Motion Of Comet Research Articles

The gauge-generalized Gyldén–Meshcherskii Problem

The Gyldén–Meshcherskii Problem (GMP) extends the classical two-body problem of Newton and Kepler by considering time-varying gravitating masses, an important extension of the two-body problem for modeling cometary motion and cosmological phenomena. In this paper, we consider the GMP in a specialized setup, the setup of gauge theory. We show that the variational equations, modeling the effect of the mass time variation on the orbital elements, can be derived by fixing a gauge of a particular form that is different from the Lagrange gauge. Thus, the orbital elements modeling the effect of a time-varying secondary mass are non-osculating. This implies that the trajectory of a celestial body whose mass is continuously changing cannot be approximated by a series of Keplerian orbits. Finally, we provide the first-order averaged equations written in terms of non-osculating elements.

Stationary orbits of comets perturbed by Galactic tides

Using the first-order normalized equations describing the heliocentric cometary motion perturbed by the Galactic tides, we identify ‘stationary solutions’ with constant values of the eccentricity, inclination, argument of perihelion and longitude of the ascending node in the reference frame rotating with the Galaxy. The families found involve circular orbits, orbits in the Galactic equatorial plane, rectilinear orbits normal to the equatorial plane, elliptic orbits symmetric with respect to the direction to the Galactic Centre or to its perpendicular, and asymmetrically oriented elliptic orbits. Linear stability of the stationary solution is studied analytically and confirmed by numerical experiments. Most, but not all, of the unstable solutions prove chaotic with the Lyapunov times at least 100 Myr.

Models for the Comet Dynamical Environment

An outgassing jet model is presented in support of spacecraft navigation for future missions to comets. The outgassing jet is modeled as an emission cone while the comet is modeled as a uniform density triaxial ellipsoid. The comet's motion about the sun is included in the model. The model is used to explore the effects on a spacecraft passing through an outgassing jet field. The outgassing jet model is also used for simulation and estimation of the physical outgassing properties of jets at and near the surface of a comet. Methods for estimating the locations and sizes of multiple outgassing jets are presented.

A new algorithm of the recurrent power series method for the non-gravitational motion of comets

In this paper, an automatic symbolic version of the recurrent power series method has been established for integrating the equations of motion of comets taking into account the perturbations of the giant planets and the non-gravitational effects terms. This new version has the advantage of selecting the coefficients of the power series solutions from the equations of motion of the respective body directly. In this case, it is no need to make derivations of many recurrence relations for the power expansions both of cometary and planetary data. The program is also provided by optimum step size integrations and elaborated using Mathematica software packages. Application to the orbital motion of short-period comets is given.

A hero for their times: early biographies of NewtonIliffeRobKeynesMiloHiggittRebekaheds. Early biographies of Isaac Newton, 1660–1885(2 vols). Pickering & Chatto, London2006. pp. lxix +387; xlvii +420. £195.00 (hardback).1-85196-778-8.

Rob Iliffe, Milo Keynes, Rebekah Higgitt. eds. Early biographies of Isaac Newton, 1660–1885 (2 vols). Pickering & Chatto, London 2006. pp. lxix +387; xlvii +420. £195.00 (hardback). 1-85196-778-8. Though biography be no longer an act of worship, it is not yet a solemn and impartial judgment: we

Vectorial elements for the Galactic disc tide effects in cometary motion

The classical Matese-Whitman theory of Oort Cloud comet perturbations has been revisited and extended. An explicit solution for the motion of the mean ascending node is given; it involves an elliptic integral of the third kind. Equations of the mean orbit are formulated in terms of the Cartesian components of the Laplace and angular momentum vectors (vectorial elements). The equations are solved in terms of elliptic functions and the solution is free of the ambiguity related to the orientation of the perihelion that was present in previous work. The Cartesian equations of motion for the vectorial elements form a Hamiltonian system of the Lie-Poisson type. This allows them to be integrated numerically by means of Hamiltonian splitting methods. The formulae of such an integrator are derived with a Hamiltonian function split into two parts.

Comet 67P/Churyumov–Gerasimenko: Modeling of orientation and structure

The comet 67P/Churyumov–Gerasimenko is the current target of the mission Rosetta, initially planned to investigate comet 46P/Wirtanen. These two comets have similar orbits, except the distance to the Sun at perihelion, but different orbital histories and different masses. Thus, structures of the nuclei can be significantly different. The evolution of comet Wirtanen was simulated by several authors, while comet Churyumov–Gerasimenko became an object of high interest only recently and is not well investigated. In the present work we simulate the evolution of the nucleus, down to tens of meters below the surface, using an extended version of the model previously applied for comet Wirtanen [Kossacki et al., 1999. Comet 46P/Wirtanen: evolution of the subsurface layer. Icarus 142, 202–218.]. The model includes strengthening of the nucleus due to sintering of the ice grains. Simulations are performed for different latitudes, accounting for the evolution of the orbit and for changes of the nucleus orientation, as well as diurnal and seasonal changes of insolation. The calculated loss of water vapor from the comet is integrated over the nucleus surface and is compared with the observational data. We have found, that the sublimation through the dust mantle can be large enough to reproduce the profile of the total water production as a function of time from perihelion. The required dependence of thickness of the dust layer on latitude qualitatively matches present distribution of the absorbed solar flux. The non-gravitational acceleration in the comet motion together with the simulated sublimation flux are used in order to estimate the mass and the bulk density of the nucleus.

Midcourse Space ExperimentObservations of Small Solar System Bodies

Eight comets, two transition objects (extinct comet candidates), and two near-Earth asteroids were imaged in four infrared bands with the SPIRIT III instrument on the Midcourse Space Experiment, namely, C/1996 B2 (Hyakutake), C/1995 O1 (Hale-Bopp), C/1996 Q1 (Tabur), 126P/IRAS, 22P/Kopff, 46P/Wirtanen, (3200) Phaethon, (4015) 107P/Wilson-Harrington, (4179) Toutatis, (4197) 1982 TA, 125P/Spacewatch, and 55P/Tempel-Tuttle. We present maps of each object detected and a description of their characteristics. Five of the comets had extended dust tails, all of which show evidence for silicate emission in the 8.3 μm band. The comet C/Hyakutake had a strong secondary dust tail along the direction of the comet's motion, which the dynamical models showed was consistent with emission from large particles. The dust trail from P/Kopff was detected more than 2° from the coma in three of the four bands and is probably composed of large particles emitted during the 1996 apparition.

Constraints on the Acceleration of the Solar System from High-Precision Timing

Many astronomers have speculated that the solar system contains undiscovered massive planets or a distant stellar companion. The acceleration of the solar system barycenter can constrain the mass and position of the putative companion. In this paper we use the most recent timing data on accurate astronomical clocks (millisecond pulsars, pulsars in binary systems, and pulsating white dwarfs) to constrain this acceleration. No evidence for nonzero acceleration has been found; the typical sensitivity achieved by our method is a⊙/c ~ a few × 10-19 s-1, comparable to the acceleration due to a Jupiter-mass planet at 200 AU. The acceleration method is limited by the uncertainties in the distances and by the timing precision for pulsars in binary systems, and by the intrinsic distribution of the period derivatives for millisecond pulsars. Timing data provide stronger constraints than residuals in the motions of comets or planets if the distance to the companion exceeds a few hundred AU. The acceleration method is also more sensitive to the presence of a distant companion (300–400 AU) than existing optical and infrared surveys. We outline the differences between the effects of the peculiar acceleration of the solar system and the background of gravitational waves on high-precision timing.

Fred Lawrence Whipple

Fred Lawrence Whipple

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.

Nongravitational Accelerations on Comets

The orbital motion of comets is difficult to characterize accurately due to the rocket-like outgassing of material from the cometary nucleus. The resulting nongravitational accelerations often appear to be fundamentally stochastic in nature and thus pose severe modeling challenges in orbit determination, especially when the comet has been observed for many revolutions. Even so, new techniques have arisen in recent years that give new insight, not only into the motion of the comets, but also into their physical characteristics and spin states. These approaches include modeling of spin axis precession over many decades and the consideration of the seasonal variation in the thrust from discrete jets acting on a rotating nucleus. Such advances have been enabled, in part, by the increasing efforts and capabilities of comet observers worldwide as more and more comets with longer and longer observing arcs become available for study. In this review we specifically consider the application of the Rotating Jet Model to several space mission targets, indicating how this model can often be used to infer the orientation of a comet’s spin axis.

Long term dynamical evolution of the Oort cloud comets: galactic and planetary perturbations

The source of long-period comets can be numerically modeled by means of Monte Carlo simulation of the Oort cloud dynamics. Tracing a comet motion under the galactic perturbations over a long time interval requires taking into account of planetary perturbations. A method for the approximate treating of the planetary perturbations in such simulations is described. Some peculiarities found in planetary action on long-period simulated cometary sample are also discussed.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Fragmentation Hierarchy of Bright Sungrazing Comets and the Birth and Orbital Evolution of the Kreutz System. I. Two‐Superfragment Model

A back-and-forth orbit integration technique, developed for our previous investigation of the splitting of the parent of the sungrazers C/1882 R1 and C/1965 S1, is now applied in an effort to understand the history and orbital evolution of the Kreutz sungrazer system, starting with the birth of two subgroups, which show prominently among the bright members and whose inception dates back to the progenitor's breakup into two superfragments. The integration technique is used to reproduce the motion of comet C/1843 D1 - the second brightest sungrazer known and presumably the most massive surviving piece of superfragment I - from the motion of C/1882 R1 - the brightest sungrazer on record and arguably the most massive surviving piece of superfragment II. Running the orbit of C/1882 R1 back to A.D. 326, the progenitor comet is found to have split at a heliocentric distance of 50 AU and nearly 30 yr before perihelion. The superfragments acquired separation velocities of similar to8 m s(-1) in opposite directions. Using the same technique, we show next that (1) the motions of two additional sungrazers, C/1880 C1 and C/1887 B1, are matched extremely well if these objects shared a common parent with C/1843 D1, and (2) C/1963 R1 (Pereyra), the second brightest subgroup I member on record, is more closely related to subgroup II objects (such as C/1882 R1 and C/1965 S1) than to C/1843 D1. This finding raises serious doubts about the major role of the subgroups in the system's orbital history and offers an incentive for considering an alternative dynamical scenario. The fragmentation models for C/1963 R1 and two additional bright sungrazers, C/1945 X1 and C/1970 K1, suggest that (1) these comets may have been the most massive pieces of the fragment populations formed from their respective disintegrating parents, and (2) the course of evolution of the Kreutz system at the upper end of the mass spectrum may be better ascertained from the distribution of the sungrazers' arrival times than from the sources of subgroups. If so, the fragment hierarchy should be determined primarily by the cascading nature of the fragmentation process, which was recently shown by Sekanina to control the evolution of minor fragments as well. The sungrazer system's estimated age is in any case very short, less than 1700 yr.

Possible chaotic motion of comets in the Sun–Jupiter system—a computer-assisted approach based on shadowing

Using the shadowing technique we give an alternative computer-assisted proof of certain results in the restricted three-body problem made plausible by Koon et al (2000 Chaos 10 427–69), and rigorously established by Wilczak and Zgliczyński (2003 Commun. Math. Phys. 234 37–75) using topological horseshoes. The approach presented here seems to be rather efficient.

Gravitational assist in celestial mechanics—a tutorial

In planning certain types of trajectories of spacecraft within the solar system, engineers rely on a technique called gravitational assist, or gravity assist. This technique underlies the feasibility of effecting a net change in both the speed and direction of motion of a spacecraft by passage through the gravitational field of a planet or a planetary satellite. The resulting increase, or decrease, in the kinetic energy of the spacecraft appears to contradict the casual expectation that in such an encounter the kinetic energy of the spacecraft after the encounter would be the same as that before the encounter. This paper describes the December 1973 encounter of the Pioneer 10 spacecraft with the planet Jupiter as a real-life example of gravitational assist. It then discusses the physical principles involved in understanding the dynamics of the encounter and concludes with remarks on the important role of gravitational assist in space exploration with artificial spacecraft and in understanding the motion of comets within the solar system.

THE INFLUENCE OF REACTIVE TORQUES ON COMET NUCLEUS ROTATION

Reactive torques, due to anisotropic sublimation on a comet nucleus surface, produce slow variations of its rotation. In this paper the secular effects of this sublimation are studied. The general rotational equations of motion are averaged over unperturbed fast rotation around the mass center (Euler-Poinsot motion) and over the orbital comet motion. We discuss the parameters that define typical properties of the rotational evolution and discover different classifications of the rotational evolution. As an example we discuss some possible scenarios of rotational evolution for the nuclei of the comets Halley and Borrelly.

Common Origin of Two Major Sungrazing Comets

Our extensive orbital calculations show that the motion of comet C/1965 S1 (Ikeya-Seki), a major member of the Kreutz sungrazing system, can be derived from the motion of its sister comet C/1882 R1 (Great September Comet) on the assumption that the two objects are fragments of a common parent that split in the year 1106, at the time when a very bright comet appeared near the Sun according to a number of historical records. Specifically, the orbit of Ikeya-Seki derived from astrometric positions in 1965-1966 is matched with remarkably high accuracy, well within the errors of observation, by (1) integrating the motion of comet C/1882 R1 back to 1106; (2) launching from the parent a fragment some 18 days after perihelion, 0.75 AU from the Sun, with a relative velocity of about 7 m s-1 nearly in the antisolar direction; and (3) integrating the fragment's motion forward to 1965. We find that having the break-up closer to the Sun or before perihelion yields grossly inferior solutions. We conclude that the fragmentation event itself was not tidal in nature, but appears to have been due to rotational, and possibly other, forces acting on the parent comet, afflicted with cracks and fissures caused by the Sun's tidal forces a few weeks earlier. We note that the derived separation velocity is in the range established for nontidal fragmentation of minor sungrazers at large heliocentric distances and that there are obvious similarities with the behavior of comet D/1993 F2 (Shoemaker-Levy 9) following its close encounter with Jupiter in 1992 July.

Possible Kreutz Sungrazing Comets Found in Historical Records

Abstract In historical records, twenty four candidates of possible Kreutz sungrazing comets have been found, and their times of perihelion passage estimated. Translated original records of comets with presumed ephemerides are given. Some uncertain candidates are also presented. Although already suggested by Marsden (1967, Astron. Jahresber. 67.9133), our calculations on the motions of comets 1882 R1 and 1965 S1 confirm that the progenitor of these comets is a comet that appeared in 1106; some trials on the linkage of sungrazing comets are discussed.

Lévy flights in comet motion and related chaotic systems

We obtain a 2-dimensional area-preserving map to study the dynamical evolution of comets. The presence of singularities in the energy-increment function leads to the Lévy flight random walks for the comet energies, which results in a linear increment of the energy with time. A model of stochastic dynamical system is proposed according to the map of the comet motion, which shows the existence of strong super-diffusive random walks so that the variance of the distributions can grow with time n as n 2 m with m⩾1/2.