Heliocentric Orbit Research Articles

Sensitivity and antenna pattern for an interplanetary laser trilateration network

An array of laser transponders, moving along orbits centered on Venus, Earth, and Mars, could provide significant new information about the distribution of mass in the solar system and beyond. In this report we begin an analysis of the sensitivity and effective antenna pattern for such a device. While the main source of changes in the lengths of the three legs of the Venus-Earth-Mars triangle is motion along the nearly circular heliocentric orbits of those bodies, measurable perturbations can be caused by other masses, either inside or outside the triangle. Our main focus here is on sources which are close to the ecliptic plane, and farther from the Sun than Jupiter. We present results on simulations of the ability of the transponder array to measure accelerations, and use that to describe the ability of the array to characterize sources of perturbing mass. Measurements of time-of-flight for short laser pulses between pairs of detectors directly constrains distance between them. Fitting a quadratic model to a daily collection of range measurements yields an estimate of the average daily difference in accelerations at those points, projected onto the baseline between them. Range measurements along a single baseline, with 1 ​cm accuracy, and a 1 ​Hz sampling cadence, will yield acceleration sensitivity of 10−15 ​m/s2, for each daily acceleration normal point. We consider two different types of sources: one is an isolated point mass, and the other is a sinusoidal variation in mass density along a circular arc. In both cases, we are able to characterize the performance of the transponder array. Simultaneous projections of acceleration differences onto the 3 baselines, at a single epoch, provide unique values for the mass and position of a single point source. Characterization of distributed sources requires a range of baseline orientations.

Solar Sail Augmented Hohmann Transfer

The aim of this Correspondence is to analyze the performance of a solar sail-based spacecraft in a two-impulse orbit transfer between circular and coplanar heliocentric orbits of assigned radii. In particular, assuming a transfer trajectory with a sweep angle and a flight time equal to those of a classical Hohmann orbit, the sail propulsive acceleration is used to minimize the total velocity variation required by the two tangential impulses. In this sense the work quantifies the optimal performance of a solar sail augmented Hohmann transfer as a function of the sail characteristics.

МЕТЕОРНА БАЗА ДАНИХ ЗА СПОСТЕРЕЖЕННЯМИ У 2019–2021 роках ІЗ ВИКОРИСТАННЯМ АВТОМАТИЗОВАНОГО ВІДЕОСПЕКТРАЛЬНОГО МЕТЕОРНОГО ПАТРУЛЯ ХАРКІВСЬКОГО НАЦІОНАЛЬНОГО УНІВЕРСИТЕТУ ІМЕНІ В. Н. КАРАЗІНА

The Database of positional and spectral observations of meteors in 2019–2021 using the automatical video and spectral meteor patrol of the Institute of Astronomy of V. N. Karazin Kharkiv National University has analyzed. The kinematic parameters and elements of the heliocentric orbits of meteoroids were calculated using the methods of meteor astronomy according to the Observation Database. This work describes the methods of processing of spectral video observations. The software “AVSMP_Pro v1” for meteor spectra analysis has been created that allows to generate synthetic spectra and compare them with observed meteor spectra. The data from the NIST ASD electronic database (https://physics.nist.gov/PhysRefData/ASD/lines_form.html) is used for obtaining the composition of chemical elements in the meteoroid. As a result, we obtain an information about the relative quantitative chemical composition of meteoroids and the physical conditions of meteor plasma formation.

Optimum Placement of PV Arrays on Arbitrarily Shaped Sites to Maximize the Amount of Light Received

Photovoltaic power generation has been done for a variety of sites. It is necessary to design the arrangement to consider the solar orbit dependent on latitude to increase the amount of light received by PV arrays. PV arrays can be packed into a site through arbitrary placement. However, this reduces the maintenance space for PV arrays. In addition, the shade created by front PV arrays reduces the amount of light received by behind PV arrays. Thus, packing PV arrays into a site is not the best solution. This study proposes optimization placement of PV arrays on arbitrarily shaped sites to maximize the amount of light received in arbitrary placement. The design variables of the PV array are the tilted angle, azimuth angle, and placement position of each PV array. The optimization problem to increase the total annual amount of light is solved using a genetic algorithm. The shaded area is calculated by ray tracing the sun rays. The effectiveness of the proposed method is demonstrated from several example analyses.

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.

Asteroid pairs: method validation and new candidates

Context. An asteroid pair can be described as two asteroids with very similar heliocentric orbits that are genetically related but not gravitationally bound. They can be produced by asteroid collisions or rotational fission. Although over 200 asteroid pairs are known, many more remain to be identified, especially among the newly discovered asteroids. Aims. The purpose of our work is to find new asteroid pairs in the inner part of the main belt with a new pipeline for asteroid pair search, and to validate the pipeline on a sample of known asteroid pairs. Methods. Initially, we selected pair candidates in the five-dimensional space of osculating orbital elements. Then the candidates were confirmed using numerical modeling with the backtrack integration of their orbits, including the perturbations from the largest main-belt asteroids and the influence of the non-gravitational Yarkovsky effect. Results. We performed a survey of the inner part of the main belt and found ten new probable asteroid pairs. Their estimated formation ages lie between 30 and 400 kyr. In addition, our pipeline was tested on a sample of 17 known pairs, and our age estimates agree with those indicated in the literature in most of the cases.

The young Hobson family: Possible binary parent body and low-velocity dispersal

Context.Asteroid families with ages younger than 1 Myr offer an interesting possibility of studying the outcomes of asteroid disruptions that are little modified by subsequent evolutionary processes.Aims.We analyze a very young asteroid family associated with (18777) Hobson in the central part of the main belt. We aim at (i) understanding its peculiar size distribution, and (ii) setting an upper limit on the characteristic dispersal velocity at subkilometer sizes corresponding to the smallest visible Hobson members.Methods.We identified the Hobson family using an up-to-date asteroid catalog. A significant increase in the number of its known members allowed us to study their size distribution and compare it with computer simulations of catastrophic disruptions. Backward orbital integrations of the heliocentric orbits allowed us to confirm the previously suggested age of Hobson and helped to estimate limits of the ejection speed.Results.The Hobson family has an unusual size distribution: two nearly equal-size bodies, followed by a population of smaller asteroids, whose distribution takes a characteristic power law. There are two possibilities to explain these data. Either a canonical impact onto a single parent body, requiring fine-tuned impact conditions that have not been studied so far, or an unconventional model for the parent object of the Hobson family, namely a binary with ≃7−9 km primary and a ≃2.5 km secondary. In the latter case, the primary was disrupted, leaving behind the largest remnant (18777) Hobson and a suite of subkilometer asteroids. The second largest asteroid, (57738) 2001 UZ160, is the nearly intact satellite of the parent binary. The excellent convergence of nominal orbits of Hobson members sets an upper limit of ≃(10−20) m s−1for the initial dispersal velocity of the known members, which is consistent with both formation models. The Hobson family provides a so far rare opportunity of studying disruptions of small asteroids in a situation in which both the material strength and reaccumulation efficiency play an important role.

An Improved Method to Measure Head Echoes Using a Meteor Radar

Abstract We present an improved methodology to obtain absolute position and velocity of meteor head echoes, which can yield orbital information, generally limited to the use of High-Power, Large-Aperture radars, using an advanced-designed specular meteor radar. The observations, which were performed during a period when an outburst of the β-Taurid meteor shower was expected, were performed with the Southern Argentine Agile MEteor Radar. Three different methodologies are utilized to confirm our results: an improved interferometric solver building on previous work, and two different target localization techniques using remote receiving stations. In addition, we performed simultaneous optical observations during the meteor shower period. Overall, 71 radar head echo events were detected and analyzed using interferometry, while 12 of those events have detected signals strong enough to be analyzed using localization methods at the remote sites. Due to poor weather, however, the optical cameras only observed two events simultaneously with the radar. Results from these events are in agreement with the radar results. We find that interferometry methods from both radar and optical data resulted in the most accurate estimation of meteor properties, while target localization techniques derived similar results, albeit with larger uncertainty. We also computed heliocentric meteoroid orbits, and while a fraction was hyperbolic, we believe these to be due to uncertainty. Two events are suspected to be β-Taurid shower members.

THOR: An Algorithm for Cadence-independent Asteroid Discovery

Abstract We present “Tracklet-less Heliocentric Orbit Recovery” (THOR), an algorithm for linking of observations of Solar System objects across multiple epochs that does not require intranight tracklets or a predefined cadence of observations within a search window. By sparsely covering regions of interest in the phase space with “test orbits,” transforming nearby observations over a few nights into the corotating frame of the test orbit at each epoch, and then performing a generalized Hough transform on the transformed detections followed by orbit determination filtering, candidate clusters of observations belonging to the same objects can be recovered at moderate computational cost and with little to no constraint on cadence. We validate the effectiveness of this approach by running on simulations as well as on real data from the Zwicky Transient Facility (ZTF). Applied to a short, two-week slice of ZTF observations, we demonstrate THOR can recover 97.4% of all previously known and discoverable objects in the targeted (a > 1.7 au) population with five or more observations and with purity between 97.7% and 100%. This includes 10 likely new discoveries, and a recovery of an e ∼ 1 comet C/2018 U1 (the comet would have been a ZTF discovery had THOR been running in 2018 when the data were taken). The THOR package and demo Jupyter notebooks are open source and available at https://github.com/moeyensj/thor.

Generalized sail trajectory approximation with applications to MagSails

This paper investigates approximate solutions to the two-dimensional equations of motion of a generalized sail-based spacecraft. A generalized sail is a propellantless propulsion system that produces a continuous thrust the magnitude of which varies with the heliocentric distance as 1/rη, where η is a positive real number that characterizes the propulsion system performance. Under the simplifying assumptions of low propulsive acceleration, constant thrust angle, and circular parking orbit, the spacecraft trajectory is approximated through closed-form relations. The general solution is then specialized to the case of a Magnetic Sail with a so-called “thick” operation mode, the latter being consistent with a kilometer-size loop radius. The effectiveness of the proposed mathematical model is verified by comparison with a numerical integration of the equations of motion, which confirms the accuracy of the analytical results even on very long timescales. Finally, the set of approximate equations is applied to the analysis of transfer trajectories towards a heliocentric target orbit with a given semimajor axis.

The Influence of Spacecraft Latitudinal Offset on the Accuracy of Corotation Forecasts

AbstractKnowledge of the ambient solar wind is important for accurate space weather forecasting. A simple‐but‐effective method of forecasting near‐Earth solar wind speed is “corotation,” wherein solar wind structure is assumed to be fixed in the reference frame rotating with the Sun. Under this approximation, observations at a source spacecraft can be rotated to a target location, such as Earth. Forecast accuracy depends upon the rate of solar wind evolution, longitudinal and latitudinal separation between the source and target, and latitudinal structure in the solar wind itself. The time‐evolution rate and latitudinal structure of the solar wind are both strongly influenced by the solar cycle, though in opposing ways. A latitudinal separation (offset) between source and target spacecraft is typically present, introducing an error to corotation forecasts. In this study, we use observations from the Solar Terrestrial Relations Observatory (STEREO) and near‐Earth spacecraft to quantify the latitudinal error. Aliasing between the solar cycle and STEREO orbits means that individual contributions to the forecast error are difficult to isolate. However, by considering an 18‐month interval near the end of solar minimum, we find that the latitudinal‐offset contribution to corotation forecast error cannot be directly detected for offsets <6°, but is increasingly important as offsets increase. This result can be used to improve solar wind data assimilation, allowing representivity errors in solar wind observations to be correctly specified. Furthermore, as the maximum latitudinal offset between L5 and Earth is ≈5°, corotation forecasts from a future L5 spacecraft should not be greatly affected by latitudinal offset.

Orbit design of a swarm for ultra-long wavelength radio interferometry with preliminary swarm and thruster sizing

Observing the universe in the Ultra-Long Wavelength (ULW) regime has been called the ‘last frontier in astronomy’—real imaging capabilities here are yet to be achieved. Obtaining an image of the sky in this frequency band can be done by employing a swarm of satellites that together act as an interferometer and collect the required imaging information pieces throughout the course of their operational life. Meeting the mission objective is challenging for such a swarm, since this imposes restrictions on the operational environment and the relative position and velocity vectors between the swarm elements. This work proposes an orbit solution in a Heliocentric Earth-Leading Orbit (HELO) for an autonomous CubeSat swarm with chemical thrusters. A distributed formation flying algorithm is used to aid the collection of the required imaging information pieces. Furthermore, the estimated total mission launch mass is reduced by optimising cost functions and finding favourable position and velocity at start of operational life, as well as by finding favourable thrust manoeuvre patterns. The results show that the mission objective—obtaining a 3D map of the Universe in ULW—can be achieved with 68 6U spacecraft (S/C). Moreover, the swarm can remain in a Radio Frequency Interference (RFI) quiet zone of >5 × 106 km, whilst not drifting further than ~ 6.6 × 106 km from Earth for an operational life of one year.

Pedal coordinates, solar sail orbits, Dipole drive and other force problems

Pedal coordinates provide a natural framework for studying force problems of classical mechanics in the plane. The trajectory of a test particle under the influence of central and Lorentz-like forces can be translated into pedal coordinates at once without the need of solving any differential equation. We generalize this result to cover more general force laws and also show the advantage of pedal coordinates in certain variational problems. These enable us to link together many dynamical systems as well as problems of the calculus of variation. Finally, we apply these results to compute orbits of Solar sail and Dipole drive.

A Theoretical Optimum Tilt Angle Model for Solar Collectors from Keplerian Orbit

Solar energy has been extensively used in industry and everyday life. A more suitable solar collector orientation can increase its utilization. Many studies have explored the best orientation of the solar collector installation from the perspective of data analysis and local-area cases. Investigating the optimal tilt angle of a collector from the perspective of data analysis, or guiding the angle of solar collector installation, requires an a priori theoretical tilt angle as a support. However, none of the current theoretical studies have taken the real motion of the Sun into account. Furthermore, a complete set of theoretical optimal tilt angles for solar energy is necessary for worldwide locations. Therefore, from the view of astronomical mechanics, considering the true orbit of the Sun, a mathematical model that is universal across the globe is proposed: the Kepler motion model is constructed from the solar orbit and transformed into the local Earth coordinate system. After that, the calculation of the optimal tilt angle solution is given. Finally, several examples are shown to demonstrate the variation of the optimal solar angle with month and latitude. The results show that for daily fixed solar collectors, the altitude angle of the collector should be about 6° above the noon solar altitude angle in summer and 6° lower in winter. For annual fixed collectors, the tilt angle should be slightly higher than the latitude. In summary, this study demonstrates that when a location is specified, this model can be used to calculate the theoretical optimum tilt angle of solar collectors for that position.

Thermal environment analysis for TianQin

TianQin is a proposed space-borne gravitational wave observatory in high geocentric orbits, exposed to radiating heat sources in space. Due to the stringent thermal stability requirements from the key payloads, the analysis of space thermal environment is of great importance. This paper studies the incident thermal radiation onto the TianQin satellites from the Sun–Earth–Moon system. The solar constant fluctuation (SCF) and the Earth’s land-type features, based on the meteorological data, are considered, and an analytic function of lunar surface temperature is used. The analysis includes the solar radiation, the infrared radiation, and the albedo. The results are discussed in both time and frequency domains. The spectral analysis indicates that in the target frequency band of 0.1 mHz–1 Hz, the SCF plays a dominant role, and that the associated incident thermal disturbance is ∼5 W m−2 Hz−1/2 for TianQin, at the same level of the LISA in heliocentric orbits. In addition, the power spectra of the Earth’s and Moon’s heating fluctuation are given, both order-of-magnitude weaker than that of the solar radiation. The results may contribute to the thermal design and the noise analysis for TianQin.

The great Chinese fireball of December 22, 2020

On December 22, 2020, at about 23h 23m 33s UTC a very bright fireball was seen in the sky of southeastern China. The fireball lasted for several seconds and ended with an atmospheric explosion that was detected by US surveillance satellites. According to CNEOS’s data, the fireball moved with a mean speed of 13.6 km/s and exploded at an altitude of about 35.5 km (Lat. 31.9^{circ } N; Long. 96.2^{circ } E). In this paper we estimate the atmospheric trajectory, the heliocentric orbit and the strewn fields for different mass/section ratio of the fragments. The trajectory was about from north to south and with low inclination (5^{circ } pm 2^{circ }) with respect to the local surface. The explosion height appears consistent with a fragmented rocky body, and the heliocentric orbit supports an asteroidal origin. The probable strewn field extends between two points with coordinates (+31.3^circ N; 96.3^circ E) and (+30.3^circ N; 96.5^circ E), for a total area of about 4000 text {km}^2. This large extension is a direct consequence of the low inclination of the trajectory. Given the unknown uncertainty of the CNEOS’s data, these results should be taken with caution.

The local dark sector

We speculate on the development and availability of new innovative propulsion techniques in the 2040s, that will allow us to fly a spacecraft outside the Solar System (at 150 AU and more) in a reasonable amount of time, in order to directly probe our (gravitational) Solar System neighborhood and answer pressing questions regarding the dark sector (dark energy and dark matter). We identify two closely related main science goals, as well as secondary objectives that could be fulfilled by a mission dedicated to probing the local dark sector: (i) begin the exploration of gravitation’s low-acceleration regime with a spacecraft and (ii) improve our knowledge of the local dark matter and baryon densities. Those questions can be answered by directly measuring the gravitational potential with an atomic clock on-board a spacecraft on an outbound Solar System orbit, and by comparing the spacecraft’s trajectory with that predicted by General Relativity through the combination of ranging data and the in-situ measurement (and correction) of non-gravitational accelerations with an on-board accelerometer. Despite a wealth of new experiments getting online in the near future, that will bring new knowledge about the dark sector, it is very unlikely that those science questions will be closed in the next two decades. More importantly, it is likely that it will be even more urgent than currently to answer them. Tracking a spacecraft carrying a clock and an accelerometer as it leaves the Solar System may well be the easiest and fastest way to directly probe our dark environment.

The Distribution of Open Clusters in the Galaxy

In this work we explore the new catalog of galactic open clusters that became available recently, containing 1,750 clusters that have been re-analyzed using the Gaia DR2 catalog to determine the stellar memberships. We used the young open clusters as tracers of spiral arms and determined the spiral pattern rotation speed of the Galaxy and the corotation radius, the strongest Galactic resonance. The sample of open clusters used here is increased by dozens of objects with respect to our previous works. In addition, the distances and ages values are better determined, using improvements to isochrone fitting and including an updated extinction polynomial for the Gaia DR2 photometric band-passes, and the Galactic abundance gradient as a prior for metallicity. In addition to the better age determinations, the catalog contains better positions in the Galactic plane and better proper motions. This allow us to discuss not only the present space distribution of the clusters, but also the space distribution of the clusters's birthplaces, obtained by integration of the orbits for a time equal to their age. The value of the rotation velocity of the arms (28.5 ± 1.0 km s−1 kpc−1) implies that the corotation radius (Rc) is close to the solar Galactic orbit (Rc/R0 = 1.01±0.08), which is supported by other observational evidence discussed in this text. A simulation is presented, illustrating the motion of the clusters in the reference frame of corotation. We also present general statistics of the catalog of clusters, like spatial distribution, distribution relative to height from the Galactic plane, and distribution of ages and metallicity. An important feature of the space distribution, the corotation gap in the gas distribution and its consequences for the young clusters, is discussed.

Accurate 3D fireball trajectory and orbit calculation using the 3D-firetoc automatic Python code

ABSTRACT The disruption of asteroids and comets produces cm-sized meteoroids that end up impacting the Earth’s atmosphere and producing bright fireballs that might have associated shock waves or, in geometrically favourable occasions excavate craters that put them into unexpected hazardous scenarios. The astrometric reduction of meteors and fireballs to infer their atmospheric trajectories and heliocentric orbits involves a complex and tedious process that generally requires many manual tasks. To streamline the process, we present a software package called SPMN 3D Fireball Trajectory and Orbit Calculator (3D-firetoc), an automatic Python code for detection, trajectory reconstruction of meteors, and heliocentric orbit computation from video recordings. The automatic 3D-firetoc package comprises of a user interface and a graphic engine that generates a realistic 3D representation model, which allows users to easily check the geometric consistency of the results and facilitates scientific content production for dissemination. The software automatically detects meteors from digital systems, completes the astrometric measurements, performs photometry, computes the meteor atmospheric trajectory, calculates the velocity curve, and obtains the radiant and the heliocentric orbit, all in all quantifying the error measurements in each step. The software applies corrections such as light aberration, refraction, zenith attraction, diurnal aberration, and atmospheric extinction. It also characterizes the atmospheric flight and consequently determines fireball fates by using the α − β criterion that analyses the ability of a fireball to penetrate deep into the atmosphere and produce meteorites. We demonstrate the performance of the software by analysing two bright fireballs recorded by the Spanish Fireball and Meteorite Network (SPMN).

A Numerical Approach to Study Ablation of Large Bolides: Application to Chelyabinsk

In this study, we investigate the ablation properties of bolides capable of producing meteorites. The casual dashcam recordings from many locations of the Chelyabinsk superbolide associated with the atmospheric entry of an 18 m in diameter near-Earth object (NEO) have provided an excellent opportunity to reconstruct its atmospheric trajectory, deceleration, and heliocentric orbit. In this study, we focus on the study of the ablation properties of the Chelyabinsk bolide on the basis of its deceleration and fragmentation. We explore whether meteoroids exhibiting abrupt fragmentation can be studied by analyzing segments of the trajectory that do not include a disruption episode. We apply that approach to the lower part of the trajectory of the Chelyabinsk bolide to demonstrate that the obtained parameters are consistent. To do that, we implemented a numerical (Runge–Kutta) method appropriate for deriving the ablation properties of bolides based on observations. The method was successfully tested with the cases previously published in the literature. Our model yields fits that agree with observations reasonably well. It also produces a good fit to the main observed characteristics of Chelyabinsk superbolide and provides its averaged ablation coefficient σ = 0.034 s2 km−2. Our study also explores the main implications for impact hazard, concluding that tens of meters in diameter NEOs encountering the Earth in grazing trajectories and exhibiting low geocentric velocities are penetrating deeper into the atmosphere than previously thought and, as such, are capable of producing meteorites and even damage on the ground.