Planetary Ephemerides Research Articles

A new multiple-arc model of the resonant Kuiper belt objects – plutinos

Abstract To incorporate the gravitational influence of Kuiper belt objects (KBOs) in planetary ephemerides, uniform-ring models are commonly employed. In this paper, for representing the KBO population residing in Neptune’s 2:3 mean motion resonance (MMR), known as the Plutinos, we introduce a three-arc model by considering their resonant characteristics. Each ‘arc’ refers to a segment of the uniform ring and comprises an appropriate number of point masses. Then the total perturbation of Plutinos is numerically measured by the change in the Sun-Neptune distance (ΔdSN). We conduct a comprehensive investigation to take into account various azimuthal and radial distributions associated with the resonant amplitudes (A) and eccentricities (e) of Plutinos, respectively. The results show that over a 100-year period: (1) at the smallest e = 0.05, the Sun-Neptune distance change ΔdSN caused by Plutinos decreases significantly as A reduces. It can deviate from the value of ΔdSN obtained in the ring model by approximately 100 km; (2) as e increases in the medium range of 0.1-0.2, the difference in ΔdSN between the arc and ring models becomes increasingly significant; (3) at the largest e ≳ 0.25, ΔdSN can approach zero regardless of A, and the arc and ring models exhibit a substantial difference in ΔdSN, reaching up to 170 km. Then the applicability of our three-arc model is further verified by comparing it to the perturbations induced by observed Plutinos on the positions of both Neptune and Saturn. Moreover, the concept of the multiple-arc model, designed for Plutinos, can be easily extended to other MMRs densely populated by small bodies.

A millisecond pulsar position determined to 0.2 mas precision with VLBI

Precise millisecond pulsar (MSP) positions determined with very long baseline interferometry (VLBI) hold the key to building the connection between the kinematic and dynamic reference frames respectively used for VLBI and pulsar timing. A frame connection would provide an important pathway to examining the planetary ephemerides used in pulsar timing, and would potentially enhance the sensitivities of the pulsar timing arrays used to detect stochastic gravitational-wave background in the nano-Hz regime. We aim to significantly improve the precision of the VLBI-based MSP position (from $ at present) by reducing the two dominant components in the positional uncertainty --- the propagation-related uncertainty and the uncertainty resulting from the frequency-dependent core shifts of the reference sources. We introduce a new differential astrometry strategy called PINPT (Phase-screen Interpolation plus frequeNcy-dePendent core shifT correction; pronounced ``pinpoint''), which entails the use of multiple calibrators observed at several widely separated frequencies. The strategy allows determination of the core shift and mitigates the impact of residual delay in the atmosphere. We implemented the strategy on an MSP that is well constrained astrometrically with VLBI and pulsar timing. Using the PINPT strategy, we determined core shifts for four AGNs around and derived a VLBI-based pulsar position with uncertainties of 0.17\,mas and 0.32\,mas in Right Ascension and Declination, respectively, approaching the uncertainty level of the best-determined timing-based MSP positions. Additionally, incorporating the new observations into historical ones, we refined the pulsar proper motion and the parallax-based distance to the $ level and the subparsec level, respectively. The realization of the PINPT strategy promises a factor-of-five positional precision enhancement (over conventional VLBI astrometry) for all kinds of compact radio sources observed at $ including most fast radio bursts.

The Influence of Different Solar System Planetary Ephemerides on Pulsar Timing

Pulsar timing offers a comprehensive avenue for exploring diverse topics in physics and astrophysics. High-precision solar system planetary ephemeris is crucial for pulsar timing as it provides the positions and velocities of solar system planets including the Earth. However, it is inevitable that inherent inconsistencies exist in these ephemerides. Differences between various ephemerides can significantly impact pulsar timing and parameter estimations. Currently, pulsar timing highly depends on the JPL DE ephemeris, for instance, the Pulsar Timing Array data analysis predominantly utilizes DE436. In this study, we examine inconsistencies across various ephemeris series, including JPL DE, EPM, and INPOP. Notably, discrepancies emerge particularly between the current ephemeris DE436 and the earliest released ephemeris DE200, as well as the most recent ephemerides, e.g., DE440, INPOP21A, and EPM2021. Further detailed analysis of the effects of ephemeris on geometric correction procedures for the conversion of measured topocentric times of arrival is presented in this study. Our researches reveal that variations in the Roemer delays across different ephemerides lead to distinct differences. The timing residuals and the fact that these discrepancies can be readily incorporated into the subsequent pulsar parameters, leading to inconsistent fitting estimates, suggest that the influence of errors in the ephemeris on the timing process might currently be underappreciated.

Multiple-arc optimization of low-thrust Earth–Moon orbit transfers leveraging implicit costate transformation

This work focuses on minimum-time low-thrust orbit transfers from a prescribed low Earth orbit to a specified low lunar orbit. The well-established indirect formulation of minimum-time orbit transfers is extended to a multibody dynamical framework, with initial and final orbits around two distinct primaries. To do this, different representations, useful for describing orbit dynamics, are introduced, i.e., modified equinoctial elements (MEE) and Cartesian coordinates (CC). Use of two sets of MEE, relative to either Earth or Moon, allows simple writing of the boundary conditions about the two celestial bodies, but requires the formulation of a multiple-arc trajectory optimization problem, including two legs: (a) geocentric leg and (b) selenocentric leg. In the numerical solution process, the transition between the two MEE representations uses CC, which play the role of convenient intermediate, matching variables. The multiple-arc formulation at hand leads to identifying a set of intermediate necessary conditions for optimality, at the transition between the two legs. This research proves that a closed-form solution to these intermediate conditions exists, leveraging implicit costate transformation. As a result, the parameter set for an indirect algorithm retains the reduced size of the typical set associated with a single-arc optimization problem. The indirect heuristic technique, based on the joint use of the necessary conditions and a heuristic algorithm (i.e., differential evolution in this study) is proposed as the numerical solution method, together with the definition of a layered fitness function, aimed at facilitating convergence. The minimum-time trajectory of interest is sought in a high-fidelity dynamical framework, with the use of planetary ephemeris and the inclusion of the simultaneous gravitational action of Sun, Earth, and Moon, along the entire transfer path. The numerical results unequivocally prove that the approach developed in this research is effective for determining minimum-time low-thrust Earth–Moon orbit transfers.

Bayesian test of Brans–Dicke theories with planetary ephemerides: Investigating the strong equivalence principle

Aims. We are testing the Brans–Dicke class of scalar tensor theories with planetary ephemerides. Methods. In this work, we apply our recently proposed Bayesian methodology to the Brans–Dicke case, with an emphasis on the issue of the strong equivalence principle (SEP). Results. We use an MCMC approach coupled to full, consistent planetary ephemeris construction (from point-mass body integration to observational fit) and compare the posterior distributions obtained with and without the introduction of potential violations of the SEP. Conclusions. We observe a shift in the confidence levels of the posteriors obtained. We interpret this shift as marginal evidence that the effect of violation of the SEP can no longer be assumed to be negligible in planetary ephemerides with the current data. We also notably report that the constraint on the Brans–Dicke parameter with planetary ephemerides is getting closer to the figure reported from the Cassini spacecraft alone, and also to the constraints from pulsars. We anticipate that data from future spacecraft missions, such as BepiColombo, will significantly enhance the constraints based on planetary ephemerides.

Testing theories of gravitation with the Interstellar Probe Radio Experiment

General Relativity (GR) will soon celebrate its 110th birthday, holding up against all experimental enquiry. Nonetheless, unification theories attempting to quantize gravity, such as string theory, are gaining footing. These hypothesize additional scalar, vector, and tensor long-range fields that couple to matter (Will, 2014), introducing violations to GR. Although such violations have never been detected, it is likely that GR will not be the ultimate theory of gravity. What is certain is that gravity tests are alive and well, pushing the validity of GR to new scales and accuracies, or -potentially- suggesting alternative routes for new physics.Building upon the legacy of Voyager and Pioneer missions, which demonstrated the capability to survive in the outer reaches of the solar system, the Interstellar Probe mission concept (McNutt et al., 2022) aims to characterise our heliosphere through state-of-the-art instrumentation, opening new frontiers also for GR testing. In this work, we investigate the possibility of constraining the Nordtvedt parameter η and the mass of the graviton via the Compton wavelength λC, by simulating the processing of 10 years of radiometric data from the Interstellar Probe. Station calibration and clock synchronisation, as well as limiting spacecraft precession manoeuvres are highlighted as key strategies for obtaining high-quality estimates. In the most favourable scenario, η can be constrained to less than 1.5·10-5, reducing the uncertainty obtained via Lunar Laser Ranging (Hofmann and Müller, 2018), and a lower bound of 1.4·1014 km is set for λC, improving the estimates obtained from planetary ephemerides (Bernus et al., 2020) and gravitational wave detection (Abbott et al., Jun 2021). Extending ranging measurement acquisition to 20 years improves the results tenfold. This experiment interrogates fundamental physics from a unique dynamical setting, investigating possible violations of the Equivalence Principle (EP) underlying GR.

The solar eclipse of A.D. 1221 May 23 and the value of ΔT

A total solar eclipse was recorded in a classic Chinese book with the title The Travels of an Alchemist: the Journey of the Taoist Ch’ang Ch’un from China to the Hindukush at the Sumons of Chingiz Khan. In the present paper, possible locations of the solar eclipse observation are investigated, taking into account the geographical characteristics of local environments. With a modern astronomical planetary ephemeris, the authors confirm the observation records and derive an upper limit of +768 seconds for the Δ T value at the epoch A.D. 1221.

Earth-Venus Mission Analysis via Weak Capture and Nonlinear Orbit Control

Exploration of Venus is recently driven by the interest of the scientific community in understanding the evolution of Earth-size planets, and is leading the implementation of missions that can benefit from new design techniques and technology. In this work, we investigate the possibility to implement a microsatellite exploration mission to Venus, taking advantage of (i) weak capture, and (ii) nonlinear orbit control. This research considers the case of a microsatellite, equipped with a high-thrust and a low-thrust propulsion system, and placed in a highly elliptical Earth orbit, not specifically designed for the Earth-Venus mission of interest. In particular, to minimize the propellant mass, phase (i) of the mission was designed to inject the microsatellite into a low-energy capture around Venus, at the end of the interplanetary arc. The low-energy capture is designed in the dynamical framework of the circular restricted 3-body problem associated with the Sun-Venus system. Modeling the problem with the use of the Hamiltonian formalism, capture trajectories can be characterized based on their state while transiting in the equilibrium region about the collinear libration point L1. Low-energy capture orbits are identified that require the minimum velocity change to be established. These results are obtained using the General Mission Analysis Tool, which implements planetary ephemeris. After completing the ballistic capture, phase (ii) of the mission starts, and it is aimed at driving the microsatellite toward the operational orbit about Venus. The transfer maneuver is based on the use of low-thrust propulsion and nonlinear orbit control. Convergence toward the desired operational orbit is investigated and is proven analytically using the Lyapunov stability theory, in conjunction with the LaSalle invariance principle, under certain conditions related to the orbit perturbing accelerations and the low-thrust magnitude. The numerical results prove that the mission profile at hand, combining low-energy capture and low-thrust nonlinear orbit control, represents a viable and effective strategy for microsatellite missions to Venus.

Комплексная оценка аналитических и численных моделей эфемерид планет Солнечной системы на примере околоземных КА

The paper presents a developed algorithm for using the high-precision numerical ephemerid models. Qualitative and quantitative comparison of analytical and numerical high-precision planetary ephemerid models was carried out, including NASA averaged elements model, Newcomb model, Mees model, DE/LE series models and EPM series models. Absolute values of the radius vector residuals for each planet of the Solar System were obtained within the framework of the considered ephemerid models. Integration methods were evaluated, including Runge—Kutta method of the 4th order, Adams method of the 16th order and Dorman-Prince method of the 5(4)th order. Results of evaluating accuracy and efficiency of calculations depending on the integration stage were obtained. Values of perturbing accelerations from the Sun, Moon and planets for a GLONASS-type spacecraft were calculated. Practical recommendations are provided for using analytical and numerical planetary ephemerides in simulation of the near-Earth spacecraft motion.

Spacecraft VLBI tracking to enhance stellar occultations astrometry of planetary satellites

Context. Stellar occultations currently provide the most accurate ground-based measurements of the positions of natural satellites (down to a few kilometres for the Galilean moons). However, when using these observations in the calculation of satellite ephemerides, the uncertainty in the planetary ephemerides dominates the error budget of the occultation. Aims. We quantify the local refinement in the central planet’s position achievable by performing Very Long Baseline Interferometry (VLBI) tracking of an in-system spacecraft temporally close to an occultation. We demonstrate the potential of using VLBI to enhance the science return of stellar occultations for satellite ephemerides. Methods. We identified the most promising observation and tracking opportunities offered by the Juno spacecraft around Jupiter as perfect test cases, for which we ran simulations of our VLBI experiment. Results. VLBI tracking at Juno’s perijove close to a stellar occultation locally (in time) reduces the uncertainty in Jupiter’s angular position in the sky to 250–400 m. This represents up to an order of magnitude improvement with respect to current solutions and is lower than the stellar occultation error, thus allowing the moon ephemeris solution to fully benefit from the observation. Conclusions. Our simulations showed that the proposed tracking and observation experiment can efficiently use synergies between ground- and space-based observations to enhance the science return on both ends. The reduced error budget for stellar occultations indeed helps to improve the moons’ ephemerides, which in turn benefit planetary missions and their science products, such as the recently launched JUICE and upcoming Europa Clipper missions.

Bayesian test of the mass of the graviton with planetary ephemerides

Bayesian test of the mass of the graviton with planetary ephemerides

PETREL19: a new numerical solution of planetary and lunar ephemeris

PETREL19: a new numerical solution of planetary and lunar ephemeris

Systematics of planetary ephemeris reference frames inferred from pulsar timing astrometry

Aims. This study aims to investigate the systematic errors in planetary ephemeris reference frames through pulsar timing observations. Methods. We used the published data sets from several pulsar timing arrays and performed timing analyses for each pulsar using different planetary ephemerides retrieved from the Jet Propulsion Laboratory’s Development Ephemeris (DE), Ephemeris of Planets and the Moon (EPM), and INPOP (Intégration Numérique Planétaire de l’Observatoire de Paris). Then, we compared the timing solutions and modeled the differences in position and proper motion by vector spherical harmonics of the first degree. The timing solutions were also compared with those determined by very long baseline interferometry (VLBI) astrometry. Results. The orientation offsets between the latest editions of the DE, EPM, and INPOP series do not exceed 0.4 milliarcseconds (mas), while the relative spins between these ephemerides are less than 5 microarcseconds per year (µasyr−1). We do not detect significant glides in either position or proper motion between these ephemerides. The orientation of the pulsar timing frames deviates from that of the VLBI frame from zero by approximately 0.4 mas when considering the formal uncertainty and possible systematics. Conclusions. The orientation of current planetary ephemeris frames is as accurate as at least 0.4 mas, and the nonrotation is better than 5 µas yr−1.

Study on Secular Change of the Earth’s Rotation Rate Based on Solar Eclipse Observation Records on October 13, 443 BC

ABSTRACT An observation of a solar eclipse that occurred on October 13, 443 BC during the reign of the Duke Ligong of Qin was recorded in the Twenty-Four Histories (China’s dynastic histories from remote antiquity till the Ming Dynasty). With modern astronomical planetary ephemeris, the observation records were studied. The results showed that the eclipse probably occurred around sunset in Yongcheng, the capital of Qin, where the sunset time was exactly between the first contact stage (partial eclipse begins) and the fourth contact stage (partial eclipse ends) of the eclipse. Furthermore, secular change of the earth’s rotation rate at that time is investigated in this work.

Reducing roundoff errors in numerical integration of planetary ephemeris

Reducing roundoff errors in numerical integration of planetary ephemeris

Astrometric observations of the main Saturnian satellites from 2004 to 2014 based on Gaia DR3

A total of 3169 astrometric positions of the seven main satellites of Saturn: Enceladus, Tethys, Dione, Rhea, Titan, Hyperion and Iapetus were obtained in the time span 2004–2014 from observations made with 1.56 m telescope at Sheshan station of Shanghai Observatory, CAS. We compared our observations to the theoretical positions retrieved from IMCCE ephemeris online service with satellite ephemeris of Lainey (2015) model and planetary ephemeris DE441. The mean residuals are between −25 mas and 39 mas in right ascension and declination, respectively. The positional standard errors are in the range 62–99 mas. Moreover, we also compared two recent orbit models of each satellite as well as three different planetary ephemerides of Saturn. These comparisons show that the differences among all the three planetary ephemerides are small.

Comparison of dynamical and kinematic reference frames via pulsar positions from timing, Gaia, and interferometric astrometry

Context. Pulsars are special objects whose positions can be determined independently from timing, radio interferometric, and Gaia astrometry at sub-milliarcsecond (mas) precision; thus, they provide a unique way to monitor the link between dynamical and kinematic reference frames. Aims. We aim to assess the orientation consistency between the dynamical reference frames represented by the planetary ephemerides and the kinematic reference frames constructed by Gaia and very long baseline interferometry (VLBI) through pulsar positions. Methods. We identified 49 pulsars in Gaia Data Release 3 and 62 pulsars with VLBI positions from the PSRπ and MSPSRπ projects and searched for the published timing solutions of these pulsars. We then compared pulsar positions measured by timing, VLBI, and Gaia to estimate the orientation offsets of the ephemeris frames with respect to the Gaia and VLBI reference frames by iterative fitting. Results. We found orientation offsets of ~10 mas in the DE200 frame with respect to the Gaia and VLBI frame. Our results strongly depend on the subset used in the comparison and they could be biased by underestimated errors in the archival timing data, reflecting the limitation of using the literature timing solutions to determine the frame rotation.

Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

The Hermean average perihelion rate ω˙2PN, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from −18 to −4 microarcseconds per century μascty−1, depending on the true anomaly at epoch f0. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun’s gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury’s perihelion rate ω˙exp recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is σω˙exp≃8μascty−1, corresponding to a relative accuracy of 2×10−7 for the combination 2+2γ−β/3 of the PPN parameters β and γ scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to ≃10–50 times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recently improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a ≃10−7 accuracy level in constraining β and γ in an extended mission, despite ≃10−6 seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not-too-distant future, it will be necessary to include the 2PN acceleration in the Solar System’s dynamics as well.

Виртуальные гравитационные маневры при проектировании межпланетных перелётов

It is shown that the backward in time extension of the spacecraft interplanetary launch trajectory from the point of the low orbit of the departure planet generates a trajectory structurally coinciding with the virtual gravity assist trajectory near the departure planet. The pericenters of the auxiliary beam of the flying by hyperbolas and the time of their pericenter passage in this case differ slightly from the corresponding parameters of the designed departure orbit when starting from the specified point. Thus, the search for the trajectory of an interplanetary flight can be separated from the need to take into account the boundary conditions of the launch from an intermediate low pre-launch orbit. The pre-launch orbit is refined on the results of the search for the trajectory of the interplanetary flight. A structurally uniform scheme of ballistic design of spacecraft flight paths using multiple gravitational maneuvers based on the consideration of planetary ephemerides is presented.

The Long-term Error Estimation Method for the Numerical Integrations of Celestial Orbits

Numerical methods have become a very important type of tool for celestial mechanics, especially in the study of planetary ephemerides. The errors generated during the computation are hard to know beforehand when applying a certain numerical integrator to solve a certain orbit. In that case, it is not easy to design a certain integrator for a certain celestial case when the requirement of accuracy were extremely high or the time-span of the integration were extremely large. Especially when a fixed-step method is applied, the caution and effort it takes would always be tremendous in finding a suitable time-step, because it is about whether the accuracy and time-cost of the final result are acceptable. Thus, finding the best balance between efficiency and accuracy with the least time cost appeared to be a major obstruction in the face of both numerical integrator designers and their users. To solve this problem, we investigate the variation pattern of truncation error and the pattern of rounding error distributions with time-step and time-span of the integration. According to those patterns, we promote an error estimation method that could predict the distribution of rounding errors and the total truncation errors with any time-step at any time-spot with little experimental cost, and test it with the Adams-Cowell method in the calculation of circular periodic orbits. This error estimation method is expected to be applied to the comparison of the performance of different numerical integrators, and also it can be of great help for finding the best solution to certain cases of complex celestial orbits calculations.