Coma Morphology And Constraints On The Rotation Of Comet Hale–Bopp (C/1995 O1)

We present constraints on the spin state of comet Hale-Bopp based on coma morphology. Three cases of rotational states are compatible with near perihelion observations: (1) principal-axis rotation, (2) complex rotational state with a small precessional angle, or (3) complex rotational state with a large ratio between the component periods. For principal axis rotators, images from 1996 (pre-perihelion) are consistent with a rotational angular momentum vector, M, directed at ecliptic longitude and latitude (250°, -5°) while images from late 1997 (post-perihelion) indicate (310°, -40°). This may suggest a change in M. A complex rotational state with small precessional angle requires only a small or no change in M over the active orbital arc. In this case, M is directed near ecliptic longitude and latitude (270°, -20°). A rotationally excited nucleus with a large ratio between component periods requires the nucleus to be nearly spherical. The transformation of dust coma morphology from near-radial jets to bright arcs and then again to near-radial jets is interpreted as a heliocentric and geocentric distance dependent evolutionary sequence. The spiral structures seen in CN filters near perihelion (in contrast to sunward side arcs seen in continuum) can be explained if the precursor of CN molecules (likely sub-micron grains) are emitted from the nucleus at low levels (≈ 10% of the peak daytime emission) during the nighttime. This may be indicative of a nucleus with a CO-rich active area(s). This revised version was published online in July 2006 with corrections to the Cover Date.     

Temporal deconvolution of the hydrogen coma: II. Pre- and post-perihelion activity of Comet Hyakutake (1996 B2)

Comet 1996 B2 (Hyakutake) displayed strong evidence for break-up, with a prominent antisunward dust spike and fragments traveling antisunward for many days after an eruptive event in late March 1996. Because of its high orbital inclination and rapid southward motion after perihelion, its post-perihelion activity was not well monitored from the ground. The SWAN all-sky Lyman-alpha camera on the SOHO spacecraft was ideally placed for long-term monitoring of the hydrogen coma of Comet Hyakutake both before and after perihelion. The SWAN images were analyzed with a new time-resolved model (TRM) that provides daily averages of the water production rate and an estimate of the hydrogen atom lifetime (dominated by charge exchange with solar wind protons) during extended periods throughout the apparition. A long-term variation of water production rate of , where r is the heliocentric distance in AU was found. The daily average values of the production rate covered the March 19 outburst and two more outbursts seen in the April before perihelion, which had progressively shorter durations at respectively smaller heliocentric distances. The long-term variation of the production rate was found to be consistent with the seasonal effect predicted by the jet rotation model of Schleicher and Woodney [2003. Analyses of dust coma morphology of Comet Hyakutake (1996 B2) near perigee: Outburst behavior, jet motion, source region locations, and the nucleus pole orientation. Icarus 162, 190-213] when added to a more steady source that is about two-thirds of the maximum of the jet source. The seasonal effect in their model found the dust jet source largely not illuminated after perihelion, coinciding with somewhat reduced overall activity and the absence of outbursts and fragmentation. The locations of the dust jets appear to be responsible for the outbursts and fragmentation before perihelion. The erratic behavior of the pre-perihelion jet sources as contrasted with the smoother variation from the rest of the surface after perihelion indicates there is a strong heterogeneity in the physical make-up of active areas on the nucleus.     

Analysis of the orbit of 1970-97b (cosmos 378 rocket)

Cosmos 378 rocket, 1970-97B, entered orbit on 17 November 1970, with orbital inclination 74.0°, period 105 min and perigee height 230 km, and decayed on 30 September 1972 after 683 days in orbit. The RAE computer program PROP was used, with more than 1900 observations from 64 stations, to determine the orbit at 39 epochs between February 1971 and September 1972.The main aim of the analysis was to determine the atmospheric rotation rate from the decrease in orbital inclination, which was determined with a mean standard deviation of 0.0010° and a best standard deviation of 0.0003°. After removal of relevant perturbations, analysis of the variation in inclination between July 1971 and April 1972 yields the surprisingly low average atmospheric rotation rate of 0.75 ± 0.05 rev/day, at a mean height of 250 km. The local time at perigee is however strongly biassed towards daytime values (07–16 hr), so the results lend support to the picture of east-to-west winds by day and west-to-east winds by night.Values of scale height are obtained by analysis of the change in perigee height.     

Analysis of the orbit of Cosmos 72 (1965-53B) near 15th-order resonance

Cosmos 72 (1965-53B) was launched on 16 April 1965 into a near-circular orbit with an average height of 570 km and inclination 56°. Over the years, the orbit has contracted slowly under the influence of air drag, and On 27 June 1972 passed through exact 15th-order resonance, when successive equator crossings are 24° apart in longitude and the ground track repeats after 15 rev. The orbit has been determined at seven epochs between April 1972 and February 1973, using the RAE orbit refinement program PROP, with 544 optical and radar observations: the average orbital accuracy is about 50 m in height and 0.0008° in inclination.For Cosmos 72 the change in inclination at 15th-order resonance, due to perturbations by 15th-order harmonics in the geopotential, is greater than for any satellite previously analysed— nearly 0.07°—and analysis of the change, using the seven PROP orbits and 45 U.S. Navy orbits, yields equations accurate to 4 per cent for the geopotential coefficients of order 15 and odd degree (15, 17, 19 …). A similar analysis of the variation in eccentricity gives less accurate equations for coefficients of order 15 and even degree (16, 18 …). The variations in right ascension of the node and argument of perigee have also been analysed.     

Thermal modeling of cometary nuclei

A new model of the sublimation of volatile ices from a cometary nucleus has been developed which includes the effects of diurnal heating and cooling, rotation period and pole orientation, and thermal properties of the ice and subsurface layers. The model also includes the contribution from coma opacity, scattering, and thermal emission, where the properties of the coma are derived from the integrated rate of volatile production by the nucleus. The model is applied to the specific case of the 1986 apparition of Halley's comet. It is found that the generation of a cometary dust coma actually increases the total energy reaching the Halley nucleus. This results because of the significantly greater geometrical cross section of the coma as compared with the bare nucleus, and because the coma provides an essentially isotropic source of multiply scattered sunlight and thermal emission over the entire nucleus surface. For Halley, the calculated coma opacity is approximately 0.2 at 1 AU from the Sun, and 1.2 at perihelion (0.587 AU). At 1 AU this has little effect on dayside temperatures (maximum ≈200°K) but raises nightside temperatures (minimum ≈150°K) by about 40°K. At perihelion the higher opacity results in a nearly isothermal nucleus with only small diurnal and latitudinal temperature variations. The general surface temperature is 205°K with a maximum of 209°K at local noon on the equator. Some possible consequences of the results with respect to the generation of nongravitational forces, observed volatile production rates for comets, and cometary lifetimes against sublimation are discussed.     

Critical inclination of Trojan asteroids

The author's earlier solution for Trojan asteroids is developed further. It is shown that depending on the amplitude of libration around the Lagrangian point L₄, there is a critical inclination which determines the sign of the variation of the ascending node. If the orbital inclination of a Trojan is smaller than the critical one, then the ascending node decreases and otherwise it increases. The variation of the eccentricity and of the longitude of the perihelion has also a dependence on the critical inclination.     

Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.     

The effect of orbital element variations on the mean seasonal daily insolation on Mars

In this paper we briefly study changes in the mean seasonal insolations on the planet Mars caused by significant large-scale variations in the following orbital elements: the eccentricity (e), the obliquity (ε) and the longitude of perihelion (λ _p ). Three orbital configurations have been investigated. In the first, the eccentricity equals successively 0, 0.075, and 0.15, whereas for the obliquity and the longitude of perihelion we took the present values which amount, respectively to 25° and 250°. In the second situation, ε=15, 25, and 35° for a circular orbit (e=0) and with λ _p =250°. In the last model we have sete=0.075 and ε=25° for λ _p =?90,0, and 90°. Although long-term periodic oscillations ofe (first case) and λ _p (third case) produce, respectively, very small or no variations in the average yearly insolation, fluctuations of the above mentioned planetary data strongly effect the mean summer and winter daily insolations. Indeed, the calculations reveal that between the two extreme values of the orbital elements used, the seasonal insolations exhibit a change in amplitude of about 15 to 20% difference over the entire latitude interval. Considering more particularly the second case it is found that the summertime insolation experiences a nearly similar variation as the mean annual daily insolation — i.e., a decrease of about 7% at the equator and a more than twofold increase at the poles. The corresponding mean winter daily insolation varies maximally by approximately 60% in the 60–80° latitude range.     

Very precise orbits of 1998 Leonid meteors

Abstract— Seventy-five orbits of Leonid meteors obtained during the 1998 outburst are presented. Thirty-eight are precise enough to recognize significant dispersion in orbital elements. Results from the nights of 1998 November 16/17 and 17/18 differ, in agreement with the dominant presence of different dust components. The shower rate profile of 1998 November 16/17 was dominated by a broad component, rich in bright meteors. The radiant distribution is compact. The semimajor axis is confined to values close to that of the parent comet, whereas the distribution of inclination has a central condensation in a narrow range. On the other hand, 1998 November 17/18 was dominated by dust responsible for a more narrow secondary peak in the flux curve. The declination of the radiant and the inclination of the orbit are more widely dispersed. The argument of perihelion, inclination, and the perihelion distance are displaced. These data substantiate the hypothesis that trapping in orbital resonances is important for the dynamical evolution of the broad component.     

Fan-shaped coma,orientation of rotation axis,and surface structure of a cometary nucleus I. Test of a model on four comets

Conspicuous anisotropy in the outgassing from comets, especially from short-period ones, appears to be the factor responsible for a frequent occurrence of a fan-shaped coma, extending in the general direction of the Sun. It is proposed that the pattern of deviations from the sunward direction contains information on the orientation of the spin axis and on the time lag in the sublimation process, which in turn provides insight into the nature of the nuclear surface. A simple model of a spherical rotating nucleus is formulated and a trial-and-error technique devised to determine the axis-orientation constants and a lage angle, a meaasure of the time lag in units of the rotation period. The results of application of this method to periodic comets Encke, Tempel 2, Borrelly, and Schwassmann-Wachmann 3 are presented. It is shown that the sense of rotation determined in this fashion is consistent with the results established for three of the four comets from the transverse component of the nongravitational force affecting their orbital motions. It is found that in general the time lag is strongly time dependent and that lag angles approaching 90° are rather common near perihelion, suggesting a complex surface structure that involves an insulting crust of dust of variable thickness and strength. These results are compared with the observed lightcurves of the four comets and with the calculated distributions of integrated insolation at the nuclear surface as functions of the cometocentric latitude and time. Noticed is a tendency of the comets to turn their spin axes to the Sun near perihelion and to replace, on the outbound leg of orbit, the established fan-orientation pattern by a “late”-tail pattern indicative of old, slowly accelerated particles. It is suggested that the motion of P/Schwassmann-Wachmann 3, which is due for a favorable return in 1979, was affected by a secular deceleration in 1930.     

Activity Profile of the Sextantid Meteor Shower

The detailed activity profile of the Sextandids - one of the day-time meteor showers - is poorly known and still unclear. Using the forward-scatter radio technique we have successfully been able to obtain further detailed overall activity profile of the Sextantids for seven consecutive years: 1991–1997. Analysis confirmed the Sextantid activity duration in solar longitude (J2000) of at least 184–193° and the maximum solar longitude at 188.35 ± 0.10° with a full width at half maximum (FWHM) of 2.0 ± 0.2°. Performing the numerical integrations, we also substantiated a possibility of the association between Apollo-type asteroid (3200) Phaethon and the Sextantids. Furthermore, we roughly estimated relative maximum flux rate of Sextantids : Geminids as 1 : 3 amplitude ratio. Depending upon the flux rates and the time lags of the orbital evolution with Phaethon, we conclude that the Sextantids are at a more progressive stage of orbital evolution than the Geminids if both meteor streams are really associated with Phaethon. This revised version was published online in July 2006 with corrections to the Cover Date.     

Upper-atmosphere features revealed by the orbit of 1980-43A

The satellite NOAA-B (1980-43A) was launched in May 1980 into an orbit with perigee height near 260 km and apogee height 1440 km, at an inclination of 92.2°.The lifetime was 11 months. The orbit has been determined at 40 epochs between October 1980 and May 1981 from about 3000 radar and optical observations. The average orbital accuracy, radial and cross-track, was about 100 m, with rather better accuracy in the final 14 days.The variation of orbital inclination has been analysed to determine two good values of atmospheric rotation rate, namely 1.10 ± 0.10 rev day^?1 at 300 km (average local time) and 1.15 ± 0.06 rev day^?1 at 225 km (evening).The effect of atmospheric rotation on the precession of the orbital plane of an actual satellite has never previously been detected; it is clearly apparent for 1980-43A in its last days and conforms to the expected theoretical change.The variation of perigee height has been analysed to determine ten values of atmospheric density scale height, for heights of 280–370 km. These values, accurate to about 3%, exceed by 15% the values indicated by the COSPAR International Reference Atmosphere. Solar activity was higher in the years 1980–1981 than at any time since early 1958 and it appears that the CIRA model underestimates the density and density scale height at high levels of solar activity.     

Orbit determination and analysis for Cosmos 482 from 1978 to 1981

The orbit of the satellite Cosmos 482 (1972-23A) has been determined at 77 epochs between 8 November 1977 and 18 April 1981 from 5650 optical and radar observations. The computations were made with the RAE orbit determination program PROP 6, and an average accuracy of 150 m radial and cross-track was achieved.Cosmos 482 was a high-drag satellite in an eccentric orbit and, between the first epoch and the last, the orbital period decreased from 157 to 94 min, the eccentricity decreased from 0.32 to 0.04, and the orbital inclination decreased from 52.14° to 51.95° due to the transverse forces caused by atmospheric rotation. The orbit was therefore ideal for determining the atmospheric rotation rate from the decrease in inclination, and seven accurate values of rotation rate have been obtained. The new values strengthen the existing overall picture of upper-atmosphere winds, and are generally in good accord with the previous results.An improved equation has been derived for calculating density scale height H from the decrease in perigee distance, and has been applied to determine seven values of H. The corresponding values of H from the COSPAR International Reference Atmosphere are on average 5% lower than the observational values, for 1980–1981.     

The determination and analysis of the orbit of NIMBUS 1 ROCKET, 1964-52B: Part 1: The orbits

Orbital parameters of the satellite NIMBUS 1 ROCKET (1964-52B) have been determined at 285 epochs using about 14,500 optical and radar observations during the last 2233 days of its life. 1964-52B was in an orbit inclined at about 98.7° to the Equator and it decayed on 13 August 1974. The orbital elements were found using the RAE orbit refinement program PROP 6 giving average orbital accuracies in perigee height and inclination at 110 m and 0.002° respectively.     

IRCS/Subaru observations of water in the inner coma of Comet 73P-B/Schwassmann-Wachmann 3: Spatially resolved rotational temperatures and ortho-para ratios

Comet 73P-B/Schwassmann-Wachmann 3 was observed with IRCS/Subaru at geocentric distance of 0.074 AU on UT 10 May 2006. Multiple H₂O emission lines were detected in non-resonant fluorescence near 2.9 μm. No significant variation in total H₂O production rate was found during the (3 h) duration of our observations. H₂O rotational temperatures and ortho-to-para abundance ratios were measured for several positions in the coma. The temperatures extracted from two different time intervals show very similar spatial distributions. For both, the rotational temperature decreased from ∼110 to ∼90 K as the projected distance from the nucleus increased from ∼5 to ∼30 km. We see no evidence for OPR change in the coma. The H₂O ortho-para ratio is consistent with the statistical equilibrium value (3.0) for all spatially resolved measurements. This implies a nuclear spin temperature higher than ∼45 K.     

Analysis of the orbital inclination of 1963-27A

The Agena B upper-stage rocket 1963-27A was launched into near-circular orbit, inclined at 82.3° to the Equator, on 29 June 1963. Its orbital elements were available at 52 epochs over the 16 month interval prior to its decay on 26 October 1969. During this period the satellite passed through 31:2 resonance and the variation in orbital inclination near this event was analysed to obtain two lumped geopotential harmonics of order 31. Since the resonance was a weak feature in the data, the resulting values are poorly defined.Either side of the resonance period, the inclination was used to estimate the mean atmospheric rotation rate Λ rev day^?1. The values obtained were Λ = 0.85 ± 0.18 at a height of 440 km for the period June 1968 to February 1969 and Λ = 1.13 ± 0.10 at 338 km for the period June to October 1969.     

Jets And Arcs In The Coma Of Comet Hale-Bopp From August 1996 To April 1997

An observation program for measuring the activity of Comet Hale-Bopp was conducted at the Observatoire de Haute Provence from August 1996 to April 1997. Narrow band images were obtained from the 120 cm telescope. A set of four filters at 513, 516, 527 and 682 nm was used to measure the C₂ emission in the (1,1) and (0,0) band and the intensity of the dust-scattered continuum. The luminosity of the central part of the coma was measured in the continuum and C₂ emissions, as a function of heliocentric distance before perihelion. The activity of the comet considerably increased between October 1996 and February 1997. The images obtained in August, September and October 1996 show the presence of strong jets. In February, March and April 1997, series of roughly concentric arcs were observed in the sunward hemisphere of the coma. The arcs were also detected in the spatial distribution of the I(682 nm)/I(527 nm) red color ratio and the I(513 nm)/I(516 nm) C₂ emission ratio. Using the I(513 nm)/I(516 nm) ratio as a parameter to measure the degree of excitation of C₂ molecules, we can show that the local production of gas, probably resulting from dust fragmentation, should be taken into account. This revised version was published online in July 2006 with corrections to the Cover Date.     

The libration of the saturnian satellite dione B

Previously published positions of Dione B are combined with new observations reported in this paper to determine the motion. The data are fit to the analytic solution of Erdi (1978) to derive the parameters of the libratory motion. The satellite oscillates about the leading equilateral libration point (L₄) of Dione with a period of 785.0±0.5 days. The maximum sepaparation in orbital longitude from Dione of 76.7° was reached on UT 1980 April 20.3±1 days; the minimum separation is 46.7°.     

Stardust-NExT,Deep Impact,and the accelerating spin of 9P/Tempel 1

The evolution of the spin rate of Comet 9P/Tempel 1 through two perihelion passages (in 2000 and 2005) is determined from 1922 Earth-based observations taken over a period of 13 year as part of a World-Wide observing campaign and from 2888 observations taken over a period of 50 days from the Deep Impact spacecraft. We determine the following sidereal spin rates (periods): 209.023 ± 0.025°/dy (41.335 ± 0.005 h) prior to the 2000 perihelion passage, 210.448 ± 0.016°/dy (41.055 ± 0.003 h) for the interval between the 2000 and 2005 perihelion passages, 211.856 ± 0.030°/dy (40.783 ± 0.006 h) from Deep Impact photometry just prior to the 2005 perihelion passage, and 211.625 ± 0.012°/dy (40.827 ± 0.002 h) in the interval 2006–2010 following the 2005 perihelion passage. The period decreased by 16.8 ± 0.3 min during the 2000 passage and by 13.7 ± 0.2 min during the 2005 passage suggesting a secular decrease in the net torque. The change in spin rate is asymmetric with respect to perihelion with the maximum net torque being applied on approach to perihelion. The Deep Impact data alone show that the spin rate was increasing at a rate of 0.024 ± 0.003°/dy/dy at JD2453530.60510 (i.e., 25.134 dy before impact), which provides independent confirmation of the change seen in the Earth-based observations.The rotational phase of the nucleus at times before and after each perihelion and at the Deep Impact encounter is estimated based on the Thomas et al. (Thomas et al. [2007]. Icarus 187, 4–15) pole and longitude system. The possibility of a 180° error in the rotational phase is assessed and found to be significant. Analytical and physical modeling of the behavior of the spin rate through of each perihelion is presented and used as a basis to predict the rotational state of the nucleus at the time of the nominal (i.e., prior to February 2010) Stardust-NExT encounter on 2011 February 14 at 20:42.We find that a net torque in the range of 0.3–2.5 × 10⁷ kg m² s^?2 acts on the nucleus during perihelion passage. The spin rate initially slows down on approach to perihelion and then passes through a minimum. It then accelerates rapidly as it passes through perihelion eventually reaching a maximum post-perihelion. It then decreases to a stable value as the nucleus moves away from the Sun. We find that the pole direction is unlikely to precess by more than ～1° per perihelion passage. The trend of the period with time and the fact that the modeled peak torque occurs before perihelion are in agreement with published accounts of trends in water production rate and suggests that widespread H₂O out-gassing from the surface is largely responsible for the observed spin-up.     

Orbital dynamics of the planetary system HD 196885

The orbital dynamics of the single known planet in the binary star system HD 196885 has been considered. The Lyapunov characteristic exponents and Lyapunov time of the planetary system have been calculated for possible values of the planetary orbit parameters. It has been shown that the dynamics of the planetary system HD 196885 is regular with the Lyapunov time of more than 5 × 10⁴ years (the orbital period of the planet is approximately 3.7 years), if the motion occurs at a distance from the separatrix of the Lidov–Kozai resonance. The values of the planet’s orbital inclination to the plane of the sky and longitude of the ascending node lie either within ranges 30° < i _p < 90° and 30° < Ω_p < 90°, or 90° < i _p < 180° and 180° < Ω_p < 300°.