Mean Motion Research Articles

A DETERMINATION OF THE MOTION BASED ON GNSS OBSERVATIONS BETWEEN 2000 AND 2021 BY USING THE IGS POINTS ON THE POLAR REGIONS

People are fascinated today more than ever by the polar regions of the Earth. One reason for this is that wide expanses of the Arctic and Antarctic have not been explored and are therefore still viewed as frontier regions. Another is that they both have very diverse histories with regard to their origins and ice formation. Their numerous aspects still pose many puzzles for science today. The regions of the Earth designated as polar are those areas located between the North or South Pole and the Arctic or Antarctic Circles, respectively. The northern polar region, called the Arctic, encompasses the Arctic Ocean and a portion of some surrounding land masses. The southern polar region, called the Antarctic, contains the continent of Antarctica and areas of the surrounding Southern Ocean. In this paper three tests (2000, 2010 and 2021) of continuous GNSS data recorded by 8 permanent International GPS Service (IGS) stations in both Polar Regions have been processed by using CSRS-PPP Software for geodetic networks. The results also show that all GNSS provide good visibility with low elevation angles, whereas with high elevation angles, which might be needed due to natural barriers, the GLONASS and other satellites provides the highest number of visible satellites. Consequently, the mean motion of the study area was found approximately 7–15 cm for horizontal components (X–Y) and 6 cm for vertical components (Ellipsoidal Height) on the eight IGS points in the both poles.

Anticipating the DART Impact: Orbit Estimation of Dimorphos Using a Simplified Model

We used the times of occultations and eclipses between the components of the 65803 Didymos binary system observed in its light curves from 2003 to 2021 to estimate the orbital parameters of Dimorphos relative to Didymos. We employed a weighted least-squares approach and a modified Keplerian orbit model in order to accommodate the effects from nongravitational forces such as binary YORP that could cause a linear change in mean motion over time. We estimate that the period of the mutual orbit at the epoch 2022 September 26.0 TDB, the day of the DART impact, is 11.921 487 ± 0.000028 hr (1σ) and that the mean motion of the orbit is changing at a rate of (5.0 ± 1.0) × 10−18 rad s−2 (1σ). The formal 3σ uncertainty in orbital phase of Dimorphos during the planned Double Asteroid Redirection Test (DART) mission is 5.°4. Observations from 2022 July to September, a few months to days prior to the DART impact, should provide modest improvements to the orbital phase uncertainty and reduce it to about 4.°2. These results, generated using a relatively simple model, are consistent with those generated using the more sophisticated model of Scheirich & Pravec, which demonstrates the reliability of our method and adds confidence to these mission-critical results.

Trojan asteroids and the co-orbital dust ring of Venus

Context. Co-orbital asteroids have been thought to be the possible source of the zodiacal dust ring around the orbit of Venus, but the conclusions about the orbital stability and thus about the existence of Venus Trojans are inconsistent in the literature. Aims. We present a systematic survey of the orbital stability of Venus Trojans that takes the dynamical influences from General Relativity and the Yarkovsky effect into account. Methods. The orbits of thousands of fictitious Venus Trojans were simulated numerically. Using a frequency analysis, we describe their orbital stabilities and the dynamical mechanisms behind them. The influences of General Relativity and of the Yarkovsky effect, which were previously either neglected or oversimplified, were investigated in long-term numerical simulations. Results. The stability maps on the (a0, i0) plane and (a0, e0) plane are depicted, and the most stable Venus Trojans are found to occupy low-inclination horseshoe orbits with low eccentricities. The resonances that carve the fine structures in the stability map are determined. General Relativity decreases the stability of orbits only little, but the Yarkovsky effect may drive nearly all Venus Trojans out of the Trojan region in a relatively short time. Conclusions. The Venus Trojans have a poor orbital stability and cannot survive to the age of the Solar System. The zodiacal dust ring found around the orbit of Venus is more likely a sporadic phenomenon, as the result of a temporary capture into the 1:1 mean motion resonance of dust particles that were probably produced by passing comets or asteroids, but not by Venus Trojans.

New Dynamical State and Habitability of the HD 45364 Planetary System

Planetary systems with multiple giant planets provide important opportunities to study planetary formation and evolution. The HD 45364 system hosts two giant planets that reside within the habitable zone (HZ) of their host star and was the first system discovered with a 3:2 mean motion resonance (MMR). Several competing migration theories with different predictions have previously provided explanations regarding the observed resonance through dynamical simulations that utilized limited data. Here, over ten years since the original discovery, we revisit the system with a substantially increased radial velocity (RV) sample from High Accuracy Radial Velocity Planet Searcher spectrograph and High Resolution Echelle Spectrometer that significantly extends the observational baseline. We present the revised orbital solutions for the two planets using both Keplerian and dynamical models. Our RV models suggest orbits that are more circular and separated than those previously reported. As a result, the predicted strong planet–planet interactions were not detected. The system dynamics were reanalyzed, and the planet pair was found to exhibit apsidal behavior of both libration and circulation, indicating a quasi-resonance state rather than being truly in MMR. The new orbital solution and dynamical state of the system confirm migration models that predicted near-circular orbits as the preferred scenario. We also study the habitability prospects of this system and found that an additional Earth-mass planet and exomoons in the HZ are possible. This work showcases the importance of continued RV observations and its impact on our knowledge of the system’s dynamical history. HD 45364 continues to be an interesting target for both planetary formation and habitability studies.

A trio of giant planets orbiting evolved star HD 184010

Abstract We report the discovery of a triple-giant-planet system around an evolved star HD 184010 (HR 7421, HIP 96016). This discovery is based on observations from Okayama Planet Search Program, a precise radial velocity survey, undertaken at Okayama Astrophysical Observatory between 2004 April and 2021 June. The star is K0 type and located at the beginning of the red giant branch. It has a mass of $1.35_{-0.21}^{+0.19}\, M_{\odot }$, a radius of $4.86_{-0.49}^{+0.55} R_{\odot }$, and a surface gravity log g of $3.18_{-0.07}^{+0.08}$. The planetary system is composed of three giant planets in a compact configuration: the planets have minimum masses of $M_{\rm {b}}\sin i = 0.31_{-0.04}^{+0.03}\, M_{\rm {J}}$, $M_{\rm {c}}\sin i = 0.30_{-0.05}^{+0.04}\, M_{\rm {J}}$, and $M_{\rm {d}}\sin i = 0.45_{-0.06}^{+0.04}\, M_{\rm {J}}$, and orbital periods of $P_{\rm {b}}=286.6_{-0.7}^{+2.4}\:$d, $P_{\rm {c}}=484.3_{-3.5}^{+5.5}\:$d, and $P_{\rm {d}}=836.4_{-8.4}^{+8.4}\:$d, respectively, which are derived from a triple Keplerian orbital fit to three sets of radial velocity data. The ratio of orbital periods are close to Pd : Pc : Pb ∼ 21 : 12 : 7, which means the period ratios between neighboring planets are both lower than 2 : 1. The dynamical stability analysis reveals that the planets should have near-circular orbits. The system could remain stable over 1 Gyr, initialized from co-planar orbits, low eccentricities (e = 0.05), and planet masses equal to the minimum mass derived from the best-fitting circular orbit fitting. Besides, the planets are not likely in mean motion resonance. The HD 184010 system is unique: it is the first system discovered to have a highly evolved star (log g < 3.5 cgs) and more than two giant planets all with intermediate orbital periods (102 < P < 103 d).

The orbital architecture and stability of the μ Arae planetary system

ABSTRACT We re-analyse the global orbital architecture and dynamical stability of the HD 160691 planetary system. We have updated the best-fitting elements and minimal masses of the planets based on literature precision radial velocity (RV) measurements, now spanning 17.3 yr. This is twice the RVs interval used for the first characterization of the system in 2006. It consists of a Saturn- and two Jupiter-mass planets in low-eccentric orbits resembling the Earth–Mars–Jupiter configuration in the Solar system, as well as the close-in warm Neptune with a mass of ≃14 Earth masses. Here, we constrain this early solution with the outermost period to be accurate to one month. The best-fitting Newtonian model is characterized by moderate eccentricities of the most massive planets below 0.1 with small uncertainties ≃0.02. It is close but meaningfully separated from the 2e:1b mean motion resonance of the Saturn–Jupiter-like pair, but may be close to weak three-body MMRs. The system appears rigorously stable over a wide region of parameter space covering uncertainties of several σ. The system stability is robust to a five-fold increase in the minimal masses, consistent with a wide range of inclinations, from ≃20° to 90°. This means that all planetary masses are safely below the brown dwarf mass limit. We found a weak statistical indication of the likely system inclination $I \simeq \, 20^{\circ }$–30°. Given the well-constrained orbital solution, we also investigate the structure of hypothetical debris discs, which are analogues of the Main Belt and Kuiper Belt, and may naturally occur in this system.

Influence of the Yarkovsky Effect on Mean Motion Resonances of Asteroids with Small Perihelion Distances

Influence of the Yarkovsky Effect on Mean Motion Resonances of Asteroids with Small Perihelion Distances

Chaotic diffusion of asteroids in the exterior 1:2 mean motion resonance with Mars

ABSTRACT The inner asteroid belt between 2.1 and 2.5 au is of particular dynamical significance because it is the dominant source of both chondritic meteorites and near-Earth asteroids. This inner belt is bounded by an eccentricity-type secular resonance and by the 1:3 mean motion resonance with Jupiter. Unless asteroid perihelia are low enough to allow scattering by Mars, escape requires transport to one of the bounding resonances. In addition Yarkovsky forces are generally ineffective in changing either the eccentricity and/or inclination for asteroids with diameter ≳30 km. Thus, large asteroids with pericentres far from Mars may only escape from the inner belt through large changes in their eccentricities. In this paper, we study chaotic diffusion of orbits near the 1:2 mean motion resonance with Mars in a systematic way. We show that, while chaotic orbital evolution in both resonant and non-resonant orbits increase the dispersion of the inclinations and eccentricities, it does not significantly change their mean values. We show further that, while the dispersive growth is greatest for resonant orbits, at high e the resonance acts to mitigate asteroid scattering by Mars - making the asteroid lifetime in the belt longer than it would have been for a non-resonant orbit. For asteroids of all sizes in both resonant and non-resonant orbits, the changes in eccentricity needed to account for the observations cannot be achieved by gravitational forces alone. The role of resonant trapping in protecting asteroids from encounters with Mars is also analysed.

The Von Zeipel–Lidov–Kozai Effect inside Mean Motion Resonances with Applications to Trans-Neptunian Objects

Secular dynamics inside mean motion resonances (MMRs) plays an essential role in governing the dynamical structure of the trans-Neptunian region and sculpting the orbital distribution of trans-Neptunian objects (TNOs). In this study, semianalytical developments are made to explore the von Zeipel–Lidov–Kozai resonance inside MMRs. To this end, a semi-secular model is formulated from averaging theory and then a single-degree-of-freedom integrable model is achieved based on the adiabatic invariance approximation. In particular, we introduce a modified adiabatic invariant, which is continuous around the separatrices of MMRs. During long-term evolution, both the resonant Hamiltonian and the adiabatic invariant remain unchanged, thus phase portraits can be produced by plotting level curves of the adiabatic invariant with a given Hamiltonian. The phase portraits provide global pictures to predict long-term behaviors of the eccentricity, inclination, and argument of pericenter. Applications to some representative TNOs inside MMRs (2018 VO137, 2005 SD278, 2015 PD312, Pluto, 2004 HA79, 1996 TR66, and 2014 SR373) show good agreements between the numerically propagated trajectories under the full N-body model and the level curves arising in phase portraits. Interestingly, 2018 VO137 and 2005 SD278 exhibit switching behaviors during their long-term evolution and currently they are inside 2:5 MMR with Neptune.

Planetesimal Dynamics in the Presence of a Giant Planet. II. Dependence on Planet Mass and Eccentricity

The presence of an early-formed giant planet in the protoplanetary disk has mixed influence on the growth of other planetary embryos. Gravitational perturbation from the planet can increase the relative velocities of planetesimals at the mean motion resonances to very high values and impede accretion at those locations. However, gas drag can also align the orbital pericenters of equal-size planetesimals in certain disk locations and make them dynamically quiet and “accretion-friendly” locations for planetesimals of similar sizes. Following the previous paper, where we investigated the effect of a Jupiter-like planet on an external planetesimal disk, we generalize our findings to extrasolar planetary systems by varying the planet parameters. In particular, we focus on the dependence of the planetesimal relative velocities on the mass and eccentricity of the existing planet. We found that the velocity dispersion of identical-mass particles increases monotonically with increasing planet mass. Meanwhile, the dependence of the relative velocity between different-mass planetesimals on their mass ratio becomes weaker as the planet mass increases. While the relative velocities generally increase with increasing planet eccentricity, the velocity dispersion of lower-mass particles (m ≲ 1018 g) is almost independent of planet eccentricity owing to their strong coupling to gas. We find that the erosion limits are met for a wider range of parameters (planet mass/eccentricity, planetesimal mass ratio) when the planetesimal size decreases. Our results could provide some clues for the formation of Saturn’s core, as well as the architecture of some exoplanetary systems with multiple cold giant planets.

Moon packing around an Earth-mass planet

ABSTRACT All four giant planets in the Solar system host systems of multiple moons, whereas the terrestrial planets only host up to two moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons could stably orbit the Earth, or an Earth-mass exoplanet. We perform a series of N-body simulations of closely spaced equal-mass moons in nested orbits around an Earth-mass planet orbiting a Sun-like star. The innermost moon begins near the host planet’s Roche radius, and the system is packed until the outermost moon begins near the stability limit for single moons. The initial spacing of the moons follows an iterative scheme commonly used for studies of compact planetary systems around single stars. For the three-moon system, we generate MEGNO maps to calculate periodic and chaotic regions and to identify the destabilizing mean motion resonances. Our calculations show that the maximum number of moons depends on the assumed masses of the satellites (Ceres-, Pluto-, and Luna-mass) that could maintain stable orbits in a tightly packed environment. Through our N-body simulations, we find stable configurations for up to 7 ± 1 Ceres-mass, 4 ± 1 Pluto-mass, and 3 ± 1 Luna-mass moons. However, outward tidal migration will likely play a substantial role in the number of moons on stable orbits over the 10 Gyr stellar lifetime of a Sun-like star.

Dynamics of co-orbital exoplanets in a first-order resonance chain with tidal dissipation

Co-orbital planets (in a 1: 1 mean motion resonance) can be formed within a Laplace resonance chain. We develop a secular model tc study the dynamics of the resonance chain p: p : p + 1, where the co-orbital pair is in a first-order mean motion resonance with the outermost third planet. Our model takes into account tidal dissipation through the use of a Hamiltonian version of the constant time-lag model, which extends the Hamiltonian formalism of the point-mass case. We show the existence of several families of equilibria, anc how these equilibria extend to the complete system. In one family, which we call the main branch, a secular resonance between the libration frequency of the co-orbitals and the precession frequency of the pericentres has unexpected dynamical consequences when tidal dissipation is added. We report the existence of two distinct mechanisms that make co-orbital planets much more stable within the p : p : p + 1 resonance chain rather than outside it. The first is due to negative real parts of the eigenvalues of the linearised system with tides, in the region of the secular resonance mentioned above. The second comes from non-linear contributions of the vector fielt and is due to eccentricity damping. These two stabilising mechanisms increase the chances of a future detection of exoplanets in the co-orbital configuration.

Radial velocities from far-red spectra of Carina Arm O and early B stars

ABSTRACT Massive O and early B stars are important markers of recent star formation and exert a significant influence on their environments during their short lives via photoionization and winds and when they explode as supernovae. In the Milky Way, they can be detected at great distances but often lie behind large dust columns, making detection at short wavelengths difficult. In this study, the use of the less extinguished far-red spectrum (8400–8800 Å) for radial velocity measurement is examined. Results are reported for a sample of 164 confirmed OB stars within a 2° field positioned on the Carina Arm. Most stars are at distances between 3 and 6 kpc, and Westerlund 2 is at the field edge. The measured radial velocities have errors concentrated in the 3–10 km s−1 range, with a systematic uncertainty of 2–3 km s−1. These are combined with Gaia-mission astrometry to allow full space motions to be constructed. Up to 22 stars are likely to be runaways, although 8 of them are as likely to be interloping (so far undetected) binaries. The mean azimuthal motion of the sample fits in with recent measurements of Galactic disc rotation. In the Galactocentric radial direction, the mean motion indicates modest infall at a speed of ∼10 km s−1. This experiment shows that weak Paschen lines in the far-red can yield credible radial velocity determination, offering the prospect of exploring OB-star kinematics over much more of the Galactic disc than has hitherto been possible.

HD 28109 hosts a trio of transiting Neptunian planets including a near-resonant pair, confirmed by ASTEP from Antarctica

ABSTRACT We report on the discovery and characterization of three planets orbiting the F8 star HD 28109, which sits comfortably in ${TESS}$’s continuous viewing zone. The two outer planets have periods of $\rm 56.0067 \pm 0.0003~d$ and $\rm 84.2597_{-0.0008}^{+0.0010}~d$, which implies a period ratio very close to that of the first-order 3:2 mean motion resonance, exciting transit timing variations (TTVs) of up to $\rm 60\, min$. These two planets were first identified by ${TESS}$, and we identified a third planet in the ${TESS}$photometry with a period of $\rm 22.8911 \pm 0.0004~d$. We confirm the planetary nature of all three planetary candidates using ground-based photometry from Hazelwood, ${ASTEP}$, and LCO, including a full detection of the $\rm \sim 9\, h$ transit of HD 28109 c from Antarctica. The radii of the three planets are ${\it R}_b=2.199_{-0.10}^{+0.098} ~{\rm R}_{\oplus }$, ${\it R}_c=4.23\pm 0.11~ {\rm R}_{\oplus }$, and ${\it R}_d=3.25\pm 0.11 ~{\rm R}_{\oplus }$; we characterize their masses using TTVs and precise radial velocities from ESPRESSO and HARPS, and find them to be ${\it M}_b=18.5_{-7.6}^{+9.1}~M_{\oplus }$, ${\it M}_c=7.9_{-3.0}^{+4.2}~{\rm M}_{\oplus }$, and ${\it M}_d=5.7_{-2.1}^{+2.7}~{\rm M}_{\oplus }$, making planet b a dense, massive planet while c and d are both underdense. We also demonstrate that the two outer planets are ripe for atmospheric characterization using transmission spectroscopy, especially given their position in the CVZ of James Webb Space Telescope. The data obtained to date are consistent with resonant (librating) and non-resonant (circulating) solutions; additional observations will show whether the pair is actually locked in resonance or just near-resonant.

Investigation of the Joint Effect of Light Pressure and Secular Resonances Associated with the Mean Motion of the Sun on the Dynamics of Objects in the LEO Region

Investigation of the Joint Effect of Light Pressure and Secular Resonances Associated with the Mean Motion of the Sun on the Dynamics of Objects in the LEO Region

Mapping Natural Orbits around Io

As the most volcanically active celestial body in the Solar System, Io is a natural satellite of Jupiter due to its proximity to the planet and the fact that it is in mean motion resonance, known as the Laplace resonance, with the natural satellites Europa and Ganymede. This natural satellite is a good candidate to be visited by future missions. In this sense, the present work has the goal of studying and mapping the best initial orbital conditions for orbits around Io, considering the symmetrical or asymmetical perturbative effects of a third body (Jupiter) and the J2 term from the mass configuration of Io. The initial orbital parameters of the probe were investigated through a set of numerical simulations. The results showed that although most orbits around Io have lifetimes of less than 6 months, some regions were found where the initial conditions of the orbits provided satisfactory times for the accomplishment of future missions around Io.

Droplets Evaporation In Turbulent Flow: Statistical Study Based On Lagrangian Tracking And In Line Holography

Turbulence has long been suspected to increase the evaporation rate of droplets via the convective effects it generates. The experimental data reported in this paper provides evidence of this increase and statistically quantify these effects. Measurements was performed following a Lagrangian approach, using Digital in-line holography based on a high speed camera and an inverse problem reconstruction algorithm. Ether droplets was released in a quasi isotropic and homogeneous turbulence generated by synthetic jets. Their Schmidt number is typically of the order of 2 and their Reynolds number is moderate (≤ 3). Results are based on a large number of droplets trajectories for various turbulence conditions. The Lagrangian statistics computed from these trajectories, totaling 1.3 million samples, show that the relative mean motion and turbulence seen by the droplets on average increases their evaporation rate. Within the parameter range investigated, this increase is not well predicted when estimating the convective effect in the Sherwood number with the norm of the instantaneous relative velocity seen by the droplets. In contrast, this increase is very well predicted when the Sherwood number is calculated using a Reynolds number based on the norm of the mean relative velocity plus its RMS fluctuation.

SAX and Random Projection Algorithms for the Motif Discovery of Orbital Asteroid Resonance Using Big Data Platforms.

The phenomenon of big data has occurred in many fields of knowledge, one of which is astronomy. One example of a large dataset in astronomy is that of numerically integrated time series asteroid orbital elements from a time span of millions to billions of years. For example, the mean motion resonance (MMR) data of an asteroid are used to find out the duration that the asteroid was in a resonance state with a particular planet. For this reason, this research designs a computational model to obtain the mean motion resonance quickly and effectively by modifying and implementing the Symbolic Aggregate Approximation (SAX) algorithm and the motif discovery random projection algorithm on big data platforms (i.e., Apache Hadoop and Apache Spark). There are five following steps on the model: (i) saving data into the Hadoop Distributed File System (HDFS); (ii) importing files to the Resilient Distributed Datasets (RDD); (iii) preprocessing the data; (iv) calculating the motif discovery by executing the User-Defined Function (UDF) program; and (v) gathering the results from the UDF to the HDFS and the .csv file. The results indicated a very significant reduction in computational time between the use of the standalone method and the use of the big data platform. The proposed computational model obtained an average accuracy of 83%, compared with the SwiftVis software.

Observational data and orbits of the comets discovered at the Vilnius Observatory in 1980–2006 and the case of the comet 322P

Abstract This article is devoted to the discovery of comets at the Vilnius Observatory together with the orbital analysis of dynamically interesting comets, namely 322P. We studied the orbital evolution of comet 322P with and without non-gravitational effects. It turned out that many of the comet’s orbital clones go into and out of retrograde orbits, sometimes repeatedly. The reason for such dramatic changes in the inclination of the orbit is the origin of comet 322P close to mean motion resonance 3:1 with Jupiter, ejecting them from there and, consequently, bringing the clones closer to the terrestrial group of planets. In this way, the clones of comet 322P enter retrograde orbits and reside there several ky to several My.

Attempt to obtain the general relativistic planet's motion by special relativity techniques

AbstractIt is attempted to derive the general relativistic equation of motion for a planet and its solution solely by the special relativity techniques. The motion of a planet relative to the Sun and that of the Sun to the planet are solved independently in a special relativistic framework using the perturbation theory in celestial mechanics. The solution reveals a nature of the structure of the spacetime under the gravitation of the Sun, and then its effect on the planet's motion is examined. When the motion thus examined are compared with the one obtained by the general relativity theory in post‐Newtonian approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession.