arXiv subjects

D. Vokrouhlicky

Publications and source records attributed to D. Vokrouhlicky.

At least 19 recordsLinked to original sources

arXiv2026

The spin state of asteroid Apophis and a prediction of its change during the 2029 close encounter with Earth

On April 13, 2029, the asteroid Apophis will pass near Earth at a geocentric distance of about 38,000 km. Numerical models have suggested that the post-encounter spin state will critically depend on the orientation of Apophis during the flyby. We aim to determine the spin state of Apophis from its photometric observations collected during two apparitions in 2012-2013 and 2020-2021. This will enable us to accurately predict the pre-encounter rotation state and, by accounting for Earth's gravitational torque, predict a range of possible post-encounter states. We used the light curve inversion method for tumbling asteroids to reconstruct the spin state of Apophis and its convex shape model. The result is adopted as the initial condition of a numerical model describing Apophis's future rotation state. The data from the two apparitions are insufficient to determine Apophis's rotation and precession periods uniquely. The formally best-fit solution is 27.374 +/- 0.001 h for the precession period and 262.2 +/- 0.1 h for the rotation period, but at least two other combinations of the periods provide a similarly good fit to the available data. All the currently acceptable models result in approximately the same pre-encounter orientation of Apophis in early 2029. This is because the accurate photometric data were collected during two apparitions separated by 8 years, which is the same interval as from 2021 to 2029. Although the close encounter with Earth in April 2029 hugely increases the post-encounter uncertainty of Apophis's spin state, the short-axis spin mode will be preserved with a high likelihood. Additional observations taken in 2027 and 2028 will break the ambiguity in Apophis's pre-encounter spin solution and allow us to get a more accurate post-encounter spin state prediction

astro-ph.EP↗

arXiv2021

Rotation acceleration of asteroids (10115) 1992 SK, (1685) Toro, and (1620) Geographos due to the YORP effect

The rotation state of small asteroids is affected by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, which is a net torque caused by solar radiation directly reflected and thermally reemitted from the surface. Due to this effect, the rotation period slowly changes, which can be most easily measured in light curves because the shift in the rotation phase accumulates over time quadratically. We collected archived light curves and carried out new photometric observations for asteroids (10115) 1992 SK, (1620) Geographos, and (1685) Toro. We applied the method of light curve inversion to fit observations with a convex shape model. The YORP effect was modeled as a linear change of the rotation frequency $\upsilon \equiv \mathrm{d}ω/ \mathrm{d}t$ and optimized together with other spin and shape parameters. We detected the acceleration $\upsilon = (8.3 \pm 0.6) \times 10^{-8}\,\mathrm{rad}\,\mathrm{d}^{-2}$ of the rotation for asteroid (10115) 1992 SK. This observed value agrees well with the theoretical value of YORP-induced spin-up computed for our shape and spin model. For (1685) Toro, we obtained $\upsilon = (3.3 \pm 0.3) \times 10^{-9}\,\mathrm{rad}\,\mathrm{d}^{-2}$, which confirms an earlier tentative YORP detection. For (1620) Geographos, we confirmed the previously detected YORP acceleration and derived an updated value of $\upsilon$ with a smaller uncertainty. We also included the effect of solar precession into our inversion algorithm, and we show that there are hints of this effect in Geographos' data. The detected change of the spin rate of (10115) 1992 SK has increased the total number of asteroids with YORP detection to ten. In all ten cases, the $\mathrm{d}ω/ \mathrm{d}t$ value is positive, so the rotation of these asteroids is accelerated. It is unlikely to be just a statistical fluke, but it is probably a real feature that needs to be explained.

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arXiv2020

Analytical solution of the Colombo top problem

The Colombo top is a basic model in the rotation dynamics of a celestial body moving on a precessing orbit and perturbed by a gravitational torque. The paper presents a detailed study of analytical solution to this problem. By solving algebraic equations of degree 4, we provide the expressions for the extreme points of trajectories as functions of their energy. The location of stationary points (known as the Cassini states) is found as the function of the two parameters of the problem. Analytical solution in terms the Weierstrass and the Jacobi elliptic functions is given for regular trajectories. Some trajectories are expressible through elementary functions: not only the homoclinic orbits, as expected, but also a special periodic solution whose energy is equal to that of the first Cassini state (unnoticed in previous studies).

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arXiv2020

Very Slow Rotators from Tidally Synchronized Binaries

A recent examination of K2 lightcurves indicates that ~15% of Jupiter Trojans have very slow rotation (spin periods Ps>100 h). Here we consider the possibility that these bodies formed as equal-size binaries in the massive outer disk at ~20-30 au. Prior to their implantation as Jupiter Trojans, tight binaries tidally evolved toward a synchronous state with Ps~Pb, where Pb is the binary orbit period. They may have been subsequently dissociated by impacts and planetary encounters with at least one binary component retaining its slow rotation. Surviving binaries on Trojan orbits would continue to evolve by tides and spin-changing impacts over 4.5 Gyr. To explain the observed fraction of slow rotators, we find that at least ~15-20% of outer disk bodies with diameters 15<D<50 km would have to form as equal-size binaries with 12<ab/R<30, where ab is the binary semimajor axis and R=D/2. The mechanism proposed here could also explain very slow rotators found in other small body populations.

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arXiv2019

Doubly eclipsing systems

Aims: Our goal was to increase number of known doubly eclipsing systems such that the resulting dataset would allow to study them via statistical means, as well as prove that they constitute gravitationally bound 2+2 quadruple system. Methods: We analysed photometric data for eclipsing binaries provided by the OGLE survey in the LMC fields. We found a large number of new doubly eclipsing systems (our discoveries are 3x more numerous than previous studies). With a typical orbital period of days for the binaries, we sought eclipse time variations (ETVs) on the timescale of years. In the cases where we were able to detect the ETV period, the difference between the inner and outer periods in the quadruple system is large enough. This allows us to interpret ETVs primarily as the light-time effect, thus providing an interesting constraint on masses of the binaries. Results: In addition to significantly enlarging the database of known doubly eclipsing systems, we performed a thorough analysis of 72 cases. ETVs for 28 of them (39% of the studied cases) showed evidence of relative motion. We note OGLE BLG-ECL-145467 as the most interesting case; it is bright (I=12.6 mag), consists of two detached binaries with periods of about 3.3 d and 4.9 d (making it a candidate for a 3:2 resonant system), mutual period about 1538 d. Distribution of the orbital period ratio P_A/P_B of binaries in 2+2 quadruples shows statistically significant excess at 1 and 1.5. The former is likely a natural statistical preference in weakly interacting systems with periods within the same range. The latter is thought to be evidence of a capture in the 3:2 mean motion resonance of the two binaries. This sets important constraints on evolutionary channels in these systems. The total number of doubly eclipsing systems increased to 146, more than 90% of which are at low declinations on the southern sky.

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arXiv2017

YORP and Yarkovsky effects in asteroids (1685) Toro, (2100) Ra-Shalom, (3103) Eger, and (161989) Cacus

The rotation states of small asteroids are affected by a net torque arising from an anisotropic sunlight reflection and thermal radiation from the asteroids' surfaces. On long timescales, this so-called YORP effect can change asteroid spin directions and their rotation periods. We analyzed lightcurves of four selected near-Earth asteroids with the aim of detecting secular changes in their rotation rates that are caused by YORP. We use the lightcurve inversion method to model the observed lightcurves and include the change in the rotation rate $\mathrm{d} ω/ \mathrm{d} t$ as a free parameter of optimization. We collected more than 70 new lightcurves. For asteroids Toro and Cacus, we used thermal infrared data from the WISE spacecraft and estimated their size and thermal inertia. We also used the currently available optical and radar astrometry of Toro, Ra-Shalom, and Cacus to infer the Yarkovsky effect. We detected a YORP acceleration of $\mathrm{d}ω/ \mathrm{d} t = (1.9 \pm 0.3) \times 10^{-8}\,\mathrm{rad}\,\mathrm{d}^{-2}$ for asteroid Cacus. For Toro, we have a tentative ($2σ$) detection of YORP from a significant improvement of the lightcurve fit for a nonzero value of $\mathrm{d}ω/ \mathrm{d} t = 3.0 \times 10^{-9}\,\mathrm{rad}\,\mathrm{d}^{-2}$. For asteroid Eger, we confirmed the previously published YORP detection with more data and updated the YORP value to $(1.1 \pm 0.5) \times 10^{-8}\,\mathrm{rad}\,\mathrm{d}^{-2}$. We also updated the shape model of asteroid Ra-Shalom and put an upper limit for the change of the rotation rate to $|\mathrm{d}ω/ \mathrm{d} t| \lesssim 1.5 \times 10^{-8}\,\mathrm{rad}\,\mathrm{d}^{-2}$. Ra-Shalom has a greater than $3σ$ Yarkovsky detection with a theoretical value consistent with observations assuming its size and/or density is slightly larger than the nominally expected values.

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arXiv2017

Origin and Evolution of Short-Period Comets

Comets are icy objects that orbitally evolve from the trans-Neptunian region (the Kuiper belt and beyond) into the inner Solar System, where they are heated by solar radiation and become active due to sublimation of water ice. Here we perform end-to-end simulations in which cometary reservoirs are formed in the early Solar System and evolved over 4.5 Gyr. The gravitational effects of Planet 9 (P9), hypothesized to circle the Sun on a wide orbit, are included in some of our simulations. Different models are considered for comets to be active, including a simple assumption that comets remain active for Np(q) perihelion passages with perihelion distance q<2.5 au. The orbital distribution and number of active comets produced in our model is compared to observations. The orbital distribution of ecliptic comets (ECs) is well reproduced in models with Np(2.5)=500 and without P9. With P9, the inclination distribution of model ECs is wider than the observed one. We find that the known Halley-type comets (HTCs) have a nearly isotropic inclination distribution (with only a slight preference for prograde orbits). In our model, the HTCs appear to be an extension of the population of returning Oort-cloud comets (OCCs) to shorter orbital periods. The inclination distribution of model HTCs becomes broader with increasing Np, but the existing observational data are not good enough to constrain Np from orbital fits. Np(2.5)>1000 is required to obtain a steady-state population of large active HTCs that is consistent with observations. To fit the ratio of the returning-to-new OCCs, by contrast, our model implies that Np(2.5)<10, possibly because the detected long-period comets are smaller and much easier to disrupt than observed HTCs.

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arXiv2016

Near-Earth asteroid (3200) Phaethon. Characterization of its orbit, spin state, and thermophysical parameters

The near-Earth asteroid (3200) Phaethon is an intriguing object: its perihelion is at only 0.14 au and is associated with the Geminid meteor stream. We aim to use all available disk-integrated optical data to derive a reliable convex shape model of Phaethon. By interpreting the available space- and ground-based thermal infrared data and Spitzer spectra using a thermophysical model, we also aim to further constrain its size, thermal inertia, and visible geometric albedo. We applied the convex inversion method to the new optical data obtained by six instruments and to previous observations. The convex shape model was then used as input for the thermophysical modeling. We also studied the long-term stability of Phaethon's orbit and spin axis with a numerical orbital and rotation-state integrator. We present a new convex shape model and rotational state of Phaethon: a sidereal rotation period of 3.603958(2) h and ecliptic coordinates of the preferred pole orientation of (319$^{\circ}$, $-$39$^{\circ}$) with a 5$^{\circ}$ uncertainty. Moreover, we derive its size ($D$=5.1$\pm$0.2 km), thermal inertia ($Γ$=600$\pm$200 J m$^{-2}$ s$^{-1/2}$ K$^{-1}$), geometric visible albedo ($p_{\mathrm{V}}$=0.122$\pm$0.008), and estimate the macroscopic surface roughness. We also find that the Sun illumination at the perihelion passage during the past several thousand years is not connected to a specific area on the surface, which implies non-preferential heating.

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arXiv2016

Dynamics and Transit Variations of Resonant Exoplanets

The Transit Timing Variations (TTVs) are deviations of the measured mid-transit times from the exact periodicity. One of the most interesting causes of TTVs is the gravitational interaction between planets. Here we consider a case of two planets in a mean motion resonance (orbital periods in a ratio of small integers). This case is important because the resonant interaction can amplify the TTV effect and allow planets to be detected more easily. We develop an analytic model of the resonant dynamics valid for small orbital eccentricities and use it to derive the principal TTV terms. We find that a resonant system should show TTV terms with two basic periods (and their harmonics). The resonant TTV period is proportional (m/M_*)^(-2/3), where m and M_* are the planetary and stellar masses. For m=10^(-4) M_*, for example, the TTV period exceeds the orbital period by ~2 orders of magnitude. The amplitude of the resonant TTV terms scales linearly with the libration amplitude. The ratio of the TTV amplitudes of two resonant planets is inversely proportional to the ratio of their masses. These and other relationships discussed in the main text can be used to aid the interpretation of TTV observations.

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arXiv2015

The Yarkovsky and YORP Effects

The Yarkovsky effect describes a small but significant force that affects the orbital motion of meteoroids and asteroids smaller than $30-40$ kilometers in diameter. It is caused by sunlight; when these bodies heat up in the Sun, they eventually re-radiate the energy away in the thermal waveband, which in turn creates a tiny thrust. This recoil acceleration is much weaker than solar and planetary gravitational forces, but it can produce measurable orbital changes over decades and substantial orbital effects over millions to billions of years. The same physical phenomenon also creates a thermal torque that, complemented by a torque produced by scattered sunlight, can modify the rotation rates and obliquities of small bodies as well. This rotational variant has been coined the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. During the past decade or so, the Yarkovsky and YORP effects have been used to explore and potentially resolve a number of unsolved mysteries in planetary science dealing with small bodies. Here we review the main results to date, and preview the goals for future work.

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arXiv2014

Orbital Perturbations of the Galilean Satellites During Planetary Encounters

The Nice model of the dynamical instability and migration of the giant planets can explain many properties of the present Solar System, and can be used to constrain its early architecture. In the jumping-Jupiter version of the Nice model, required from the terrestrial planet constraint and dynamical structure of the asteroid belt, Jupiter has encounters with an ice giant. Here we study the survival of the Galilean satellites in the jumping-Jupiter model. This is an important concern because the ice-giant encounters, if deep enough, could dynamically perturb the orbits of the Galilean satellites, and lead to implausible results. We performed numerical integrations where we tracked the effect of planetary encounters on the Galilean moons. We considered three instability cases from Nesvorny & Morbidelli (2012) that differed in the number and distribution of encounters. We found that in one case, where the number of close encounters was relatively small, the Galilean satellite orbits were not significantly affected. In the other two, the orbital eccentricities of all moons were excited by encounters, Callisto's semimajor axis changed, and, in a large fraction of trials, the Laplace resonance of the inner three moons was disrupted. The subsequent evolution by tides damps eccentricities and can recapture the moons in the Laplace resonance. A more important constraint is represented by the orbital inclinations of the moons, which can be excited during the encounters and not appreciably damped by tides. We find that one instability case taken from Nesvorny & Morbidelli (2012) clearly fails this constraint. This shows how the regular satellites of Jupiter can be used to set limits on the properties of encounters in the jumping-Jupiter model, and help us to better understand how the early Solar System evolved.

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arXiv2014

Capture of Irregular Satellites at Jupiter

The irregular satellites of outer planets are thought to have been captured from heliocentric orbits. The exact nature of the capture process, however, remains uncertain. We examine the possibility that irregular satellites were captured from the planetesimal disk during the early Solar System instability when encounters between the outer planets occurred (Nesvorny, Vokrouhlicky & Morbidelli 2007, AJ 133; hereafter NVM07). NVM07 already showed that the irregular satellites of Saturn, Uranus and Neptune were plausibly captured during planetary encounters. Here we find that the current instability models present favorable conditions for capture of irregular satellites at Jupiter as well, mainly because Jupiter undergoes a phase of close encounters with an ice giant. We show that the orbital distribution of bodies captured during planetary encounters provides a good match to the observed distribution of irregular satellites at Jupiter. The capture efficiency for each particle in the original transplanetary disk is found to be (1.3-3.6)x10^-8. This is roughly enough to explain the observed population of jovian irregular moons. We also confirm NVM07's results for the irregular satellites of Saturn, Uranus and Neptune.

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arXiv2012

Near Earth Asteroids with measurable Yarkovsky effect

We seek evidence of the Yarkovsky effect among Near Earth Asteroids (NEAs) by measuring the Yarkovsky-related orbital drift from the orbital fit. To prevent the occurrence of unreliable detections we employ a high precision dynamical model, including the Newtonian attraction of 16 massive asteroids and the planetary relativistic terms, and a suitable astrometric data treatment. We find 21 NEAs whose orbital fits show a measurable orbital drift with a signal to noise ratio (SNR) greater than 3. The best determination is for asteroid (101955) 1999 RQ36, resulting in the recovery of one radar apparition and an orbit improvement by two orders of magnitude. In addition, we find 16 cases with a lower SNR that, despite being less reliable, are good candidates for becoming stronger detections in the future. In some cases it is possible to constrain physical quantities otherwise unknown by means of the detected orbital drift. Furthermore, the distribution of the detected orbital drifts shows an excess of retrograde rotators that can be connected to the delivery mechanism from the most important NEA feeding resonances and allows us to infer the distribution for NEAs obliquity. We discuss the implications of the Yarkovsky effect for impact predictions. In particular, for asteroid (29075) 1950 DA our results favor a retrograde rotation that would rule out an impact in 2880.

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arXiv2012

Analysis of the rotation period of asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger - search for the YORP effect

The spin state of small asteroids can change on a long timescale by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, the net torque that arises from anisotropically scattered sunlight and proper thermal radiation from an irregularly-shaped asteroid. The secular change in the rotation period caused by the YORP effect can be detected by analysis of asteroid photometric lightcurves. We analyzed photometric lightcurves of near-Earth asteroids (1865) Cerberus, (2100) Ra-Shalom, and (3103) Eger with the aim to detect possible deviations from the constant rotation caused by the YORP effect. We carried out new photometric observations of the three asteroids, combined the new lightcurves with archived data, and used the lightcurve inversion method to model the asteroid shape, pole direction, and rotation rate. The YORP effect was modeled as a linear change in the rotation rate in time dω/dt. Values of dω/ dt derived from observations were compared with the values predicted by theory. We derived physical models for all three asteroids. We had to model Eger as a nonconvex body because the convex model failed to fit the lightcurves observed at high phase angles. We probably detected the acceleration of the rotation rate of Eger dω/ dt = (1.4 +/- 0.6) x 10^{-8} rad/d (3σerror), which corresponds to a decrease in the rotation period by 4.2 ms/yr. The photometry of Cerberus and Ra-Shalom was consistent with a constant-period model, and no secular change in the spin rate was detected. We could only constrain maximum values of |dω/ dt| < 8 x 10^{-9} rad/d for Cerberus, and |dω/ dt| < 3 x 10^{-8} rad/d for Ra-Shalom.

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arXiv2010

Formation of asteroid pairs by rotational fission

Asteroid pairs sharing similar heliocentric orbits were found recently. Backward integrations of their orbits indicated that they separated gently with low relative velocities, but did not provide additional insight into their formation mechanism. A previously hypothesized rotational fission process4 may explain their formation - critical predictions are that the mass ratios are less than about 0.2 and, as the mass ratio approaches this upper limit, the spin period of the larger body becomes long. Here we report photometric observations of a sample of asteroid pairs revealing that primaries of pairs with mass ratios much less than 0.2 rotate rapidly, near their critical fission frequency. As the mass ratio approaches 0.2, the primary period grows long. This occurs as the total energy of the system approaches zero requiring the asteroid pair to extract an increasing fraction of energy from the primary's spin in order to escape. We do not find asteroid pairs with mass ratios larger than 0.2. Rotationally fissioned systems beyond this limit have insufficient energy to disrupt. We conclude that asteroid pairs are formed by the rotational fission of a parent asteroid into a proto-binary system which subsequently disrupts under its own internal system dynamics soon after formation.

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arXiv2010

A unified solution for the orbit and light-time effect in the V505 Sgr system

The multiple system V505 Sagittarii is composed of at least three stars: a compact eclipsing pair and a distant component, which orbit is measured directly using speckle interferometry. In order to explain the observed orbit of the third body in V505 Sagittarii and also other observable quantities, namely the minima timings of the eclipsing binary and two different radial velocities in the spectrum, we thoroughly test a fourth-body hypothesis - a perturbation by a dim, yet-unobserved object. We use an N-body numerical integrator to simulate future and past orbital evolution of 3 or 4 components in this system. We construct a suitable chi^2 metric from all available speckle-interferometry, minima-timings and radial-velocity data and we scan a part of a parameter space to get at least some of allowed solutions. In principle, we are able to explain all observable quantities by a presence of a fourth body, but the resulting likelihood of this hypothesis is very low. We also discuss other theoretical explanations of the minima timings variations. Further observations of the minima timings during the next decade or high-resolution spectroscopic data can significantly constrain the model.

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arXiv2009

Light-time computations for the BepiColombo radioscience experiment

The radioscience experiment is one of the on board experiment of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian (PN) parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the space-time coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.

gr-qc↗

arXiv2003

The IAU 2000 resolutions for astrometry, celestial mechanics and metrology in the relativistic framework: explanatory supplement

This paper discusses the IAU Resolutions B1.3, B1.4, B1.5 and B1.9 (2000) that were adopted during the 24th General Assembly in Manchester, 2000 and provides details and explanations for these Resolutions. It is explained why they present significant progress over the corresponding IAU 1991 Resolutions and why they are necessary in the light of present accuracies in astrometry, celestial mechanics and metrology. In fact most of these Resolutions are consistent with astronomical models and software already in use. The metric tensors and gravitational potentials of both the Barycentric Celestial Reference System and Geocentric Celestial Reference System are defined and discussed. The necessity and relevance of the two celestial reference systems are explained. The transformations of coordinates and gravitational potentials are discussed. Potential coefficients parameterizing the post-Newtonian gravitational potentials are expounded. Simplified versions of the time transformations suitable for modern clock accuracies are elucidated. Various approximations used in the Resolutions are explicated and justified. Some models (e.g. for higher spin moments) that serve the purpose for estimating orders of magnitude have actually never been published before.

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