Heliocentric Motion Research Articles

A simplified analytical approach for determining eclipses of satellites occulted by a celestial body

The primary objective of this paper is to construct an analytical model for determining the total duration of eclipse events of satellites. The approach is based on the assumption that the trace formed in the orbital plane, cutting body’s shadow under the classical conical shadow model, can be described as an ellipse. This allows for the derivation of its parameters through the use of classical orbital elements and solar position in the body’s centric frame. Consequently, the problem of identifying satellite occultation events is simplified to searching for points of intersection between two ellipses: the satellite orbit and the shadow. The developed model has been demonstrated to be applicable for a wide range of inclinations, with the exception of cases where the orbital plane of the satellite's motion coincides with that of the sun's in the body-centric frame. It is shown that the shadow function constructed under the aforementioned assumptions can be simplified in the cylindrical shadow model. Several simplifications are provided in the research. The paper also considers the extension of the model to account for the non-spherical shape of celestial bodies and presents an algorithm for accounting for changes in eclipse duration caused by the heliocentric motion of celestial bodies. The model has been validated through numerous tests with a numerical algorithm and satellite real data, as well as with other analytical models.

Optimization of Solar-Sail Control When a Vehicle Moves along Cyclic Heliocentric Trajectories

This paper considers the problem of constructing time-optimal trajectories for a spacecraft (SC) with a solar sail. The trajectories under consideration consist of repeated cycles of spacecraft movement to the target heliocentric orbit and back to the initial one. A model of a perfectly reflecting sail is used, which allows using the programs for optimal control of the sail angle, obtained on the basis of the Pontryagin maximum principle. The heliocentric motion is modeled in a flat polar coordinate system, and the spacecraft itself makes cyclic flights between two terrestrial planets along a closed trajectory. A boundary-value problem is formulated, in the solution of which the approach of the spacecraft to the target planet with the equalization of velocities is ensured (the encounter problem). Simulations of four cycles of Earth–Mercury–Earth and Earth–Mars–Earth motion with a characteristic acceleration of the solar sail of 0.25 mm/s2 have been carried out, for which the duration of one cycle is on average 2000 and 2341 days, respectively. Optimal sail-orientation control programs are obtained for a wide range of launch dates, and methods of searching for and choosing the initial values of conjugate variables are shown. The obtained results demonstrate the ability of a spacecraft with a solar sail to implement controlled motion along closed trajectories with a minimum duration of individual Earth–destination planet–Earth flights.

Optical characteristics of a multilayer solar sail and their effect on its heliocentric motion

The purpose of this work is to determine the influence of the optical characteristics of a thin multilayer solar sail on its orbital motion. First of all, the influence of the coefficients of reflection, scattering and absorption is investigated. These coefficients are computed on the basis of a mathematical model of the optical characteristics of a multilayer epitaxial thin film which is a solar sail itself. The paper considers the effect of temperature changes and sail surface degradation on its optical properties. Modeling of changes in optical characteristics is carried out drawing on an example of heliocentric flight from the Earth to Mercury applying locally optimal control laws. Applying the transfer matrix method and considering the distribution of solar spectral radiation optical parameters for two distinct constructions of a solar sail were obtained (aluminum and silver front coating).

The meteoroid stream of comet 109P/Swift-Tuttle, Perseids, and further related meteor showers

The meteoroid stream of comet 109P/Swift-Tuttle, the well-known parent body of the Perseids, #7, is studied. The meteoroids released from the comet’s surface more than about 20kyr ago evolved to orbits similar to the mean orbits of 49 Andromedids, #549, and, possibly, also of the o-Aurigids, #696. These showers are similar to the Perseids and can be regarded as Perseid sub-structures. Interestingly, the modeled, as well as the real, o-Aurigids have a smaller perihelion distance. If they are regarded as a sub-structure of the Perseids, then we can speak about the bimodal structure of this major shower. Some meteoroids of the 109P’s stream, which could evolve over a longer period than about 40kyr, moved into the orbits on which they approach the Earth from the southern sky. They constitute a further shower related to 109P, the o-Hydrids, #569. We found an indication that the January β-Craterids, #582, moving in orbits similar to the o-Hydrids, could also be related to the comet. The radiant areas of the Perseids, 49 Andromedids and o-Aurigids are symmetrical to the radiant areas of the o-Hydrids and January β-Craterids in respect to the apex of the Earth’s heliocentric motion.

Trajectory approximation of a passively actuated solar balloon in near-Earth mission scenarios

The aim of this paper is to investigate the heliocentric motion of a passively actuated solar balloon placed at a distance of about one astronomical unit from the Sun. The analysis exploits a recent thrust model, according to which a solar balloon undergoes a passive control of its lightness number (that is, the ratio of the generated thrust to the local weight of the entire spacecraft) in the form a proportional feedback controller of constant gain. The spacecraft trajectory is obtained with a regularization of the equations of motion, in such a way that the heliocentric dynamics of the passively actuated solar balloon becomes equivalent to that of a nonlinear oscillator with a single degree of freedom. The approximate solution available for this type of nonlinear oscillator is then used to accurately describe the heliocentric motion of the passively actuated solar balloon and to analyze a couple of mission scenarios, that is, the execution of a phasing maneuver on an elliptical working orbit and the rotation of the apse line of the osculating orbit.

Meteoroid Stream of Comet C/1961 T1 (Seki) and Its Relation to the December ρ-Virginids and γ-Sagittariids

Abstract We answer the question of whether long-period comet C/1961 T1 (Seki) is the parent body of a meteor shower observed in Earth’s atmosphere. We model discrete parts of a meteoroid stream associated with this comet and follow the orbital evolution of its particles via a numerical integration of their orbits. The gravitational perturbations of major planets and the Poynting–Robertson effect, which influences the motion of the particles, are taken into account. We predict two showers which are related to C/1961 T1. One of these showers was identified with the December ρ-Virginids, #502. This identification confirms an earlier suggested relationship between the shower and the comet. The second predicted shower was identified with the γ-Sagittariids, #657. The radiant areas of both showers are symmetrical in respect to the apex of Earth’s heliocentric motion.

Influence of temperature restrictions on the heliocentric motion controlling of a solar-sailing spacecraft

Solar sailing spacecraft uses the light pressure to change the trajectory and are most effective in the immediate Sun vicinity, but the sail surface temperature most significant increases in the same area. Therefore, when designing solar sailing “hot” missions, we should consider the temperature restriction when choosing the control laws. The paper proposes the following approach to the implementation of the temperature restriction. When exceeding a predetermined temperature limit values the sail deviates from the direction of the radiation flux so that the direction of the acceleration projection on the Ecliptic plane is not changed, but the total sail orientation angle increased. The additional acceleration that occurs when using this approach, directed along the Ecliptic normal, can be used to rotate the orbital plane, if this is necessary to fulfill the flight purpose or to form a cylindrical orbit.

Non-coplanar interplanetary flight simulation considering motion relative to the center of mass peculiarities of solar sail spacecraft

The paper is devoted to the non-coplanar interplanetary Earth–Venus flight of a spacecraft equipped with a non-perfectly reflecting solar sail, the magnitude and direction of acceleration from which is calculated taking into account specular and diffuse reflections, absorption and transmission of photons by the surface of the solar sail. The goal of the heliocentric motion is to transfer the solar sail spacecraft into the Hill sphere of Venus with zero hyperbolic excess of speed. A feature of the paper is the study of the motion of a non-perfectly reflecting solar sail spacecraft taking into account the motion relative to the center of mass. The problem is divided into three stages. At the first stage, a nominal program for controlling the motion of the spacecraft center of mass is formed. At the second stage, sufficient angular velocities are determined to ensure the obtained nominal control program and the parameters of the spacecraft controls – thin-film controls located along the perimeter of the solar sail – are calculated. The operating principle of the thin-film controls is quite simple. When the voltage applied to the thin-film controls changes, they become transparent or opaque, there is a difference in the normal components of the light pressure forces, which provides a control torque for changing the orientation of the spacecraft in space. At the third stage, the joint motion of the center of mass and relative to the center of mass of the spacecraft is simulated to demonstrate the feasibility of the obtained control program. As a result, a comparison is made of non-coplanar interplanetary Earth–Venus flights with and without thin-film control elements.

An effective-gravity perspective on the Sun–Jupiter–comet three-body system

Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the framework of Newtonian gravity. The exact relativistic treatment of the problem is not an easy task, but this paper develops an approximate calculational scheme which computes for the first time the tiny effective-gravity correction to the equation of the surface for all points of which it is equally advantageous to regard the heliocentric motion as being perturbed by the attraction of Jupiter, or the jovicentric motion as being perturbed by the attraction of the Sun. This analysis completes the previous theoretical investigations of effective-gravity corrections to the Newtonian analysis of three-body systems, and represents an intermediate step towards relativistic effects on cometary motions.

Observations of Disintegrating Long-period Comet C/2019 Y4 (ATLAS): A Sibling of C/1844 Y1 (Great Comet)

Abstract We present a study of C/2019 Y4 (ATLAS) using Sloan gri observations from 2020 mid-January to early April. During this time span, the comet brightened with a growth in the effective cross-section of m2 s−1 from the beginning to ∼70 days preperihelion in late 2020 March, followed by a brightness fade and the comet gradually losing the central condensation. Meanwhile, the comet became progressively bluer, and was even bluer than the Sun (g − r ≈ 0.2) when the brightness peaked, likely due to activation of subterranean fresh volatiles exposed to sunlight. With the tailward bias-corrected astrometry we found an enormous radial nongravitational parameter, au day−2 in the heliocentric motion of the comet. Taking all of these findings into consideration, we conclude that the comet has disintegrated since 2020 mid-March. By no means was the split new to the comet, as we quantified that the comet had undergone another split event around last perihelion ∼5 kyr ago, during which its sibling C/1844 Y1 (Great Comet) was produced, with the in-plane component of the separation velocity ≳1 m s−1. We constrained that the nucleus of C/2019 Y4 before disintegration was ≳60 m in radius, and has been protractedly ejecting dust grains of ∼10–40 μm (assuming a dust bulk density of 0.5 g cm−3) with an ejection speed of ∼30 m s−1 in early 2020 March and increased to ∼80 m s−1 toward the end of the month for grains of ∼10 μm.

Simulating Kepler’s Geocentric Mars Orbit

The word ’Geocentric’ comes from the Greek word Γεωκεντρικό which is a compound word composed from two words: “γεω” means Earth and “κεντρικό” means centric. Geocentric aspect, appears for the first time in ancient Greece. Pythagoras had formulated the geocentric system with the Earth at the center of the Universe surrounded by the orbiting planets with Sun included. Later Greek ancient astronomers, trying to explain the weird planetary motion in the sky, introduced the epicyclic theory.33The epicyclic theory was well formulated by Hipparchus and Apollonius. Using this theory the two famous Greek astronomers managed to explain the weird planetary motion on the sky. This theory states that the geocentric planetary motion could be considered as a combination of circular motions. Today this idea is quite sensible if we consider that the geocentric motion could be perceived as synthesis of two independent motions; one is the rotation of the planet around the Sun and the other is the apparent rotation of the Sun around the Earth. Someone could say that the heliocentric motion is hidden inside the geocentric planetary path as one of two superimposed motions. This logical conclusion is supported by F. Hoyle Hoyle (1975) who states “We know that the difference between a heliocentric theory and a geocentric theory is one of relative motion only, and that such a difference has no physical significance.” In other words Geocentrism isn’t completely wrong excluding only the arbitrary claim that the Earth is fixed and immobile at the center of the Universe.Geocentrism lasted many years until Nicolaus Copernicus at the middle of 15th century, proposed the heliocentric system by transferring the reference origin from Earth to Sun. Although Copernican model was capable explaining the geocentric orbits of planets with negligible eccentricity, it failed to give a convincing explanation in cases of planets with considerable eccentricity like Mars. The lack of symmetry in Mar’s trajectory led Kepler to discover that planet’s orbits weren’t circular, as it was already believed, but elliptical. According to (Evans, 1998, p.431) Kepler said “I therefore once again think it to have happened by divine arrangement, that I arrived at the same time in which he was intent upon Mars, whose motions provide the only possible access to the hidden secrets of astronomy, without which we would remain forever ignorant of those secrets.” In this article we are trying to simulate the process followed by Kepler, studying the apparent geocentric Mar’s orbit which triggered him to discover elliptical planetary orbits.The relation between heliocentrism and geocentrism is highlighted during this study. Besides, this aspect is mentioned by David R. Topper...But this fact is then sometimes generalized to positing that geocentrism and Heliocentrism are equivalent, that they are the same geometrically or mathematically or even exactly the same; in a phrase, there is an isomorphism between them... Topper (2007) The methodology which was used, in the whole process, relies on mathematical modeling. This approach is based mainly on dynamic position change over time, which the interactive mathematic software GeoGebra can generously provide. The end of this historical approach shows that the heliocentric view was revealed throughout a geocentric model, proving the equivalence of these two different aspects. Finally the theoretical numerical results of this study seem to be in full agreement with the astronomical records of that era with minimal discrepancies.

An analysis of the geodesy and relativity experiments of BepiColombo

BepiColombo is a ESA-JAXA mission aimed to a comprehensive exploration of Mercury, the innermost planet of the solar system. The Mercury Orbiter Radio science Experiment (MORE) will exploit a state of the art microwave tracking system, including an advanced Ka-band transponder, to determine the gravity field and the rotational state of the planet, and to perform extensive tests of relativistic gravity. In this work we analyze all the aspects of the radio science investigation, which include: (i) the solar conjunction experiment in cruise; (ii) the gravimetry and rotation experiments; (iii) the fundamental physics test. We report on the results of numerical simulations based on the latest mission scenario, with launch in October 2018 and arrival at Mercury in December 2025. We show that the gravity and rotation measurements expected from BepiColombo will allow to better characterize the size of an inner solid core inside the outer liquid core, and the properties of the outer mantle and the crust. We discuss how the current estimate of several parametrized post-Newtonian (PPN) parameters can be improved by MORE through the determination of the heliocentric motion of Mercury and by measuring the propagation time of radio waves. We also assess in a quantitative way the benefits of an extended mission.

Feasibility analysis of the angular momentum reversal trajectory via hodograph method for high performance solar sails

In this paper a new phase space of hodograph method is adopted to investigate and better understand the two-dimensional angular momentum reversal (H-reversal) trajectories for high performance solar sails within a fixed cone angle. As the hodograph method and the H-reversal trajectory are not very common, both of them are briefly introduced. The relationship between them are constructed and addressed with a sample trajectory. How the phase space varies according to the sail quality and the fixed sail cone angle is also studied. Through variation of the phase space, the minimum sail lightness number can be obtained by solving a set of algebraic equations instead of a parameter optimization problem. For a given sail lightness number, there are three types of the two-dimensional possible heliocentric motion, including the spiral inward trajectories towards the Sun, the H-reversal trajectories and the directly outward escape trajectories. The boundaries that separate these different groups are easily determined by using the phase space. Finally, the method and procedures to achieve the feasible region of the H-reversal trajectory with required perihelion distance are presented in detail.

The SPM kinematic catalogue of Galactic planetary nebulae

AbstractThe San Pedro Mártir kinematic catalogue of galactic planetary nebulae provides spatially resolved, long-slit, Echelle spectra for about 600 planetary nebulae, representing 55 observing runs and about 4000 individual integrations to date in this first release. The project is ongoing and will continue adding spectra to the database. The data are presented wavelength calibrated and corrected for heliocentric motion. This is the most extensive and homogeneous single source of data concerning the internal kinematics of the ionized nebular material in planetary nebulae. The catalogue is available through the world wide web at http://kincatpn.astrosen.unam.mx and an article will a full description of the catalogue will soon appear in the RevMexAA.

The YORP effect on 25 143 Itokawa

Context. The asteroid 25143 Itokawa is one of the candidates for the detection of the Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect in the rotation period. Previous studies were carried out up to the 196 608 facets triangulation model and were not able to provide a good theoretical estimate of this effect, raising questions about the influence of the mesh resolution and the centre of mass location on the evolution the rotation period. Aims. The YORP effect on Itokawa is computed for different topography models up to the highest resolution Gaskell mesh of 3 145 728 triangular faces in an attempt to find the best possible YORP estimate. Other, lower resolution models are also studied and the question of the dependence of the rotation period drift on the density distribution inhomogeneities is reexamined. A comparison is made with 433 Eros models possessing a similar resolution. Methods. The Rubincam approximation (zero conductivity) is assumed in the numerical simulation of the YORP effect in rotation period. The mean thermal radiation torques are summed over triangular facets assuming Keplerian heliocentric motion and uniform rotation around a body-fixed axis. Results. There is no evidence of YORP convergence in Gaskell model family. Differently simplified meshes may converge quickly to their parent models, but this does not prove the quality of YORP computed from the latter. We confirm the high sensitivity of the YORP effect to the fine details of the surface for 25 143 Itokawa and 433 Eros. The sensitivity of the Itokawa YORP to the centre of mass shift is weaker than in earlier works, but instead the results prove to be sensitive to the spin axis orientation in the body frame. Conclusions. Either the sensitivity of the YORP effect is a physical phenomenon and all present predictions are questionable, or the present thermal models are too simplified.

The MESSENGER mission to Mercury: Status after the Venus flybys

NASA's MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft, launched on 3 August 2004, is well into its voyage to initiate a new era in our understanding of the terrestrial planets. The mission, spacecraft, and payload are designed to answer six fundamental questions regarding the innermost planet during three flybys and a one-year-long, near-polar-orbital observational campaign. The cruise phase to date has been used to commission the spacecraft and instruments and begin the transition to automated use of the instruments with on-board, time-tagged commands. An Earth flyby one year after launch, a large propulsive maneuver in December 2005, and Venus flybys in October 2006 and June 2007 began the process of changing MESSENGER's heliocentric motion. The second Venus flyby was also used to complete final rehearsals for Mercury flyby operations in January 2008 while coordinating observations with the European Space Agency's Venus Express mission. The upcoming Mercury flyby will be the first since that of Mariner 10 in 1975. Along with the second and third MESSENGER flybys in October 2008 and September 2009, that flyby will provide images of the hemisphere of Mercury never seen before by spacecraft as well as the first high-resolution information on Mercury's surface mineralogy. These three flybys, interspersed with deep space maneuvers, finish adjusting the spacecraft motion sufficiently for Mercury orbit injection to follow in March 2011. In the orbital phase, the spacecraft's nominal periapsis latitude of 60∘N will gradually drift northward as the periapsis altitude of 200km gradually drifts upward due to solar gravitational perturbations. The 12-h period and 80∘ inclination are maintained while the altitude is readjusted downward to 200km every Mercury revolution about the Sun. The profile enables mapping of the entire planet and acquiring detailed elemental and topographic data over the northern hemisphere. After conclusion of the nominal mission in March 2012, an additional year of data analysis and archiving is planned before the conclusion of the MESSENGER project. To broaden scientific participation in the mission, NASA has established a Participating Scientist Program, bringing a full complement of international scientific researchers into the mission. The MESSENGER team is also continuing its informal interaction with members of the BepiColombo project to maximize the overall scientific return from both missions.

Algorithms for Stellar Perturbation Computations on Oort Cloud Comets

We investigate different approximate methods of computing the perturbations on the orbits of Oort cloud comets caused by passing stars, by checking them against an accurate numerical integration using Everhart’s RA15 code. The scenario under study is the one relevant for long-term simulations of the cloud’s response to a predefined set of stellar passages. Our sample of stellar encounters simulates those experienced by the Solar System currently, but extrapolated over a time of 1010 years. We measure the errors of perihelion distance perturbations for high-eccentricity orbits introduced by several estimators – including the classical impulse approximation and Dybczynski’s (1994, Celest. Mech. Dynam. Astron. 58, 1330–1338) method – and we study how they depend on the encounter parameters (approach distance and relative velocity). We introduce a sequential variant of Dybczynski’s approach, cutting the encounter into several steps whereby the heliocentric motion of the comet is taken into account. For the scenario at hand this is found to offer an efficient means to obtain accurate results for practically any domain of the parameter space.

Yarkovsky detection opportunities: II. Binary systems

We consider the possibility of detecting the Yarkovsky orbital perturbation acting on binary systems among the near-Earth asteroids. This task is significantly more difficult than for solitary asteroids because the Yarkovsky force affects both the heliocentric orbit of the system's center of mass and the relative orbit of the two components. Nevertheless, we argue these are sufficiently well decoupled so that the major Yarkovsky perturbation is in the simpler heliocentric motion and is observable with the current means of radar astrometry. Over the long term, the Yarkovsky perturbation in the relative motion of the two components is also detectable for the best observed systems. However, here we consider a simplified version of the problem by ignoring mutual non-spherical gravitational perturbations between the two asteroids. With the orbital plane constant in space and the components' rotation poles fixed (and assumed perpendicular to the orbital plane), we do not examine the coupling between Yarkovsky and gravitational effects. While radar observations remain an essential element of Yarkovsky detections, lightcurve observations, with their ability to track occultation and eclipse phenomena, are also very important in the case of binaries. The nearest possible future detection of the Yarkovsky effect for a binary system occurs for (66063) 1998 RO 1 in September 2006. Farther out, even more statistically significant detections are possible for several other systems including 2000 DP 107, (66391) 1999 KW 4 and 1996 FG 3.

Resonant returns to close approaches: Analytical theory

We extend Öpik's theory of close encounters of a small body (either an asteroid or a comet) by explicitly introducing the nodal distance and a time coordinate. Assuming that the heliocentric motion between consecutive close encounters is Keplerian, or given by an explicit propagator, we can compute the initial conditions for an encounter as functions of the outcomes of a previous one; in this way it is possible to obtain a completely analytical theory of resonant returns. It is found that the initial conditions of a close encounter that lead to a resonant return must lie close to easily computable circles on the b-plane of the first encounter. By further assuming that the nodal distance varies uniformly with time, due to secular perturbations, and considering the derivatives of the coordinates on the b-plane of the second encounter with respect to those on the b-plane of the first encounter, we compute in the latter the location, shape and size of collision keyholes.

Is the Redshift Clustering of Long-Duration Gamma-Ray Bursts Significant?

The 26 long-duration gamma-ray bursts (GRBs) with known redshifts form a distinct cosmological set, selected differently than other cosmological probes such as quasars and galaxies. Since the progenitors are now believed to be connected with active star formation and since burst emission penetrates dust, one hope is that with a uniformly selected sample, the large-scale redshift distribution of GRBs can help constrain the star formation history of the universe. However, we show that strong observational biases in ground-based redshift discovery hamper a clean determination of the large-scale GRB rate and hence the connection of GRBs to the star formation history. We then focus on the properties of the small-scale (clustering) distribution of GRB redshifts. When corrected for heliocentric motion relative to the local Hubble flow, the observed redshifts appear to show a propensity for clustering: eight of 26 GRBs occurred within a recession velocity difference of 1000 km s-1 of another GRB. That is, four pairs of GRBs occurred within 30 h Myr in cosmic time, despite being causally separated on the sky. We investigate the significance of this clustering using a simulation that accounts for at least some of the strong observational and intrinsic biases in redshift discovery. Comparison of the numbers of close redshift pairs expected from the simulation with that observed shows no significant small-scale clustering excess in the present sample; however, the four close pairs occur in only about 20% of the simulated data sets (the precise significance of the clustering is dependent on the modeled biases). We conclude with some impetuses and suggestions for future precise GRB redshift measurements.