Orbital Velocity Research Articles

Space Debris In-Orbit Detection with Commercial Automotive LiDAR Sensors

This article presents an alternative approach to detecting and mapping space debris in low Earth orbit by utilizing commercially available automotive LiDAR sensors mounted on CubeSats. The main objective is to leverage the compact size, low weight, and minimal power consumption of these sensors to create a “Large Cosmic LiDAR” (LCL) system. This LCL system would operate similarly to a giant radar circling the Earth, with strategically positioned LiDAR sensors along the target orbit. The article examines the feasibility of this concept by analyzing the relative orbital velocity between the sensor and debris objects, and calculating the time required to scan a complete orbit.

Characterisation of turbulence at sites with coexisting waves and currents: An analysis by empirical mode decomposition

This paper presents a novel side information assisted Empirical Mode Decomposition (EMD) method for separating wave orbital velocity from a combined wave-tidal current velocity data, measured by three different Acoustic Doppler Current Profilers (ADCPs) deployed in the Pentland Firth, Orkney Waters, UK. The effectiveness of this technique is confirmed through two methods: (1) the spectra of the wave-removed velocity align with the Kolmogorov −5/3 power law, and (2) the extracted wave orbital velocities were used to derive significant wave heights, which were validated against wave heights measured by the same ADCPs and through numerical modelling carried out with a coupled wave-current tool (TOMAWAC-TELEMAC 3D).The decomposed data was further used to calculate three-dimensional turbulence intensities (TI) for combined wave-current, wave-only, and current-only conditions, across different flow speeds and wave heights. The results demonstrate the robustness of the decomposition method in various scenarios and quantify the individual TI contributions from waves, currents, and their combined effects. This work provides valuable insights into the dynamics of areas where waves and currents coexist.

Describing Kepler Orbits with the Ulianov Orbital Model

This paper presents the Ulianov Orbital Model (UOM), a simplified approach to two-body orbital mechanics. The UOM provides equations to calculate the standard ellipse parameters (a and b) and orbital trajectories and velocities from three UOM basic parameters (Ue, R0, and V0). It introduces a new kind of elliptical trigonometric functions, which simplify plotting orbital trajectories and their velocities over time and in elliptical angular steps. The Ulianov Elliptic Transform (UET), generates an impressive effect of rotating and scaling an ellipse, transferring its center from one of the foci to the geometric center of the ellipse. The UET offers a new and easy way to create and manipulate ellipses using both numerical and analytical methods.

Hot spots around Sagittarius A*. Joint fits to astrometry and polarimetry

Observations of Sagittarius A* ( in the near-infrared (NIR) show irregular flaring activity. Flares coincide with the astrometric rotation of the brightness centroid and with looping patterns in fractional linear polarization. These signatures can be explained with a model of a bright hot spot, transiently orbiting the black hole. We extend the capabilities of the existing algorithms to perform parameter estimation and model comparison in the Bayesian framework using NIR observations from the GRAVITY instrument, and simultaneously fitting the astrometric and polarimetric data. Using the numerical radiative transfer code we defined several geometric models describing a hot spot orbiting Sgr A*, threaded with a magnetic field, and emitting synchrotron radiation. We then explored the posterior space of our models with a nested sampling code We used Bayesian evidence to make comparisons between the models. We have used 11 models to sharpen our understanding of the importance of various aspects of the orbital model, such as non-Keplerian motion, hot-spot size, and off-equatorial orbit. All considered models converge to realizations that fit the data well, but the equatorial super-Keplerian model is favoured by the currently available NIR dataset. We have inferred an inclination of $ deg, which corroborates previous estimates, a preferred period of $ minutes, and an orbital radius of $ gravitational radii with the orbital velocity of $ times the Keplerian value. A hot spot with a diameter smaller than 5 gravitational radii is favoured. Black hole spin is not constrained well.

Optical parameter design model of hemispherical laser retroreflector arrays for satellite laser ranging

A laser retroreflector array (LRA) with multiple retroreflectors is used to directionally reflect an incident laser beam and aims to enhance the received signal strength into laser ranging ground stations. A comprehensive mathematical equation of the received photons is established by modelling the LRA far field diffraction intensity (FFDI) and the satellite velocity aberration position. Based on this received photon model, a novel method on designing the dihedral angle offset and the aperture of retroreflectors is proposed, which maximizes the received photon under the minimal elevation angle of the ground station. Taking the hemispherical structure parameters of Chinese HY-2 satellite LRA and the specification parameters of the Shanghai Astronomical Observatory, the optimal aperture and the dihedral angle offset of the HY-2 laser retroreflectors are 17 mm and 1.6″, respectively. These two optimal optical parameters make the received photon under the elevation angle of 0° reach ∼0.9 count per laser shot. Until now, ∼851,400 successful observations have been successfully obtained by global ground stations since the first launch of HY-2 satellite series in 2011, which guarantees the high-precise orbit determination of HY-2 satellite series.

Investigating new aspects of Bocharova–Bronnikov–Melnikov–Bekenstein spacetime: ionized thin accretion disk model

Accretion processes near black hole candidates are associated with the high-energy emission of radiation from relativistic particles and outflows. It is widely believed that the magnetic field plays a crucial role in explaining these high-energy processes near these astrophysical sources. In this work, we analyze thin accretion disks in the Bocharova–Bronnikov–Melnikov–Bekenstein (BBMB) spacetime framework using the Novikov–Thorne model. Our study examines the thermal and optical characteristics of these disks, including their emission rate and luminosity in the specified spacetime. Later, we extend the Novikov–Thorne model to ionized thin accretion disk. We propose that the black hole is embedded in an asymptotically uniform magnetic field. We investigate the dynamics of charged particles near a weakly magnetized black hole. Our findings show that, in the presence of a magnetic field, the radius of the marginally stable circular orbit (MSCO) for a charged particle is close to the black hole’s horizon. The orbital velocity of the charged particle, as measured by a local observer, has been computed in the presence of the external magnetic field. We also present an analytical expression for the four-acceleration of the charged particle orbiting around black holes. Finally, we determine the intensity of the radiation emitted by the accelerating relativistic charged particle orbiting the magnetized black hole.

VELOcities of CEpheids (VELOCE)

Classical Cepheids provide valuable insights into the evolution of stellar multiplicity among intermediate-mass stars. Here, we present a systematic investigation of single-lined spectroscopic binaries (SB1s) based on high-precision velocities measured by the VELOcities of CEpheids (VELOCE) project. We detected 76 (29%) SB1 systems among the 258 Milky Way Cepheids in the first VELOCE data release, 32 (43%) of which were not previously known to be SB1 systems. We determined 30 precise and three tentative orbital solutions, 18 (53%) of which are reported for the first time. This large set of Cepheid orbits provides a detailed view of the eccentricity e and orbital period Porb distribution among evolved intermediate-mass stars, ranging from e ∈ [0.0, 0.8] and Porb ∈ [240, 9000] d. The orbital motion on timescales exceeding the 11 yr VELOCE baseline was investigated using a template-fitting technique applied to literature data. Particularly interesting objects include (a) R Cru, the Cepheid with the shortest orbital period in the Milky Way (∼238 d); (b) ASAS J103158−5814.7, a short-period overtone Cepheid exhibiting time-dependent pulsation amplitudes as well as orbital motion; and (c) 17 triple systems with outer visual companions, among other interesting objects. Most VELOCE Cepheids (21/23) that exhibit evidence of a companion based on a Gaia proper motion anomaly are also spectroscopic binaries, whereas the remaining do not exhibit significant (> 3σ) orbital radial velocity variations. Gaia quality flags, notably the renormalized unit weight error (RUWE), do not allow Cepheid binaries to be identified reliably although statistically the average RUWE of SB1 Cepheids is slightly higher than that of non-SB1 Cepheids. A comparison with Gaia photometric amplitudes in G-, Bp, and Rp also does not allow one to identify spectroscopic binaries among the full VELOCE sample, indicating that the photometric amplitudes in this wavelength range are not sufficiently informative of companion stars.

An improved particle filtering projectile trajectory estimation algorithm fusing velocity information

This study proposes an improved particle-filtering projectile trajectory estimation method that fuses velocity information to address the susceptibility to interference and large fluctuations in position and velocity measurements of a single-antenna-two-dimensional trajectory correction fuze. By considering the Doppler effect in satellite velocity measurements and the residuals between the model-derived velocity and velocity derived from the translational Doppler frequency shift, a sliding time window was established to generate velocity weight coefficients that dynamically adjust the weight of the velocity in filtering. By modifying the likelihood function, a particle-filtering algorithm was designed to achieve a fusion estimation of the projectile trajectory. Tests indicate that this method provides more accurate estimates of the position and velocity of the projectile compared to other existing methods, which can reduce the impact of velocity fluctuations to a certain extent. In addition, the computational burden is not increased and can directly replace existing mature algorithms in engineering.

Galileo's ship and the relativity principle

AbstractIt is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It is also commonly believed that this principle holds the key to answering why, for example, we do not notice the orbital velocity of the Earth as we go about our day. And yet, I argue in this paper that the precise content of this principle is ambiguous: standard presentations, in both physics and philosophy, fail to distinguish between two principles that are ultimately inequivalent, the “External Galilean Relativity Principle” (EGRP) and the “Internal Galilean Relativity Principle” (IGRP). I demonstrate that EGRP and IGRP play distinct roles in physics practice (e.g., EGRP is connected to the concept of Galilean invariance, but IGRP is not) and that many classical systems that satisfy IGRP fail to satisfy EGRP. I further show that the Relativity Principle famously discussed by Einstein in 1905—which is not restricted to classical systems—also leads to two inequivalent principles, an external one analogous to EGRP, and an internal one analogous to IGRP. I conclude by highlighting that the phenomenon originally captured by Galileo's famous ship passage is much more general than contemporary discussions in the philosophy of symmetries suggest.

Shocking and Mass Loss of Compact Donor Stars in Type Ia Supernovae

Type Ia supernovae arise from thermonuclear explosions of white dwarfs accreting from a binary companion. Following the explosion, the surviving donor star leaves at roughly its orbital velocity. The discovery of the runaway helium subdwarf star US 708, and seven hypervelocity stars from Gaia data, all with spatial velocities ≳900 km s−1, strongly support a scenario in which the donor is a low-mass helium star or a white dwarf. Motivated by these discoveries, we perform three-dimensional hydrodynamical simulations with the Athena++ code, modeling the hydrodynamical interaction between a helium star or helium white dwarf and the supernova ejecta. We find that ≈0.01–0.02 M ⊙ of donor material is stripped, and explain the location of the stripped material within the expanding supernova ejecta. We continue the postexplosion evolution of the shocked donor stars with the MESA code. As a result of entropy deposition, they remain luminous and expanded for ≈105–106 yr. We show that the postexplosion properties of our helium white dwarf donor agree reasonably with one of the best-studied hypervelocity stars, D6-2.

The Resident Space Object Detection Method Based on the Connection between the Fourier Domain Image of the Video Data Difference Frame and the Orbital Velocity Projection

The Resident Space Object Detection Method Based on the Connection between the Fourier Domain Image of the Video Data Difference Frame and the Orbital Velocity Projection

Parametrizing nonlinearity in orbital velocity at fetch-limited, low-energy beaches

Wave nonlinearity plays an important role in cross-shore beach morphodynamics and is often parameterized in engineering-type morphodynamic models through a nonlinear relationship with the Ursell number. It is not evident that the relationship established in previous studies also holds for sheltered sites with fetch-limited seas as they are more prone to effects of local winds and currents, the waves are generally steeper, and the beaches are typically reflective. This study investigates near-bed orbital velocity nonlinearity from wave records collected at two sheltered beaches in The Netherlands and contrasts them to earlier observations made along the exposed, wave-dominated North Sea coast. Our observations at sheltered beaches show that the Ursell number has comparable skill in predicting wave nonlinearity as it has on previously studied exposed coasts. However, the orbital velocities at sheltered coasts are more asymmetric for the same Ursell number than on exposed coasts. When exposed coast data were examined for moments with comparable high-steepness waves, a similar effect on asymmetry was observed. In addition, following and opposing winds were found to have a clear relationship with total nonlinearity, while they did not affect the phase between skewness and asymmetry at the sheltered beaches. Refitting the free parameters of an Ursell-based predictor improved the bias for the asymmetry parameterization. Whether this has implications for modeling of the magnitude of wave-nonlinearity-driven sediment transport using engineering type models is strongly dependent on the sediment transport formulation used, as these formulations depend on additional calibration coefficients too.

High-resolution Transmission Spectroscopy of Warm Jupiters: An ESPRESSO Sample with Predictions for ANDES

Abstract Warm Jupiters are ideal laboratories for testing the limitations of current tools for atmospheric studies. The cross-correlation technique is a commonly used method to investigate the atmospheres of close-in planets, leveraging their large orbital velocities to separate the spectrum of the planet from that of the star. Warm Jupiter atmospheres predominantly consist of molecular species, notably water, methane, and carbon monoxide, often accompanied by clouds and hazes muting their atmospheric features. In this study, we investigate the atmospheres of six warm Jupiters, K2-139 b, K2-329 b, TOI-3362 b, WASP-130 b, WASP-106 b, and TOI-677 b, to search for water absorption using the ESPRESSO spectrograph, reporting nondetections for all targets. These nondetections are partially attributed to planets having in-transit radial velocity changes that are typically too small (≲15 km s−1) to distinguish between the different components (star, planet, Rossiter-McLaughlin effect, and telluric contamination), as well as the relatively weak planetary absorption lines as compared to the signal-to-noise ratio of the spectra. We simulate observations for the upcoming high-resolution spectrograph ANDES at the Extremely Large Telescope for the two favourable planets on eccentric orbits, TOI-3362 b and TOI-677 b, searching for water, carbon monoxide, and methane. We predict a significant detection of water and CO, if ANDES indeed covers the K-band, in the atmospheres of TOI-677 b and a tentative detection of water in the atmosphere of TOI-3362 b. This suggests that planets on highly eccentric orbits with favourable orbital configurations present a unique opportunity to access cooler atmospheres.

Evidence of Water Vapor in the Atmosphere of a Metal-rich Hot Saturn with High-resolution Transmission Spectroscopy

Transmission spectroscopy presents one of the most successful approaches for investigating the atmospheres of exoplanets. We analyzed the near-infrared high-resolution transmission spectrum of a hot Saturn, HD 149026 b, taken using CARMENES spectrograph ( R∼80,400 ). We found evidence of H2O at a signal-to-noise ratio (S/N) of ∼4.8. We also performed grid search using a Bayesian framework and constrained the orbital velocity K p and rest velocity V rest to 158.17−7.90+8.31 km s−1 and 2.57−0.57+0.54 km s−1, respectively. While the retrieved K p value is consistent with theoretical prediction, the retrieved V rest value is highly redshifted (>3σ). This might be an indication of either anomalous atmospheric dynamics at play or an orbit with nonzero eccentricity. Additionally, we searched for HCN but no successful detection has been made, possibly due to the relatively low-S/N data set. The detection of H2O and subsequent retrieval of its abundance, coupled with analysis of other species such as CO in the K band, for example, might help us to get some information about the atmospheric C/O ratio and metallicity, which in turn could give us some insight into the planet’s formation scenario.

Kinematics of nonlinear waves over variable bathymetry. Part I: Numerical modelling, verification and validation

Fluid particle kinematics due to wave motion (i.e. orbital velocities and accelerations) at and beneath the free surface is involved in many coastal and ocean engineering applications, e.g. estimation of wave-induced forces on structures, sediment transport, etc. This work presents the formulations of these kinematics fields within a fully nonlinear potential flow (FNPF) approach. In this model, the velocity potential is approximated with a high-order polynomial expansion over the water column using an orthogonal basis of Chebyshev polynomials of the first kind. Using the same basis, original analytical expressions of the components of velocity and acceleration are derived in this work. The estimation of particle accelerations in the course of the simulation involves the time derivatives of the decomposition coefficients, which are computed with a high-order backward finite-difference scheme in time. The capability of the numerical model in computing the particle kinematics is first validated for regular nonlinear waves propagating over a flat bottom. The model is shown to be able to predict both the velocity and acceleration of highly nonlinear and nearly breaking waves with negligible error compared to the corresponding stream function wave solution. Then, for regular waves propagating over an uneven bottom (bar-type bottom profile), the simulated results are confronted with existing experimental data, and very good agreement is achieved up to the sixth-order harmonics for free surface elevation, velocity and acceleration.

Research on relative reachable domain in target orbit for maneuvering spacecraft

PurposeLots of successful space missions require that the maneuvering spacecraft can reach the target spacecraft. Therefore, research on relative reachable domain (RRD) in target orbit for maneuvering spacecraft is particularly important and is currently a hot-debated topic in the field of aerospace. This paper aims at analyzing and simulating the RRD in target orbit for maneuvering spacecrafts with a single fixed-magnitude impulse and continuous thrust, respectively, to provide a basis for analyzing the feasibility of spacecraft maneuvering missions and improving the design efficiency of spacecraft maneuvering missions.Design/methodology/approachBased on the kinematics model of relative motion, RRD in target orbit for maneuvering spacecraft with a single fixed-magnitude impulse can be calculated via analyzing the relationship between orbital elements, position vector and velocity vector of spacecrafts, and relevant studies are introduced to compare simulation results for the same case and validate the method proposed in the paper. With analysis of the dynamic model of relative motion, the calculation of RRD in target orbit for maneuvering spacecraft with continuous thrust can be transformed as the solution of the optimal control problem, and example emulations are carried out to validate the method.FindingsFor the case with a single fixed-magnitude impulse, simulation results show preliminarily that the method is in agreement with the method in Ref. (Wen et al., 2016), which treats the same case and thus is plausibly correct and feasible. For the case with continuous thrust, analysis and simulation results confirm the validity of the proposed method. The methods based on relative motion in this paper can efficiently determining the RRD in target orbit for maneuvering spacecraft.Originality/valueBoth theoretical analyses and simulation results indicate that the method proposed in this paper is comparatively simple but efficient for determine the RRD in target orbit for maneuvering spacecraft swiftly and precisely.

Monitoring tides, currents, and waves along coastal habitats using the Mini Buoy

AbstractIntertidal habitats are shaped by the actions of tides and waves which are difficult to monitor in shallow water. To address this challenge, the “Mini Buoy” and associated open‐source App were recently developed for the low‐cost and long‐term monitoring of tidal inundation and current velocities simultaneously. The Mini Buoy is a bottom‐mounted float that measures tilt to infer near‐bed hydrodynamics. Here, we present significant updates to the Mini Buoy and App. Two new Mini Buoy designs were calibrated: the “Pendant” that requires minimal assembly for deployment, and the “B4+” that can also measure wave orbital velocity. Comparisons against industry‐standard water‐level and velocity sensors deployed in the field showed that each new design was effective at detecting tidal inundation (overall accuracy of 86–97%) and current velocities (R2 = 0.73–0.91; accuracies of ± 0.14–0.22 m s−1; detection limits between 0.02 and 0.8 m s−1). The B4+ could reasonably measure wave orbital velocities (R2 = 0.56; accuracies of ± 0.18 m s−1; detection limits between 0.02 and 0.8 m s−1). Reducing the sampling rate to prolong survey durations did not markedly reduce the precision of velocity measurements, except in the original Mini Buoy design (uncertainty increased by ± 2.11 m s−1 from 1 to 10 s sampling). The updated App enhances user experience, accepts data from any Mini Buoy design, is suitable for generic use across any tidal setting, and presents multiple options to understand and contrast local hydrodynamic regimes. Improvements to the Mini Buoy designs and App offer greater opportunities in monitoring hydrodynamics for purposes including ecosystem restoration and flood risk management.

Viva ‘Vis-viva’

Long live the vis-viva equation. There is sometimes more than one way of telling a story with the same ending, and this is particularly true in the field of applied mathematics where there are often different ways of obtaining the same result to a given problem, so that what might be lost or not appreciated in one approach can be found and appreciated in another. It is the purpose here to illustrate this by presenting a well-known example drawn from the field of orbital dynamics, namely the development of what is called the Vis-viva equation. This equation is simply an expression relating the square of the velocity of an orbiting object, for example a planet orbiting a sun, to orbit parameters and scientific constants. It is a standard workhorse equation that is used extensively today by orbit control specialists wishing to determine and affect velocities of spacecraft orbiting significantly larger masses, and it was developed from work carried out centuries ago by Gottfried Leibniz (1646 – 1716). The first story will simply acknowledge the equation and how it arose. The second story will present an alternative approach based on calculus, trigonometry, algebra and computations set against the backdrop of an ellipse geometry. This second story leads to the vis-viva equation in disguise, so to speak, and examples of the speeds of two planets, Earth and Mercury, orbiting the Sun will be discussed. Where relevant, the nomenclature of orbit dynamics will be acknowledged. The discussion will involve primarily a planet’s orbit velocity of translation and detailed considerations will not be given to effects due to its speed of rotation.

Calculating Global Navigation Satellite System Satellite Velocities and Accelerations by Utilizing the Orbit Fitting and Orbit Integration Methods

Calculating Global Navigation Satellite System Satellite Velocities and Accelerations by Utilizing the Orbit Fitting and Orbit Integration Methods

Neutron emission from a source moving in a gravitational field

This work is devoted to the problem of neutron field formation near elliptical orbits of space objects equipped with nuclear power plants. The high-energy part of the fission spectrum is not affected by the gravitational field. Radiation safety is ensured by the triad fair for a point source: activity-distance-time. The connection between space object orbit parameters and neutron flux density occurs for the thermal (near-thermal) part of the spectrum. The possibility of formation of a stable neutron trace in the volume of a «torus» around the orbit of a space object is considered. The paper presents theoretical and numerical evidence of the validity of the hypothesis put forward. The introduction considers the separation effect of Galileo's relativity principle in the case of rectilinear uniform motion of a point isotropic neutron source on a plane. The occurrence of angular asymmetry of the neutron distribution in a stationary coordinate system when their relative velocity is close to the transport velocity of the source is illustrated. Under these conditions, a significant velocity dispersion of initially monochromatic neutrons is also recorded. This expected fundamental kinematic effect determines the characteristic distribution of neutrons in the gravitational field when the source moves along the Kepler orbit. The solution of the problem is carried out in the velocity space. It is argued that if the distribution of neutrons in the velocity space is such that their velocities are collinear to the orbital velocity of the source, this indicates the existence of a neutron flux near the orbit. The problem is analysed on the example of one revolution of a hypothetical space station by simulation modelling. For this purpose, thermal neutron packets with isotropic angular distribution were generated at eight points of an elliptical orbit. The neutron and source velocity fluxes at the selected points of the orbit were compared in a coordinate system related to the earth. The obtained data made it possible to calculate the densities of neutron velocity fluxes to the front and rear hemispheres relative to the source orbital motion as a function of the polar angle, while the value of the determinant of the correlation matrix – an indicator of collinearity of neutron velocity vectors in the flux - was fixed. The results of the studies confirm the hypothesis put forward about the possibility of formation of a «trace» in the orbit of a thermal neutron source, which determines the need to take it into account as a significant component of radiation risk.