed and implemented in Cython. We demonstrate results that accurately solve Kepler’s equation for any value of the eccentricity $\mathrm{e}\in [0,1-ϵ]$, with $ϵ=2.22\times {10}^{-16}$, which is the limiting error in double precision. Even with modest current hardware, the CPU generation time for obtaining the solution with high accuracy in a large number of points of the co-domain can be kept to around a few nanoseconds per point. Full article

We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. on global and regional scales. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation. Full article

Mercury, the enigmatic innermost planet in the solar system, is one of the most important targets of space exploration. High-quality gravity field data are significant to refine the physical characterization of Mercury in planetary exploration missions. However, Mercury’s gravity model is limited by relatively low spatial resolution and stripe noises, preventing fine-scale analysis and applications. By analyzing Mercury’s gravity data and topography data in the 2D spatial field, we find they have fairly high spatial structure similarity. Based on this, in this paper, a novel convolution neural network (CNN) approach is proposed to improve the quality of Mercury’s gravity field data. CNN can extract the spatial structure features of gravity data and construct a nonlinear mapping between low- and high-degree data directly. From a low-degree gravity input, the corresponding initial high-degree result can be obtained. Meanwhile, the structure characteristics of the high-resolution digital elevation model (DEM) are extracted and fused to the initial data, to get the final stripe-free result with improved resolution. Given the paucity of Mercury’s data, high-quality lunar datasets are employed as pretraining data after verifying the spatial similarity between gravity and terrain data of the Moon. The HgM007 gravity field obtained by the MErcury Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) mission at Mercury is selected for experiments to test the ability of the proposed algorithm to remove the stripes caused by quality differences of the highly eccentric orbit data. Experimental results show that our network can directly obtain stripe-free and higher-degree data via inputting low-degree data and implicitly assuming a lunar-like relation between crustal density and porosity. Albeit the CNN-based method cannot be sensitive to subsurface features not present in the initial dataset, it still provides a new perspective for the gravity field refinement. Full article

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of $1047\mathrm{km}$ and a slow, 21-h path with a low perigee height of $642\mathrm{km}$ . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment $J_2$ of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 $\mathrm{cm}{\mathrm{yr}}^{-1}$ , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as $0.7\mathrm{cm}{\mathrm{yr}}^{-1}$ . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the $G{J}_2/c^2$ signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles $J_{\ell }$ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors ${\mathsf{\sigma }}_{J_{\ell }}$ of a recent global Earth’s gravity field model are better than $1\%$ for all the post-Newtonian effects considered, with a peak of $\simeq {10}^{-7}$ for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable. Full article

On 6 February 2018, SpaceX launched a Tesla Roadster on a Mars-crossing orbit. We perform N-body simulations to determine the fate of the object over the next 15 Myr. The orbital evolution is initially dominated by close encounters with the Earth. While a precise orbit can not be predicted beyond the next several centuries due to these repeated chaotic scatterings, one can reliably predict the long-term outcomes by statistically analyzing a large suite of possible trajectories with slightly perturbed initial conditions. Repeated gravitational scatterings with Earth lead to a random walk. Collisions with the Earth, Venus and the Sun represent primary sinks for the Roadster’s orbital evolution. Collisions with Mercury and Mars, or ejections from the Solar System by Jupiter, are highly unlikely. We calculate a dynamical half-life of the Tesla of approximately 15 Myr, with some 22%, 12% and 12% of Roadster orbit realizations impacting the Earth, Venus, and the Sun within one half-life, respectively. Because the eccentricities and inclinations in our ensemble increase over time due to mean-motion and secular resonances, the impact rates with the terrestrial planets decrease beyond a few million years, whereas the impact rate on the Sun remains roughly constant. Full article

Independent tests aiming to constrain the value of the cosmological constant $\Lambda$ are usually difficult because of its extreme smallness $(\Lambda \simeq 1\times {10}^{-52}{\mathrm{m}}^{-2},\mathrm{or}2.89\times {10}^{-122}\mathrm{in}\mathrm{Planck}\mathrm{units})$ . Bounds on it from Solar System orbital motions determined with spacecraft tracking are currently at the $\simeq {10}^{-43}$ – ${10}^{-44}{\mathrm{m}}^{-2}$ $(5$ – $1\times {10}^{-113}\mathrm{in}\mathrm{Planck}\mathrm{units})$ level, but they may turn out to be optimistic since $\Lambda$ has not yet been explicitly modeled in the planetary data reductions. Accurate $({\sigma }_{{\tau }_{\mathrm{p}}}\simeq 1$ – $10\mathsf{\mu }\mathrm{s})$ timing of expected pulsars orbiting the Black Hole at the Galactic Center, preferably along highly eccentric and wide orbits, might, at least in principle, improve the planetary constraints by several orders of magnitude. By looking at the average time shift per orbit ${\overline{\Delta \delta \tau }}_{\mathrm{p}}^{\Lambda }$ , an S2-like orbital configuration with $e=0.8839,P_{\mathrm{b}}=16\mathrm{yr}$ would permit a preliminarily upper bound of the order of $\left|\Lambda \right|\lesssim 9\times {10}^{-47}{\mathrm{m}}^{-2}\left(\lesssim 2\times {10}^{-116}\mathrm{in}\mathrm{Planck}\mathrm{units}\right)$ if only ${\sigma }_{{\tau }_{\mathrm{p}}}$ were to be considered. Our results can be easily extended to modified models of gravity using $\Lambda$ -type parameters. Full article

This study addresses the potential contribution of the first pair of Galileo FOC satellites sent into incorrect highly eccentric orbits for geodetic and surveying applications. We began with an analysis of the carrier to noise density ratio and the stochastic properties of GNSS measurements. The investigations revealed that the signal power of E14 & E18 satellites is higher than for regular Galileo satellites, what is related to their lower altitude over the experiment area. With regard to the noise of the observables, there are no significant differences between all Galileo satellites. Furthermore, the study confirmed that the precision of Galileo data is higher than that of GPS, especially in the case of code measurements. Next analysis considered selected domains of precise instantaneous medium-range positioning: ambiguity resolution and coordinate accuracy as well as observable residuals. On the basis of test solutions, with and without E14 & E18 data, we found that these satellites did not noticeably influence the ambiguity resolution process. The discrepancy in ambiguity success rate between test solutions did not exceed 2%. The differences between standard deviations of the fixed coordinates did not exceed 1 mm for horizontal components. The standard deviation of the L1/E1 phase residuals, corresponding to regular GPS and Galileo, and E14 & E18 satellite signals, was at a comparable level, in the range of 6.5–8.7 mm. The study revealed that the Galileo satellites with incorrect orbits were fully usable in most geodetic, surveying and many other post-processed applications and may be beneficial especially for positioning during obstructed visibility of satellites. This claim holds true when providing precise ephemeris of satellites. Full article

By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S ^-1 of the cosmic scale factor S(t), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S ^-1 around the present epoch t₀, a non-vanishing shift per orbit (Δr) of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H₀ at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period P_b ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2–4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S^-1(t). More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose “elastic” parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ₁ of the first-order term of the power expansion of κ(t) can be preliminarily constrained in a model-independent way down to a κ₁ ≲ 2 x 10^-13 year^-3 level from latest Solar System’s planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≲ 10^-8 year^-3. Full article