Asteroids in cometary orbits

Orbital integrations are presented for a total of 14 asteroids with perihelia inside 1.7 AU and with aphelion distances in excess of 4 AU, 10 of which were discovered in 1979–1984. The integrations were normally extended over approximately ±1000 years in a three-body model (Sun-Jupiter-asteroid). The effects of uncertainties of starting orbits are not treated in this work, and as far as the real asteroids are concerned, the results should be regarded mostly as preliminary indications. A wide variety of orbital evolutions is found, and some of them evidently belong to the cometary, chaotic type. Three such cases are identified with certainty (1983 SA, 1983 XF, and 1984 BC) and two or three more with various degrees of likelihood. An asteroidal motion is found for the well-observed object 1979 VA. A stable libration around the $\text{2}\text{1}$ resonance is found for 1981 FD, which obviously adds to the Griqua group. A long-lasting libration around the $\text{5}\text{3}$ resonance performed by 1982 YA is probably unstable. Temporary librations are also found for 1983 SA ($\text{4}\text{3}$ resonance) and 1983 XF ($\text{2}\text{1}$ resonance), but these objects appear to transit into irregular motions with close approaches to Jupiter (less than 0.01 AU for 1983 XF). A very rapid large-amplitude ω libration around 90° is found in the future motion of 1983 VA. If this will indeed occur for the real asteroid, the object will oscillate with a period of only 750 years between a main-belt orbit of very high inclination and a low-inclination Apollo-type orbit.     

Numerical investigation on the orbital evolution of 1:2 resonant asteroids between Jupiter and Saturn

According to some investigations (Lecar and Franklin, 1973; Franklin et al., 1989; Soper et al., 1990) asteroids cannot remain for along time between Jupiter and Saturn. But as it is well known there is a near 5:2 commensurability between Jupiter and Saturn. So there might be a possibility that asteroids between Jupiter and Saturn could be trapped in a resonant relation.In order to investigate this possibility, the changes of orbital elements of an asteroid whose initial value of semi-major axis corresponds to that of a 1:2 resonant orbit were investigated by means of a double precision Cowell method. The integration routine was kindly supplied by Dr Yoshikawa.We considered first a planar restricted problem of three bodies, Sun-Jupiter-Asteroid, then a four body problem, Sun-Jupiter-Asteroid-Saturn. When integrating the equations of motion, short periodic terms were not eliminated and in the second test the interactions between Jupiter and Saturn were retained. Whether a close approach occured or not was not investigated. In every case a _j = 5.20, a _s = 9.54 and a = 8.26 were adopted as initial values of the semi-major axis of Jupiter, Saturn and Asteroid respectively.     

Tidal dissipation in the solid cores of the major planets

If the orbital resonances in the Jovian and Saturnian satellite systems are the result of orbital evolution due to tidal dissipation then the present rates of energy dissipation ($\text{E}\text{dot}$) are >2 × 10²⁰ ergs sec^?1 (Jupiter) and ?2 × 10¹⁶ ergs sec^?1 (Saturn). These values of $\text{E}\text{dot}$ can be accounted for if the planets have rocky cores with volumes equal to those suggested by current models of the interiors and if the material of these cores is both solid and imperfectly elastic (Q_e ～ 34). The calculated values of Q_e are not strongly dependent on either the rigidity of the core or the densities of the core and the mantle. Thus, these quantities need not be known precisely. It may be significant that approximately the same value of Q_e is needed for all the major planets (Jupiter, Saturn, and Uranus) even though the values of $\text{E}\text{dot}$ for these planets differ by a factor greater than 10⁴.     

On the origin and initial temperature of Jupiter and Saturn

A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 10⁷ years in Jupiter's zone and ～2 × 10⁸ years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～10²⁸ g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m_⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m₁ ≈ 50 m_⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m₂ ≈ 130 m_⊕), the width of the exhausted zone being $\text{～}\text{built1}\text{3}$ of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 10⁵?10⁶ years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m₁ > m₂ ≈ 30 m_⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m_⊕, when the luminosity of the planet reaches 3 × 10^?3 L_⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m_⊕) and a luminosity up to 10^?4 L_⊙.     

The albedo of Titan

The irradiance of Titan has been measured from 0.50 to 1.08μ in 30 Å band-passes spaced 0.01–0.02μ apart. Geometric albedos have been computed at the wavelenghts of measurement using a standard solar flux distribution after Labs and Neckel. The maximum value of p_λ(0) is 0.37 at 0.68, 0.75, and 0.834μ, the minimum value, in the centers of the strongest methane absorption bands, is 0.10 at 0.887 and 1.012μ.The brightness of Titan at the time of the present measurements has been compared with that of previous modern photoelectric measurements. Within the apparent consistency of the different photoelectric systems, the brightness of Titan appears to undergo changes with time.A provisional curve of the geometric albedo from 0.30 to 4.0μ has been made by combining the present results with those of other authors, i.e., relative measurements of Titan from 0.30 to 0.50μ, and measurements of Jupiter and Saturn from 1.08 to 4.00μ. The latter are used to estimate the strengths of the methane absorption bands of Titan in that spectral range. The bolometric geometric albedo, $\text{p}{}^1\text{(0)}$, is computed to be 0.21. A variety of current measurements of Titan indicate a substantial atmosphere, suggesting a value of the phase integral $\text{q}\text{= 1.30 ± 0.20}$. The bolometric Bond albedo, $\text{A}{}^1$, is then 0.27 ± 0.04, giving an effective radiative temperature T_e= 84 ± 2°K.The absorption band contours of Titan have been compared with those of Jupiter and Saturn at the same resolution. The bands of the planets are known to be due primarily to methane, and they show a very regular relationship, with those of Saturn being consistently deeper and wider. For Titan, the strengths of the bands are equal or less than those of Jupiter in the band centers, while the wings are stronger than those of Saturn.Previous photoelectric and photographic spectra have been examined for evidence of temporal variation of the methane path length in the atmosphere of Titan. Differences in measurement techniques prohibit detection of small differences. The only potential differences beyond experimental uncertainties are those of Kuiper (1944) and Harris (mid-fifties). Taking Kuiper's results at face value, Titan appears to have a shorter methane path length in 1972. Harris's results can be reconciled only by the doubtful hypothesis of an almost complete absence of methane at that time.     

Discovery of a New Class of Predicted Resonance Objects beyond Jupiter

In the regions of mean diurnal motions between the orbits of Jupiter and Saturn, predicted earlier by the authors, five asteroids have been discovered that move in 1:2 and 2:3 Lindblad orbital resonances with Jupiter (external orbital commensurability) and in 2:1 resonance with Saturn (internal version of commensurability). In addition to this, in the precalculated stable resonance zones between the giant planets Saturn and Uranus, three objects have been found that possess third-order (2:5) orbital commensurability with Saturn; nine objects have been discovered between the orbits of Uranus and Neptune, whose mean motions are in 1:3 and 1:4 orbital resonances with Saturn, and more than 200 libration-stable objects, linked by lower-order orbital resonances with Neptune and Uranus have been found in the Kuiper belt.     

Hyperion: Collisional disruption of a resonant satellite

Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in $\text{4}\text{3}$ resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity $\text{?0.1}\text{km}\text{/}\text{sec}$ rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ～ 10 km/sec with a projectile-to-target mass ratio of the order of 10^?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration.     

On the Instability of Jupiter's Trojans

We have numerically explored the mechanisms that destabilize Jupiter's Trojan orbits outside the stability region defined by Levison et al. (1997, Nature385, 42-44). Different models have been exploited to test various possible sources of instability on timescales on the order of ∼10⁸ years.In the restricted three-body model, only a few Trojan orbits become unstable within 10⁸ years. This intrinsic instability contributes only marginally to the overall instability found by Levison et al.In a model where the orbital parameters of both Jupiter and Saturn are fixed, we have investigated the role of Saturn and its gravitational influence. We find that a large fraction of Trojan orbits become unstable because of the direct nonresonant perturbations by Saturn. By shifting its semimajor axis at constant intervals around its present value we find that the near 5:2 mean motion resonance between the two giant planets (the Great Inequality) is not responsible for the gross instability of Jupiter's Trojans since short-term perturbations by Saturn destabilize Trojans, even when the two planets are far out of the resonance.Secular resonances are an additional source of instability. In the full six-body model with the four major planets included in the numerical integration, we have analyzed the effects of secular resonances with the node of the planets. Trojan asteroids have relevant inclinations, and nodal secular resonances play an important role. When a Trojan orbit becomes unstable, in most cases the libration amplitude of the critical argument of the 1:1 mean motion resonance grows until the asteroid encounters the planet. Libration amplitude, eccentricity, and nodal rate are linked for Trojan orbits by an algebraic relation so that when one of the three parameters is perturbed, the other two are affected as well. There are numerous secular resonances with the nodal rate of Jupiter that fall inside the region of instability and contribute to destabilize Trojans, in particular the ν₁₆. Indeed, in the full model the escape rate over 50 Myr is higher compared to the fixed model.Some secular resonances even cross the stability region delimited by Levison et al. and cause instability. This is the case of the 3:2 and 1:2 nodal resonances with Jupiter. In particular the 1:2 is responsible for the instability of some clones of the L4 Trojan (3540) Protesilaos.     

Numerical studies of chaotic Hilda-type orbits

Earlier work indicates a comparatively rapid chaotic evolution of the orbits of some Hilda asteroids that move at the border of the domain occupied by the characteristic parameters of the objects at the 3/2 mean motion resonance. A simple Jupiter–Saturn model of the forces leads to numerical results on some of these cases and allows a search for additional resonances that can contribute to the chaotic evolution. In this context the importance of the secondary resonances that depend on the period of revolution of the argument of perihelion is pointed out. Among the studied additional resonances there are three-body resonances with arguments that depend on the mean longitudes of Jupiter, Saturn, and asteroid, but on slowly circulating angular elements of the asteroid as well, and the frequency of these arguments is close to a rational ratio with respect to the frequency of the libration due to the basic resonance.     

The DH ratio in the atmosphere of Uranus: Detection of the R5(1) line of HD

Observations of Uranus during the 1975, 1976, and 1978 apparitions reveal a weak absorption at the wavelength of the R₅(1) line of HD with equivalent width $\text{1.0 ± 0.4}\text{m}\text{A}\text{?}$. The $\text{D}\text{H}$ ratio in Uranus' atmosphere implied by this line and other published spectra is (4.8 ± 1.5) × 10^?5, and may not be significantly different from that in the atmospheres of Jupiter and Saturn. In addition, the spectra exhibit two weak absorption at $\text{6044.76 ± 0.02}\text{and}\text{6045.54 ± 0.02}\text{A}\text{?}$ which we were unable to identify. No trace of absorption is visible near these wavelengths or near the HD wavelength in a laboratory spectrum of 4.92 km-am CH₄ which we obtained in an attempt to identify these absorption features and to verify that the HD feature does not arise from CH₄.     

Love numbers of the giant planets

We calculate the Love numbers k_n for n = 2 to 10, and determine the “gravitational noise” from tides. The new values k₂ for Jupiter, Saturn, and Uranus yield new estimates for the planetary dissipation functions: $\text{Q}{}_{\mathrm{<mtext>J</mtext>}}\text{? 2.5 × 10}{}^4$, $\text{Q}{}_{\mathrm{<mtext>S</mtext>}}\text{? 1.4 × 10}{}^4\text{, Q}{}_{\mathrm{<mtext>U</mtext>}}\text{? 5 × 10}{}^3$.     

Hilda asteroids among Jupiter family comets

Hilda asteroids and comets are similar from the compositional point of view. The D-taxonomic class prevailing among Hildas has all the characteristics found in cometary spectra. Jupiter Family Comets (JFCs) coming from the trans-neptunian region are under the gravitational control of Jupiter, making them a dynamically unstable population with a mean dynamical lifetime of 10⁴ to ¹⁰⁵ years. In contrast, Hilda asteroids residing in the 3:2 mean motion resonance with Jupiter are a very stable population. But once they escape from the resonance, they are dynamically controlled by Jupiter, and in this sense their behavior resembles that of JFC. We performed a numerical simulation to analyze the dynamical evolution that Hildas follow after escaping from the resonance, and their contribution to the JFC population. We found that 8% of the particles leaving the resonance end up impacting Jupiter. 98.7% of the escaped Hildas live at least 1000 years as a JFC, with a mean lifetime of 1.4×¹⁰⁶ years. In particular, escaped Hildas stay mainly in the region of perihelion distances greater than 2.5 AU. On the other hand, the number of escaped Hildas reaching the inner Solar System (q<2.5 AU) is negligible. So, there are almost no Hilda asteroids among the NEO population. We also analyzed the possibility that the Shoemaker-Levy 9 were an escaped Hilda asteroid. In this case, it would be possible to give stronger constraints to its pre-capture orbital elements.     

Asteroids with large secular orbital variations

As the classical linear theory of secular perturbations for asteroids is known not to be adequate for computing the perturbations of asteroids with high eccentricities and/or inclinations, a seminumerical method to calculate the secular perturbations by including higher-degree terms in the disturbing function has been developed. It is here applied to asteroids with small values of $\text{(1 ? e}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{cos}\text{i}$, since the secular variations as well as their deviations from the results derived by the classical linear theory are generally large for such asteroids. It is found that the arguments of perihelion for five of the numbered asteroids are librating around 90 or 270°. For asteroids with $\text{(1 ? e}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>cos</mtext><mtext>\; i</mtext>}}$ less than 0.85 the results of the secular variations are tabulated. Also the stability of such orbits is discussed by comparing the orbital properties of short-periodic comets with them. Generally speaking, orbits of the asteroids are more stable than those of the short-periodic comets, and asteroids with librating arguments of perihelion are more stable than those with circular coplanar orbits although their orbital elements are changed more by secular perturbations.     

Far-infrared and submillimeter observations of the planets

New broadband observations in several passbands between 30 and 500 μm of Mercury, Venus, Mars, Jupiter, Saturn, and Uranus are presented. The best agreement between the data and various thermal models of Mars, Jupiter, and Uranus is obtained with a slightly cooler absolute temperature scale than that previously adopted by Armstrong et al. (1972). The effective temperature of Uranus is 58 ± 2°K, which is in agreement with its solar equilibrium temperature. The existence of an internal energy source of Saturn has been reconfirmed and must lie within the range of 0.9 to 3.2 times the absorbed solar flux. A depression exists in the spectra of Jupiter, Saturn, and Uranus between 80 and 300 μm, which may be a result of NH₃ opacity.     

Models of Jupiter and Saturn after Galileo mission

New models of Jupiter are based on observational data provided by the Galileo spaceprobe, which considerably improved previously existing estimates of the helium abundance in the atmosphere of Jupiter. These data yield for Jupiter’s atmosphere 20% of the solar oxygen abundance and do not agree with the results of the analysis of the collision of comet Shoemaker-Levy 9 with Jupiter (10 times the solar value). Therefore, both the models of Jupiter with water-depleted and water-enriched atmosphere are considered. By analogy with Jupiter, trial models of Saturn with a water-depleted external envelope are also developed. The molecular-metallic phase transition pressure of hydrogen P_m was taken to be 1.5, 2 and 3 Mbar. Since Saturn’s internal molecular envelope is noticeably enriched in the IR-component (its weight concentration, 0.25–0.30, being by a factor of 3–4 higher than in Jupiter), the phase transition pressure in Saturn can be lower than in Jupiter. In the constructed models, the IR-core masses are 3–3.5 M_⊕ for Jupiter and 3–5.5 M_⊕ for Saturn. Jupiter’s and Saturn’s IR-cores can be considered embryos onto which the accretion of the gas occurred during the formation of the planets. The mass of the hydrogen–helium component dispersed in the zone of planetary formation constitutes ≈2–5 planetary masses for Jupiter and ≈11–14 planetary masses for Saturn.     

Populating the asteroid belt from two parent source regions due to the migration of giant planets—“The Grand Tack”

Abstract– The asteroid belt is found today in a dramatically different state than that immediately following its formation. It is estimated that it has been depleted in total mass by a factor of at least 1000 since its formation, and that the asteroids’ orbits evolved from having near‐zero eccentricity and inclination to the complex distributions we find today. The asteroid belt also hosts a wide range of compositions, with the inner regions dominated by S‐type and other water‐poor asteroids and the outer regions dominated by C‐type and other primitive asteroids. We discuss a model of early inner solar system evolution whereby the gas‐driven migration of Jupiter and Saturn brings them inwards to 1.5 AU, truncating the disk of planetesimals in the terrestrial planet region, before migrating outwards toward their current locations. This model, informally titled “The Grand Tack,” examines the planetary dynamics of the solar system bodies during the final million years of the gaseous solar nebula lifetime—a few million years (Myr) after the formation of the first solids, but 20–80 Myr before the final accretion of Earth, and approximately 400–600 Myr before the Late Heavy Bombardment of the inner solar system. The Grand Tack attempts to solve some outstanding problems for terrestrial planet formation, by reproducing the size of Mars, but also has important implications for the asteroid population. The migration of Jupiter causes a very early depletion of the asteroid belt region, and this region is then repopulated from two distinct source regions, one inside the formation region of Jupiter and one between and beyond the giant planets. The scattered material reforms the asteroid belt, producing a population the appropriate mass, orbits, and with overlapping distributions of material from each parent source region.     

Asteroid rotation: IV. 1979 observations

Results of photoelectric lightcurve observations made during 1979 are reported. Of a total of 53 asteroids observed, reliable rotation periods are reported for 22 asteroids for which no previous values are known, 7 periods are reported which are revisions of previously reported values, and for 12 other asteroids periods are suggested which are admittedly of low reliability and those objects should be reobserved. In addition, phase relations are presented for many of the asteroids, fitted to the theoretical phase function of Lumme and Bowell (Astron. J., 86, 1705, 1981). Adopting their formalism, mean absolute magnitudes at zero phase angle, $\text{V}\text{(0°)}$, for 52 asteroids, and values of the multiple scattering parameter, Q, for 22 asteroids are reported. For comparison purposes, the absolute magnitude, V(1,0) and the linear phase coefficient, βv, in the traditional system are computed. In the appendixes (1) the methods of observation and data reduction are discussed, which are recommended to other lightcurve observers in the hope of standardizing reporting practices as much as possible; and (2) a cumulative index of all asteroid rotation data of which the authors are aware is presented.