Nongravitational Parameters Research Articles

Asteroids discovered in the Baldone Observatory between 2017 and 2022: The orbits of asteroid 428694 Saule and 330836 Orius

Abstract We discovered 83 asteroids at the Baldone Astrophysical Observatory (MPC code 069) in 2017–2022. We studied one of the dynamically interesting Apollo (Near Earth object) observed at the Baldone Astronomical Observatory, namely 428694 Saule (2008 OS9) and the Centaur-type asteroid 330836 Orius (2009 HW77). We studied the evolution of the asteroid Saule’s rotation period, obliquity, and spin axis together with its non-gravitational parameter d a ∕ d t {\rm{d}}a/{\rm{d}}t connected with the Yarkovsky effect. Additionally, we studied the orbit of the Amor-type asteroid 2017 UW42, which has the significant non-gravitational parameter A 2 A2 .

Physical parameters and orbital evolution of asteroids in retrograde orbits

Context. We studied the dynamical orbital and physical evolution of all 21 numbered and 13 selected unnumbered asteroids in retrograde orbits. Aims. Based on all published observations of studied asteroids in retrograde orbits, we computed their starting orbital elements, absolute magnitudes, and diameters, together with the non-gravitational parameters A2 and da/dt. Methods. Using publicly available orbital computation methods, we studied the dynamical evolution of orbital elements and the physical parameters of asteroids: rotation period, spin direction, and the non-gravitational parameters A2. Results. Lyapunov times (LT) for studied asteroids are short, from 60 to 36 496 yr, with a mean of 5978. Without considering non-gravitational effects, LT is longer: values range from 328 to 63 165 yr, with a mean of 6392. Over the next 10 Myr and beyond, the rotation period of the studied asteroids P decreases by approximately 8%. Moreover, 15% of the clones slow down. Conclusions. The starting spin distribution becomes flatter, with only one large maximum in the range (0–5) deg containing 279 clones (i.e. approximately 13%). However, the non-gravitational parameter da/dt has a maximum value of around (0–0.04)× 10−5 au day−2 .

Non-gravitational parameters and orbital stability of asteroids in retrograde orbits

ABSTRACT We studied the dynamical evolution of all numbered and selected unnumbered asteroids in a retrograde orbit. We computed the absolute magnitude, size range, and non-gravitational parameters A2 and $Lyapunov\, times$ during the 2 Myr forward and backward orbital evolution of all 21 studied retrograde asteroids. We also studied non-gravitation parameters of 10 unnumbered retrograde asteroids brighter than 18.1 mag. It turns out that the values of A2 are of a similar order as for comets, i.e. on average, a few orders more than in the case of asteroids that are moving in prograde orbits. We investigated how the change of the non-gravitational effect influences the Lyapunov time and the evolution of the semimajor-axis-selected retrograde orbits during the forward and backward integration. We also indicated the roles of Lidov–Kozai resonance in the orbital evolution of the retrograde asteroid.

Tadpole type motion of charged dust in the Lagrange problem with planet Jupiter

We investigate the dynamics of charged dust interacting with the interplanetary magnetic field in a Parker spiral type model and subject to the solar wind and Poynting–Robertson​ effect in the vicinity of the 1:1 mean motion resonance with planet Jupiter. We estimate the shifts of the location of the minimum libration amplitude solutions close to the location of the L4 and L5 points of the classical – gravitational – problem and provide the extension of the ‘librational regimes of motion’ and the width of the resonance in dependency of the nongravitational parameters related to the dust grain size and surface potential of the particles. Our study is based on numerical simulations in the framework of the spatial, elliptic restricted three-body problem and semi-analytical estimates obtained by averaging of Gauss’ planetary equations of motion.

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.

Orbital Deflection of Comets by Directed Energy

Abstract Cometary impacts pose a long-term hazard to life on Earth. Impact mitigation techniques have been studied extensively, but they tend to focus on asteroid diversion. Typical asteroid interdiction schemes involve spacecraft physically intercepting the target, a task feasible only for targets identified decades in advance and in a narrow range of orbits—criteria unlikely to be satisfied by a threatening comet. Comets, however, are naturally perturbed from purely gravitational trajectories via solar heating of their surfaces, which activates sublimation-driven jets. Artificial heating of a comet, such as by a laser, may supplement natural heating by the Sun to purposefully manipulate its path and thereby avoid an impact. Deflection effectiveness depends on the comet’s heating response, which varies dramatically depending on factors including nucleus size, orbit, and dynamical history. These factors are incorporated into a numerical orbital model to assess the effectiveness and feasibility of using high-powered laser arrays in Earth orbit and on the ground for comet deflection. Simulation results suggest that a diffraction-limited 500 m orbital or terrestrial laser array operating at 10 GW for 1% of each day over 1 yr is sufficient to fully avert the impact of a typical 500 m diameter comet with primary nongravitational parameter A 1 = 2 × 10−8 au day−2. Strategies to avoid comet fragmentation during deflection are also discussed.

CONSTRAINTS ON COMET 332P/IKEYA-MURAKAMI

ABSTRACT Encke-type comet 332P/Ikeya-Murakami is experiencing cascading fragmentation events during its 2016 apparition. It is likely the first splitting Encke-type comet ever observed. A nongravitational solution to the astrometry reveals a statistical detection of the radial and transverse nongravitational parameters, au day−2 and au day−2, respectively, which implies a nucleus erosion rate of ‰ per orbital revolution. The mass-loss rate likely has to be supported by a much larger fraction of an active surface area than known cases of short-period comets; it may be relevant to the ongoing fragmentation. We failed to detect any serendipitous pre-discovery observations of the comet in archival data from major sky surveys, whereby we infer that 332P used to be largely inactive, and is perhaps among the few short-period comets that have been reactivated from weakly active or dormant states. We therefore constrain an upper limit to the nucleus size as 2.0 ± 0.2 km in radius. A search for small bodies in similar orbits to that of 332P reveals comet P/2010 B2 (WISE) to be the best candidate. From an empirical generalized Jupiter-family (Encke-type included) comet population model, we estimate the likelihood of a chance alignment of the 332P–P/2010 B2 pair to be 1 in 33, a small number indicative of a genetic linkage between the two comets on a statistical basis. The pair possibly originated from a common progenitor, which underwent a disintegration event well before the twentieth century.

THE PROGRESSIVE FRAGMENTATION OF 332P/IKEYA–MURAKAMI

ABSTRACT We describe 2016 January–April observations of the fragments of 332P/Ikeya–Murakami, a comet earlier observed in a 2010 October outburst. We present photometry of the fragments and perform simulations to infer the time of breakup. We argue that the eastern-most rapidly brightening fragment (F4) best corresponds to the original nucleus, rather than the initial bright fragment F1. We compute radial and tangential nongravitational parameters, A 1 = (1.5 ± 0.4) × 10−8 au day−2 and (7.2 ± 1.9) × 10−9 au day−2; both are consistent with zero at the 4σ level. Monte Carlo simulations indicate that the fragments were emitted on the outbound journey well after the 2010 outburst, with bright fragment F1 splitting in early 2014 and the fainter fragments within months of the 2016 January recovery. Western fragment F7 is the oldest, dating from 2011. We suggest that the delayed onset of the splitting is consistent with a self-propagating crystallization of water ice.

Use of long-term models for analysis of comet Encke’s motion

This paper is focused on the problem of the reactive non-gravitational effects change in the cometary motion caused by the comet’s activity fading. The modern researches have been reviewed. The necessity of a new model compatible with Marsden’s model of non-gravitational forces is shown. Modifications of Marsden’s model for the cases in which the main factors of the parameters change are the deposition of the significant non-volatile mass and the growth of the superficial crust are developed. They contain besides the usual Marsden’s parameters two and three additional values correspondingly. The developed equations have been used to explain the known change of Marsden’s non-gravitational parameters for the comet Encke during 225years of its observational interval. Although the model with significant non-volatile mass contains less free values, it explains the characteristic features of the comet’s non-gravitational parameters behavior better. The model can be further applied for the comet’s observed astrometric positions fitting.

GONE IN A BLAZE OF GLORY: THE DEMISE OF COMET C/2015 D1 (SOHO)

We present studies of C/2015 D1 (SOHO), the first sunskirting comet ever seen from ground stations over the past half century. The Solar and Heliospheric Observatory (SOHO) witnessed its peculiar light curve with a huge dip followed by a flareup around perihelion: the dip was likely caused by sublimation of olivines, directly evidenced by a coincident temporary disappearance of the tail. The flareup likely reflects a disintegration event, which we suggest was triggered by intense thermal stress established within the nucleus interior. Photometric data reveal an increasingly dusty coma, indicative of volatile depletion. A catastrophic mass loss rate of $\sim$10$^{5}$ kg s$^{-1}$ around perihelion was seen. Ground-based Xingming Observatory spotted the post-perihelion debris cloud. Our morphological simulations of post-perihelion images find newly released dust grains of size $a \gtrsim 10$ $\mu$m in radius, however, a temporal increase in $a_{\min}$ was also witnessed, possibly due to swift dispersions of smaller grains swept away by radiation forces without replenishment. Together with the fading profile of the light curve, a power law dust size distribution with index $\gamma = 3.2 \pm 0.1$ is derived. We detected no active remaining cometary nuclei over $\sim$0.1 km in radius in post-perihelion images acquired at Lowell Observatory. Applying radial non-gravitational parameter, $\mathcal{A}_{1} = \left(1.209 \pm 0.118 \right) \times 10^{-6}$ AU day$^{-2}$, from an isothermal water-ice sublimation model to the SOHO astrometry significantly reduces residuals and sinusoidal trends in the orbit determination. The nucleus mass $\sim$10$^{8}$--10$^{9}$ kg, and the radius $\sim$50--150 m (bulk density $\rho_{\mathrm{d}} = 0.4$ g cm$^{-3}$ assumed) before the disintegration are deduced from the photometric data; consistent results were determined from the non-gravitational effects.

Coupling the nongravitational forces and modified Newton dynamics for cometary orbits

In recent work (Milgrom 2009, Blanchet & Novak 2011), the authors showed that MOdified Newton Dynamics (MOND) have a non-negligible secular perturbation effect on planets with large semi-major axes (gaseous planets) in the Solar System. Some comets also have a very eccentric orbit with a large semi-major axis (Halley family comets) going far away from the Sun (more than 15 AU) in a low acceleration regime where they would be subject to MOND perturbation. They also approach the Sun very closely (less than 3 AU) and are affected by the sublimation of ices from their nucleus, triggering so-called non-gravitational forces. The main goal of this paper is to investigate the effect of MOND perturbation on three comets with various orbital elements (2P/Encke, 1P/Halley and 153P/Ikeya-Zhang) and then compare it to the non-gravitational perturbations. It is motivated by the fact that when fitting an outgassing model for a comet, we have to take into account all of the small perturbing effects to avoid absorbing these effects into the non-gravitational parameters. Otherwise, we could derive a completely wrong estimation of the outgassing. For this work, we use six different forms of MOND functions and compute the secular variations of the orbital elements due to MOND and non-gravitational perturbations. We show that, for comets with large semi-major axis, the MONDian effects are not negligible compared to the non-gravitational perturbations.

ARCHIVAL OBSERVATIONS OF ACTIVE ASTEROID 313P/GIBBS

We present prediscovery observations of active asteroid 313P/(2014 S4) Gibbs taken in 2003 and 2004. Sloan Digital Sky Survey observations from 2003 establish that, after 133P/Elst‐Pizarro and 238P/Read, 313P is only the third main-belt active asteroid to show mass loss in different orbits. This repetitive activity is consistent with mass loss driven by the sublimation of ice. A Finson-Probstein model is used to analyze the morphology of the object, showing that the activity was continuous but declining steadily over two months of observation in 2003. Ejected dust particles are dominated by relatively large sizes with radii from ! 25 to ! 600 ! m. We estimate from photometry the dust mass loss rate to be 10.2kg s ! 1 . In contrast, Subaru telescope observations from 2004 show no evidence for mass loss and suggest a bare nucleus. The color, nucleus size, and the mass loss rates of 313P measured in 2003 are consistent with published values obtained from data taken in 2014. However, the effective cross-section was larger than in 2014 by a factor of ! 2, indicating a decline in the activity between orbits. A new orbital solution gives a 5 upper limit to the transverse non-gravitational parameter q � A 1 2.45 10 2 8 AU day ! 2 .

Near-parabolic comets observed in 2006–2010. The individualized approach to 1/a-determination and the new distribution of original and future orbits

Dynamics of a complete sample of 22 small perihelion distance near-parabolic comets discovered in the years 2006 - 2010 is studied. First, osculating orbits are obtained after a careful positional data inspection and processing, including where appropriate, the method of data partitioning for determination of pre- and post-perihelion orbit for tracking then its dynamical evolution. The nongravitational acceleration in the motion is detected for 50 per cent of investigated comets, in a few cases for the first time. Different sets of nongravitational parameters are determined from pre- and post-perihelion data for some of them. The influence of the positional data structure on the possibility of the detection of nongravitational effects and the overall precision of orbit determination is widely discussed. Secondly, both original and future orbits were derived by means of numerical integration of swarms of virtual comets obtained using a Monte Carlo cloning method. This method allows to follow the uncertainties of orbital elements at each step of dynamical evolution. The complete statistics of original and future orbits that includes significantly different uncertainties of 1/a-values is presented, also in the light of our results obtained earlier. Basing on 108 comets examined by us so far, we conclude that only one of them, C/2007 W1 Boattini, seems to be a serious candidate for an interstellar comet. We also found that 53 per cent of 108 near-parabolic comets escaping in the future from the Solar system, and the number of comets leaving the Solar system as so called Oort spike comets is 14 per cent. A new method for cometary orbit quality assessment is also proposed that leads to a better diversification of orbit quality classes for contemporary comets.

CONGO, model of cometary non-gravitational forces combining astrometric and production rate data

The gravitational orbit of a comet is affected by the sublimation of water molecules by the nucleus when the comet approaches perihelion. This outgassing triggers a non-gravitational force (NGF) that significantly modifies the orbit of the comet. Up to now, modelling of this effect is mostly based on an empirical model defined in the early 70s that uses a simplified outgassing model. Attempts have been made to use advanced anisotropic thermal models both to calculate the NGF taking several observational constraints into account and to retrieve the nucleus’s mass and density, but (i) this approach is restricted to a handful of cometary nuclei that are sufficiently well known to allow this type of modelling, and (ii) the authors usually do not fit the astrometric measurements directly but rather non-gravitational parameters calculated with the above-mentioned empirical model. We present a new model for non-gravitational forces with the aim of revisiting the problem of NGF calculation and nucleus density determination. Our model is closer to the nucleus outgassing physics with only a few free parameters. The amplitude of the perturbation depends on several parameters describing the comet activity that can be constrained by visible, infrared, and radio observations of the coma and the nucleus of the comet. It also depends on the nucleus mass, which can in turn be determined by modelling the effect of the NGF on the orbit of a comet. The method is based on the decomposition of the surface of the nucleus in several elements located at different latitudes. The contribution of each surface element to the overall NGF is fitted from the astrometric measurements, together with the density of the nucleus. This method is the only one available so far to estimate the density of cometary nuclei from ground-based observations. This method is tested on the well-known comet 19P/Borrelly. The density found for these comet is between 150 and 600 kg m −3 .

Masses of long-period comets derived from non-gravitational effects - analysis of the computed results and the consistency and reliability of the non-gravitational parameters

We estimate masses for a selected sample of long-period comets (LPCs) (with orbital periods P > 1000 yr and perihelion distances q < 2 au), with good photometric visual light curves and known non-gravitational parameters. We follow a procedure similar to that developed by Szutowicz et al. to estimate the masses of comets C/1995 O1 (Hale–Bopp) and C/1996 B2 (Hyakutake). The method also requires the knowledge of the water production rates Q ,f or which we find a new correlation between Q and the visual total heliocentric magnitude mh of LPCs, which can be expressed as log10Q = 30.53 − 0.234mh. The computed masses are in the range [0.5, 10] × 10 12 kg. From these masses, and by assuming a cometary bulk density ρ of 0.4 g cm −3 , we estimate the effective nuclear radii RN for the studied LPCs to be in the range [0.7, 1.8] km. From the computed values of RN ,w e find that the active surface areas are (in most cases) greater than the geometric ones (fractions f ranging from 0.8 to 2.4). We argue that this could be understood as a state of hyperactivity, which can be explained if a significant fraction of the sublimated water molecules come from the sublimation of icy grains in the coma. Hyperactivity would make LPC nuclei smaller (i.e. less massive) than expected from their coma brightness. Other effects, like extremely low densities or overestimated non-gravitational parameters, might also contribute to the rather high computed value of f . For comet C/1995 O1 (Hale–Bopp), we find a seeming inconsistency between some size estimates and some computed non-gravitational parameters. We analyse some alternatives to this apparent paradox. We also compute absolute total magnitudes and photometric indices for the studied sample of LPCs and find a new correlation between masses and absolute total visual magnitudes H. By assuming ρ = 0.4 g cm −3 , we can convert masses to diameters D, leading to a relation log10D(km) = 1.5 − 0.13H.

Where do long-period comets come from? Moving through the Jupiter-Saturn barrier

Past and future dynamical evolution of all 64 long period comets having 1/aori< 1\times10-4 au-1 and qosc > 3.0 au and discovered after 1970 is studied. For all of them we obtained a new, homogeneous set of osculating orbits, including 15 orbits with detected non-gravitational parameters. The non-gravitational effects for eleven of these 15 comets have been determined for the first time. These were propagated numerically back and forth up to the 250 au heliocentric distance, constituting sets of original and future orbits together with their uncertainties. Next we followed the dynamical evolution under the Galactic tides for one orbital revolution to the past and future, obtaining orbital elements at previous/next perihelion passages. We obtained a clear dependence of the last revolution change in perihelion distance with respect to the 1/aori, what confirmed theoretical expectations. We show that about 50 per cent of all investigated comets have their previous perihelion distance below the 15 au limit. This resulted in classifying 31 comets as dynamically new, 26 as dynamically old and 7 having unclear status. We also present several examples of cometary motion through the Jupiter-Saturn barrier, some of them with the previous perihelion distance smaller than the observed one. New interpretations of the long period comets source pathways are also discussed in the light of suggestions of Kaib & Quinn (2009).

The effect of non-gravitational forces on the median inclination of short-period comets

The numbered Jupiter family comets (orbital periods P < 20 yr) have a median orbital inclination of about 10°0 ± 1°1. In this paper, we integrate the orbits of these comets into the future, under the influence of both typical non-gravitational forces and planetary perturbation, using a Bulirsch-Stoer integrator. In the case where non-gravitational forces were not acting, the median inclination of those comets that remained on P < 20 yr orbits increased at the rate of (1.92 ± 0.12) x 10- 3 deg yr -1 for the first 3600 yr of the integration. During this time the population of the original family decreases, such that the half-life is about 13 200 ± 800 yr. The introduction of non-gravitational forces slows down the rate of increase in inclination to a value of around (1.23 ± 0.16) x 10 -3 deg yr -1 . This rate of increase in inclination was found to be only weakly dependent on the non-gravitational parameters used during the integration. After a few thousand years, the rate of change in inclination decreases, and after 20 000 yr the inclinations of those initial Jupiter family members that still have orbits with P < 20 yr become constant at about 20°.0, independent of whether non-gravitational forces are acting or not. The presently known Jupiter family of comets is losing members at the rate of one in every 67 yr. To maintain the family in equilibrium, Jupiter has to capture comets at a similar rate, and these captured comets have to be of low inclination to compensate for the pumping up of inclinations by gravitational perturbation.

Long-period comets with non-gravitational effects

The influence of non-gravitational effects on the motion of long-period comets is analyzed. Investigations were performed for about 60 nearly-parabolic comets discovered during the last thirty years. All three non-gravitational parameters were detected in the motion of 19 comets on the basis of positional observations only. For these comets the standard g(r) function as well as some of its modifications were used to model the ice sublimation from the cometary nucleus. For 14 of 19 comets the orientation of spin axes of the nucleus were also determined. Finally, the magnitude of the non-gravitational effects derived for the long-period comets have been compared with observed the non-gravitational perturbations on periodic comets.

The Hypothesis of Additional Acceleration in the Motion of Comet Harrington–Abell from Jupiter

By processing 494 observations of Comet Harrington–Abell, we obtained a unified system of elements that includes its turn around the Sun during which it closely approached Jupiter to a minimum distance of 0.037 AU in 1974. A study of the cometary orbit before and after the approach showed that, probably, at the approach of the comet to Jupiter, apart from the well-known gravitational perturbations, its motion was affected by an additional force. An improvement of the cometary orbit by assuming that an additional acceleration inversely proportional to the square of the distance to Jupiter exists in its motion yielded the following values: (4.57 ± 0.42) × 10–10 and (–7.20 ± 0.42) × 10–10 AU day–2 for the radial and transversal acceleration components, respectively. As a plausible explanation of the changes in the cometary orbit, we additionally considered a model based on the hypothesis of partial disintegration of the cometary nucleus. The parameter that characterizes the instant displacement of the center of inertia along the jovicentric radius vector was estimated to be –1.83 ± 0.75 km. Based on a unified numerical theory of cometary motion, we determined the nongravitational parameters using Marsden's model for two periods: A1 = (11.68 ± 1.74) × 10–10 AU day–2, A2 = (0.53 ± 0.0357) × 10–10 AU day–2 for 1975–1999 and A1′ = (5.92 ± 5.86) × 10–10 AU day–2, A2′ = (0.08 ± 0.028) × 10–10 AU day–2 for 1955–1969, under the assumption that the nongravitational acceleration changed at the approach of the comet to Jupiter.

From Jupiter-family to Encke-like orbits

We investigate numerically the transfer routes from Jupiter-family towards Encke-like cometary orbits, including in the model all the planets as well as non-gravitational forces. The numerical integrations are started from orbital elements similar to those of 2P/Encke, changing the perihelion distance q, to obtain starting orbits in the Jupiter family, and the non-gravitational parameter A2. The results show that some of the model orbits reach the Encke-like stage within a reasonable time, comparable to a typical active cometary lifetime; along the way, at the crossing of mean motion resonances with Jupiter, temporary captures in resonance may occur. Thus, resonances and non-gravitational forces appear to be key factors in the transfer of orbits from the Jupiter family to the Encke region.