Ionospheric models of Saturn,Uranus, and Neptune

Model ionospheres are calculated for Saturn, Uranus, and Neptune. Protons are the major ions above 150 km altitude measured from a reference level where the hydrogen density is 1 × 10¹⁶ molecules cm^?3, while below 150 km quick conversion of protons to H₃⁺ ions by a three-body association mechanism leads to a rapid removal of ionization in dissociative recombination of H₃⁺. Electron density maxima are found at about 260 km for Saturn and Uranus and 200 km for Neptune. Present knowledge of the physical and chemical processes in the atmospheres of these planets suggests that their ionospheres probably will not be Jupiter-like.     

Measurements of the H2 4-0 quadrupole bands of Uranus and Neptune

We find that the equivalent widths of the lines of the 4-0 H₂ quadrupole band on Uranus and Neptune are substantially smaller than the values found by some previous observers. An analysis of our results based on a range of atmospheric models yields H₂ abundances of 240 ± 60 km-amagats for Uranus and ?200 km amagats for Neptune.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

Sizes, shapes, and albedos of the inner satellites of Neptune

Based on 87 resolved Voyager images of the five innermost satellites of Neptune, their shapes were measured and fit by tri-axial ellipsoids with the semi-axes of 48 × 30 × 26 km for Naiad, 54 × 50 × 26 km for Thalassa, 90 × 74 × 64 km for Despina, 102 × 92 × 72 km for Galatea, and 108 × 102 × 84 km for Larissa. Thomas and Veverka published a similar shape for Larissa (104 × 89 km, J. Geophys. Res. 96, 19261-19268, 1991). The other satellites had no published shapes. Using Voyager photometry of the six inner satellites by the same authors and the revised sizes, including the published size of Proteus, the reflectivity within this inner system was found to vary by about 30%. Geometric albedos in the visible are estimated between 0.07 for Naiad and 0.10 for Proteus. The rotational lightcurves of these satellites seem to be due to satellite shapes.     

The occultation of MKE 31 by Neptune on September 12, 1983

The predicted occultation of the star No. 31 (Mink et al., 1981) by Neptune on September 12, 1983 was observed photoelectrically. Four secondary occultations were recorded before the immersion event.     

The 7 and 25 June 1985 Neptune occultations: Constraints on the putative Neptune “arc”

Stellar occultations by Neptune on 7 and 25 June 1985 were observed in the K band from Sutherland (SAAO) to search for conforming evidence of the ring-like “arc” reported by Hubbard et al. (W.B. Hubbard, A. Brahic, B. Sicardy, L.-R. Elicer, F. Roques, and F. Vilas (1986). Nature 319, 636–640). A binary star was occulted on 7 June 1985, and since both components were occulted by the planet, their relative positions could be precisely determined. A single sharp dip, of high signal-to-noise ratio, was observed in the post-emersion occultation trace. If this feature were caused by material near Neptune, its corresponding projected equatorial plane radius is either 62,600 ± 160 km or 63,760 ± 120 km, depending on which of the binary star pair was occulted. The equatorial radius, width, and optical depth of the 7 June feature are similar to those described by Hubbard et al. The absence of a corresponding post-emersion dip due to the occultation of the companion star suggests that the ring-like material is discontinuous over a scale of several thousand kilometers in ring circumference. No ring-like features were observed during pre-immersion. The 25 June 1985 occultation was also successfully observed, including atmospheric occultation profiles for both immersion and emersion. No evidence for ring-like material was found in the region probed by this occultation during post-emersion, which included the entire range of equatorial radii over which “arc” events have been previously reported.     

Embedded star clusters and the formation of the Oort cloud: II. The effect of the primordial solar nebula

This paper deals with Oort cloud formation while the Sun was in an embedded cluster and surrounded by its primordial nebula. This work is a continuation of Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82], building on the model presented therein, and adding the aerodynamic drag and gravitational potential of the primordial solar nebula. Results are presented of numerical simulations of comets subject to the gravitational influence of the Sun, Jupiter, Saturn, star cluster and primordial solar nebula; some of the simulations included the gravitational influence of Uranus and Neptune as well. The primordial solar nebula was approximated by the minimum-mass Hayashi model [Hayashi, C., Nakozawa, K., Nakagawa, Y., 1985. In: Black, D.C., Matthews, M.S. (Eds.). Protostars and Planets II. Univ. of Arizona Press, Tucson, AZ] whose inner and outer radii have been truncated at various distances from the Sun. A comet size of 1.7 km was used for most of our simulations. In all of our simulations, the density of the primordial solar nebula decayed exponentially with an e-folding time of 2 Myr. It turns out that when the primordial solar nebula extends much beyond Saturn or Neptune, virtually no material will end up in the Oort cloud (OC) during this phase. Instead, the majority of the material will be on circular orbits inside of Jupiter if the inner edge of the disk is well inside Jupiter's orbit. If the disk's inner edge is beyond Jupiter's orbit, most comets end up on orbits in exterior mean-motion resonances with Saturn when Uranus and Neptune are not present. In those cases where the outer edge of the disk is close to Saturn or Neptune, the fraction of material that ends up in the subsequently formed OC is much less than that found in Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82] for the same cluster densities. This implies that for comets of roughly 2 km in size, the presence of the primordial solar nebula hinders OC formation. A byproduct of some of our simulations are endresults with a substantial fraction of the comets in the Uranus-Neptune scattered disk. A subsequent followup of this material is planned for the near future. In order to determine the effect of the size of the comets on OC formation efficiency, a set of runs with the same initial conditions but different cometary radii have been performed as well, from which it is determined that the threshold comet size to begin producing significant Oort clouds is roughly 20 km. This implies that the presence of the primordial solar nebula acts as a size-sorting mechanism, with large bodies unaffected by the gas drag and ending up in the OC while small bodies remain trapped in the planetary region, in the models studied.     

The atmospheres of Uranus and Neptune: A review

Plausible models for the atmospheres of Uranus and Neptune are reviewed. Current ideas favor the presence of massive atmospheres above solid cores. Observations of Uranus imply the presence of a visible cloud layer (probably composed of solid methane) beneath about 100 km amagats of hydrogen. A number of other cloud layers far below this upper layer are also possible. However, before any of these conclusions can be considered firm, a number of further crucial observations are required.     

Neptune: Limb brightening within the 7300-Angstrom methane band

Narrow-waveband (100 Å) photoelectric slit-scan photometry of the Neptune disk is reported. Observations were concentrated within the strong CH₄ band at λ7300 Å. For comparison, measurements were also made within a continuum waveband at λ6800 Å. Point spread function data were obtained in both colors. Qualitative estimates of the true intensity distribution over the Neptune disk were made. Within the λ6800-Å continuum band, Neptune appears as an essentially uniform disk. Within the λ7300 Å CH₄ band, the planet exhibits strong limb brightening. Our results appear to require the presence of an optically thin layer of brightly scattering aerosol particles high in the Neptune atmosphere.     

Uranus and Neptune: Shape and rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several 100 m s⁻¹. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets’ radio signals and of fits to the planets’ magnetic fields; 17.24 h and 16.11 h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet’s deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ∼16.58 h for Uranus and ∼17.46 h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.     

A Symplectic Mapping Model for the Study of 2:3 Resonant Trans-Neptunian Motion

A symplectic mapping is constructed for the study of the dynamical evolution of Edgeworth-Kuiper belt objects near the 2:3 mean motion resonance with Neptune. The mapping is six-dimensional and is a good model for the Poincaré map of the real system, that is, the spatial elliptic restricted three-body problem at the 2:3 resonance, with the Sun and Neptune as primaries. The mapping model is based on the averaged Hamiltonian, corrected by a semianalytic method so that it has the basic topological properties of the phase space of the real system both qualitatively and quantitatively. We start with two dimensional motion and then we extend it to three dimensions. Both chaotic and regular motion is observed, depending on the objects' initial inclination and phase. For zero inclination, objects that are phase-protected from close encounters with Neptune show ordered motion even at eccentricities as large as 0.4 and despite being Neptune-crossers. On the other hand, not-phase-protected objects with eccentricities greater than 0.15 follow chaotic motion that leads to sudden jumps in their eccentricity and are removed from the 2:3 resonance, thus becoming short period comets. As inclination increases, chaotic motion becomes more widespread, but phase-protection still exists and, as a result, stable motion appears for eccentricities up to e = 0.3 and inclinations as high as i = 15°, a region where plutinos exist.     

Oblateness,radius, and mean stratospheric temperature of Neptune from the 1985 August 20 occultation

The occultation of a bright (K∼6) infrared star by Neptune revealed a central flash at two stations and provided accurate measurements of the limb position at these and several additional stations. We have fitted this data ensemble with a general model of an oblate atmosphere to deduce the oblateness e and equatorial radius a₀ of Neptune at the 1-μbar pressure level, and the position angle p_n of the projected spin axis. The results are e=0.0209±0.0014, a₀=25269±10 km, p_n=20.1°±1°. Parameters derived from fitting to the limb data alone are in excellent agreement with parameters derived from fitting to central flash data alone (E. Lellouch, W.B. Hubbard, B. Sicardy, F. Vilas, and P. Bouchet, 1986, Nature 324, 227–231), and the principal remaining source of uncertainty appears to be the Neptune-centered declination of the Earth at the time of occultation. As an alternative to the methane absorption model proposed by Lellouch et al., we explain an observed reduction in the central flash intensity by a decrease in temperature from 150 to 135°K as the pressure rises from 1 to 400 μbar. Implications of the oblateness results for Neptune interior models are briefly discussed.     

Neptune Trojans: a Revisit and a New Membertwo

Up to now, 17 Neptune Trojan asteroids have been detected with their orbits being well determined by continuous observations. This paper analyzes systematically their orbital dynamics. Our results show that except for two temporary members with relatively short lifespans on Trojan orbits, the vast majority of Neptune Trojans located within their orbital uncertainties may survive in the solar system age. The escaping probability of Neptune Trojans, through slow diffusion in the orbital element space in 4.5 billion years, is estimated to be ～50%. The asteroid 2012 UW177 classified as a Centaur asteroid by the IAU Minor Planet Center currently is in fact a Neptune Trojan. Numerical simulations indicate that it is librating on the tadpole-shaped orbit around the Neptune's L₄ point. It was captured into the current orbit approximately 0.23 million years ago, and will stay there for at least another 1.3 million years in the future. Its high inclination of i ≈ 54^° not only makes it the most inclined Neptune Trojan, but also makes it exhibit the complicated and interesting co-orbital transitions between the leading and trailing Trojans via the quasi-satellite orbit phase.     

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 10⁸ years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 10⁴ AU)is about 10⁹ years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 10⁸ years.     

Comparative thermal evolution of Uranus and Neptune

We extend a Jovian convective-cooling model to Uranus and Neptune. The model assumes that efficient interior convection prevails, so that escape of interior heat is governed by the radiative properties of the atmosphere. A comparison of the thermal evolution of Uranus and Neptune indicates that the larger amount of solar radiation absorbed in Uranus' atmosphere tends to differentially suppress the escape of interior heat. The model is shown to be consistent with recent infrared observations of the thermal balance of Uranus and Neptune, and with the presumed age of these planets.     

Some dynamical aspects of the accretion of Uranus and Neptune: The exchange of orbital angular momentum with planetesimals

The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 10⁸ years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.     

The rotational periods of Uranus and Neptune

Observations of tilts of spectral lines in the spectrum of Uranus and Neptune yield the following rotational periods: “Uranus,” 24 ± 3 hr; “Neptune,” 22 ± 4 hr. Neptune is confirmed to rotate in a direct sense. The position angle of the pole of Uranus, projected onto the plane of the sky, is found to be 283 ± 4°. The value for Neptune is 32 ± 11°. These results agree with the direction of the pole of Uranus inferred from the common plane of its four brightest satellites and with the direction of the pole of Neptune as inferred from the precession of Triton's orbit. The rotational period of Uranus is found to be consistent with modern values of its optical and dynamical oblateness and the theory of solid-body rotation with hydrostatic equilibrium. This is barely the case for the period derived for Neptune and we suspect that future observations made under better seeing conditions may lead to a shorter rotation period between 15 and 18 hr. Because of a substantial difference between our results and those of earlier spectroscopic and photometric investigations we include an assessment of several previously published photometric studies and a new reduction of the original Lowell and Slipher spectroscopic plates of Uranus [Lowell Obs. Bull. 2, 17–18, 19–20 (1912)]. The early visual photometry of Campbell (Uranus) and Hall (Neptune) is found to be more satisfactorily accounted for by periods of 21.6 and 23.1 hr, respectively, than by the periods originally suggested by the observers. Our reduction of the Lowell and Slipher Uranus plates yields a period near 33 hr uncorrected for seeing. This value is consistent with the results based on the 4-m echelle date.     

Connecting atmospheric science and atmospheric models for aerocapture at Titan and the outer planets

Many atmospheric measurement systems, such as the sounding instruments on Voyager, gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level due to seasonal, latitudinal, and diurnal variations is also not large. However, many engineering needs for atmospheric models relate not to temperature versus pressure level but atmospheric density versus geometric altitude. This need is especially true for design and analysis of aerocapture systems. Drag force available for aerocapture is directly proportional to atmospheric density. Available aerocapture “corridor width” (allowable range of atmospheric entry angle) also depends on height rate of change of atmospheric density, as characterized by density scale height. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature versus pressure profiles can integrate at high altitudes to very large differences in density versus altitude profiles. Thus, a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes (∼150-300 km) on the various outer planets, and significantly different density scale heights (∼20-50 km) can occur at these periapsis altitudes. This paper will illustrate these effects and discuss implications for improvements in atmospheric measurements to yield significant impact on design of aerocapture systems for future missions to Titan and the outer planets. Relatively small-scale atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations can also have significant effect on design details for aerocapture guidance and control systems. This paper will discuss benefits that would result from improved understanding of Titan and outer planetary atmospheric perturbation characteristics. Details of recent engineering-level atmospheric models for Titan and Neptune will be presented, and effects of present and future levels of atmospheric uncertainty and variability characteristics will be examined.     

The internal structures and the relative rotation rates of Uranus and Neptune

The difference between the interior structures of Uranus and Neptune is presented, based on models which fit the observed mass, radius, and gravitational moments for the assumed rotation periods of these planets. If Uranus and Neptune are assumed to be as similar in internal structure as they are in mass and radius, the rotation period for Neptune must be shorter than that for Uranus. It is suggested that the true rotation period is given by Neptune's oblateness, while the photometric period corresponds to the motion of Rossby waves in the upper atmosphere.     

Restored methane band images of Uranus and Neptune

Charge-coupled device images of Uranus and Neptune taken in the 8900-Å absorption band of methane are presented. The images have been digitally processed by means of nonlinear deconvolution techniques to partially remove the effects of atmospheric seeing. The restored Uranus images show strong limb brightening consistent with previous observations and theoretical models of the planet's atmosphere. The computer-processed images of Neptune show discreted cloud features similar to those reported previously by B. A. Smith, H. J. Reitsema and S. M. Larson (1979 Bull. Amer. Astron. Soc.11, 570). A time series of the restored Neptune images shows a continuous variation which may be due to the planet's rotation.