The rotation period of Neptune's upper atmosphere

Significant variations in the near-infrared brightness of Neptune during July and August 1980 were observed. These observations show a well-defined, large-amplitude variation in Neptune's J-K color, with a period of 17.73 ± 0.1 hr and are interpreted as diurnal variations resulting from the 17.73-hr rotation period of the upper atmosphere of Neptune in the presence of inhomogeneous weather. These results qualitatively corroborate those of D. P. Cruikshank (1978, Astrophys. J.220, L57-L59) in an earlier study using similar techniques. In addition, variations were observed in the 5-μm spectral region which are in phase with the variations seen at shorter wavelengths. A new 5-μm measurement of Uranus is also reported.     

Neptune's rotation period: A correction and a speculation on the difference between photometric and spectroscopic results

An error in the Hayes and Belton (1977), Icarus32, 383–401) estimate of the rotation period of Neptune is corrected. If Neptune exhibits the same degree of limb darkening as Uranus near 4900 Å, the rotation period is 15.4 ± 3 hr. This value is compatible with a recent spectroscopic determination of Munch and Hippelein (1979) who find a period of 11.2_?1.2^+1.8 hr. However, if, as indirect evidence suggests, the law of darkening on Neptune at these wavelengths is less pronounced than on Uranus, then the above estimates may need to be lengthened by several hours. Recent photometric data are independently analyzed and are found to admit several possible periods, none of which can be confidently assumed to be correct. The period of Neptune most probably falls somewhere in the range 15–20 hr. The Hayes-Belton estimate of the period of Uranus is essentially unaffected by the above-mentioned error and remains at 24 ± 4 hr. All observers agree that the rotation period of Uranus is longer than that of Neptune.     

Gravitational signature of rotationally distorted Jupiter caused by deep zonal winds

Both deep zonal winds, if they exist, and the basic rotational distortion of Jupiter contribute to its zonal gravity coefficients J_n for n ? 2. In order to capture the gravitational signature of Jupiter that is caused solely by its deep zonal winds, one must take into account the full effect of rotational distortion by computing the coefficients J_n in non-spherical geometry. This represents a difficult and challenging problem because the widely-used spherical-harmonic-expansion method becomes no longer suitable. Based on the model of a polytropic Jupiter with index unity, we compute Jupiter’s gravity coefficients J₂, J₄, J₆, … , J₁₂ taking into account the full effect of rotational distortion of the gaseous planet using a finite element method. For the model of deep zonal winds on cylinders parallel to the rotation axis, we also compute the variation of the gravity coefficients ΔJ₂, ΔJ₄, ΔJ₆, … , ΔJ₁₂ caused solely by the effect of the winds in non-spherical geometry. It is found that the effect of the zonal winds on lower-order coefficients is weak, ∣ΔJ_n/J_n∣ < 1%, for n = 2, 4, 6, but it is substantial for the high-degree coefficients with n ? 8.     

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.     

Frozen orbits for satellites close to an Earth-like planet

We say that a planet is Earth-like if the coefficient of the second order zonal harmonic dominates all other coefficients in the gravity field. This paper concerns the zonal problem for satellites around an Earth-like planet, all other perturbations excluded. The potential contains all zonal coefficientsJ ₂ throughJ ₉. The model problem is averaged over the mean anomaly by a Lie transformation to the second order; we produce the resulting Hamiltonian as a Fourier series in the argument of perigee whose coefficients are algebraic functions of the eccentricity — not truncated power series. We then proceed to a global exploration of the equilibria in the averaged problem. These singularities which aerospace engineers know by the name of frozen orbits are located by solving the equilibria equations in two ways, (1) analytically in the neighborhood of either the zero eccentricity or the critical inclination, and (2) numerically by a Newton-Raphson iteration applied to an approximate position read from the color map of the phase flow. The analytical solutions we supply in full to assist space engineers in designing survey missions. We pay special attention to the manner in which additional zonal coefficients affect the evolution of bifurcations we had traced earlier in the main problem (J ₂ only). In particular, we examine the manner in which the odd zonalJ ₃ breaks the discrete symmetry inherent to the even zonal problem. In the even case, we find that Vinti's problem (J ₄+J ₂ ² =0) presents a degeneracy in the form of non-isolated equilibria; we surmise that the degeneracy is a reflection of the fact that Vinti's problem is separable. By numerical continuation we have discovered three families of frozen orbits in the full zonal problem under consideration; (1) a family of stable equilibria starting from the equatorial plane and tending to the critical inclination; (2) an unstable family arising from the bifurcation at the critical inclination; (3) a stable family also arising from that bifurcation and terminating with a polar orbit. Except in the neighborhood of the critical inclination, orbits in the stable families have very small eccentricities, and are thus well suited for survey missions.     

Perturbation of a satellite orbiter by the oblateness of the primary planet

The perturbation of an orbiter around a large satellite of a giant planet (Jupiter, Saturn, Uranus or Neptune) produced by the oblateness of the planet is investigated. The perturbing force of theJ ₂-term (general case) and theJ ₄-term (special case of small eccentricity and inclination) is expanded in an appropriate form and the main term and the parallactic term are given explicitly. The variations of the orbital elements are derived using the stroboscopic method. An example shows that the perturbation of the orbit cannot be neglected.     

Analytical solutions for J 2-perturbed unbounded equatorial orbits

While solutions for bounded orbits about oblate spheroidal planets have been presented before, similar solutions for unbounded motion are scarce. This paper develops solutions for unbounded motion in the equatorial plane of an oblate spheroidal planet, while taking into account only the J ₂ harmonic in the gravitational potential. Two cases are distinguished: A pseudo-parabolic motion, obtained for zero total specific energy, and a pseudo-hyperbolic motion, characterized by positive total specific energy. The solutions to the equations of motion are expressed using elliptic integrals. The pseudo-parabolic motion unveils a new orbit, termed herein the fish orbit, which has not been observed thus far in the perturbed two-body problem. The pseudo-hyperbolic solutions show that significant differences exist between the Keplerian flyby and the flyby performed under the the J ₂ zonal harmonic. Numerical simulations are used to quantify these differences.     

Impact processing of nitrogen on early Mars

An intense impact flux upon a planet having a CO₂ + N₂ atmosphere, such as Mars, provides energy to synthesize nitric oxide, NO, which is likely converted into nitrate minerals. The same impact flux can decompose nitrate minerals if present in the crust. We build a numerical model to study the effects of early impact processes on the evolution of nitrogen in a dominantly CO₂ atmosphere. We model the period of intense post-accretionary bombardment, the roughly 500 Myr period after crustal stabilization that locks in previously accreted volatiles. A best-guess, “fiducial” set of parameters is chosen, with a fixed “veneer” of post-accretionary impactors (δR=950 m thick), assumed to contain carbon at 1 wt% (fg=0.01), with a molar C/N ratio of 18, an initial atmospheric pressure of 1 bar (with CO₂/N₂ = 36), and a power law impactor mass distribution slope b=0.75. This model produces a nitrate reservoir RNO₃?0.5×¹⁰¹⁹ moles, equivalent to ∼30 mbars of N₂, during the intense impact phase. Starting with 1 bar, the atmosphere grows to 2.75 bars. Results of models with variations of parameter values show that RNO₃ responds sluggishly to changes in parameter values. To significantly limit the size of this reservoir, one is required to limit the initial total atmospheric pressure be less than about 0.5 bars, and the impactor volatile content fg to be less than 0.003. The value of fg substantially determines whether the atmosphere grows or not; when fg=0.01, the atmosphere gains about 1.7 bars, while for fg=0.003, the atmosphere gains less than 200 mbars, and for fg=0.001, it loses about 400 mbars. Impact erosion is a minor sink of N, constituting generally less than 10% of the total supply. The loss of impactor volatile plumes can take almost 50% of incoming N and C under fiducial parameters, when atmospheric pressures are low. This nitrogen does not significantly interact with Mars, and hence is not properly delivered. When the initial N is greater than the delivered N, most of the nitrogen ends up as nitrates; when delivered N is larger, most nitrogen ends up in the atmosphere. The reason for this dichotomy seems to be that initial nitrogen is present during the whole bombardment, while delivered N, on average, only experiences half the bombardment. The operating caveat here is that the above results are all conditioned on the assumption that impact processes dominate this period of Mars atmospheric evolution.     

Variability of Neptune

Earth-based observers of Neptune have found that the planet varies in brightness at various wavelengths in ways that suggest that changes occur in the planet's atmosphere on several different time scales. Global inhomogeneities in high-altitude haze distribution that are stable for several days permit measurements of the planet's rotation period (about 18 hr), but this stability sometimes breaks down, obscuring the diurnal lightcurve. In addition, there is an apparent long-term variability of the brightness of Neptune in anticorrelation with the cycle of solar activity. This slow variability of low amplitude may be punctuated by outburst of high-altitude condensation of particles in the atmosphere whose decay time is several months.     

A possible rotation period for the minor planet 164 Eva

The minor planet 164 Eva passed through opposition on December 1, 1975 with a magnitude B_opp = 11.3 mag. Photoelectric observations at the Observatory of Torino, Italy, were carried out in two nights on Oct. 27/28 and Nov. 11, each with a run of about 3 hr. Two further successful photoelectric observations were carried out at the OHP, France, each with a run of about 6 hr. From all observed parts of the lightcurve a resulting synodic period of rotation of about 27.3 hr can be deduced, with a range of the total amplitude of at least Δm = 0.07 mag. With this period of 27.3 hr the minor planet 164 Eva is one more long period object, falling now between 654 Zelinda (H. J. Schober, 1975, Astron. Astrophys.44, 85–89) and 139 Juewa (J. Goguen et al., 1976, Icarus29, 137–142), at the high end in the histogram of the distribution of minor planet rotation periods.     

Indications of supersaturated stratospheric methane in Neptune from its atmospheric thermal profile

An iterative inversion method is used to retrieve the thermal structure of Neptune from available infrared measurements. The most plausible thermal profile leads to an effective temperature of 58.4°K, implying the presence of an internal heat source equal to about 1.6 times the solar-absorbed power. The interpretation of Neptunian infrared measurements in the 8-μm range requires a very strong supersaturation of CH₄ in the upper atmosphere of the planet.     

Survival of Trojan-type companions of Neptune during primordial planet migration

We investigate the survivability of Trojan-type companions of Neptune during primordial radial migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. We adopt the usual planet migration model in which the migration speed decreases exponentially with a characteristic time scale τ (the e-folding time). We perform a series of numerical simulations, each involving the migrating giant planets plus ∼1000 test particle Neptune Trojans with initial distributions of orbital eccentricity, inclination, and libration amplitude similar to those of the known jovian Trojans asteroids. We analyze these simulations to measure the survivability of Neptune's Trojans as a function of migration rate. We find that orbital migration with the characteristic time scale τ=10⁶ years allows about 35% of preexisting Neptune Trojans to survive to 5τ, by which time the giant planets have essentially reached their final orbits. In contrast, slower migration with τ=10⁷ years yields only a ∼5% probability of Neptune Trojans surviving to a time of 5τ. Interestingly, we find that the loss of Neptune Trojans during planetary migration is not a random diffusion process. Rather, losses occur almost exclusively during discrete prolonged episodes when Trojan particles are swept by secondary resonances associated with mean-motion commensurabilities of Uranus with Neptune. These secondary resonances arise when the circulation frequencies, f, of critical arguments for Uranus-Neptune mean-motion near-resonances (e.g., f^UN_1:2, f^UN_4:7) are commensurate with harmonics of the libration frequency of the critical argument for the Neptune-Trojan 1:1 mean-motion resonance (f^NT_1:1). Trojans trapped in the secondary resonances typically have their libration amplitudes amplified until they escape the 1:1 resonance with Neptune. Trojans with large libration amplitudes are susceptible to loss during sweeping by numerous high-order secondary resonances (e.g., f^UN_1:2≈11f^NT_1:1). However, for the slower migration, with τ=10⁷ years, even tightly bound Neptune Trojans with libration amplitudes below 10° can be lost when they become trapped in 1:3 or 1:2 secondary resonances between f^UN_1:2 and f^NT_1:1. With τ=10⁷ years the 1:2 secondary resonance was responsible for the single greatest episode of loss, ejecting nearly 75% of existing Neptune Trojans. This episode occurred during the late stages of planetary migration when the remnant planetesimal disk would have been largely dissipated. We speculate that if the number of bodies liberated during this event was sufficiently high they could have caused a spike in the impact rate throughout the Solar System.     

Modeling of the spectrum of Cygnus OB2 No. 7 supergiant

We report the results of modeling of the spectrum of the O3 If_* Cyg OB2 No. 7 supergiant in a broad wavelength range. We determine the physical properties and chemical composition of its atmosphere not assuming the presence of local thermodynamic equilibrium. The atmosphere reveals an excess of nitrogen X(N)/X(N)_⊙ = 3.2 and the carbon and oxygen deficiency X(C)/X(C)_⊙ = 0.08, X(O)/X(O)_⊙ = 0.09. The lines in the stellar spectrum are divided into three groups which fail to be describedwithin a single model. Themodels describing each of these groups differ by themass-loss rate and the law of wind velocity variation. Thus, the numerical modeling suggests that the wind of the supergiant is heterogeneous. In addition, this paper describes the features of the CMFGEN code used and investigates the sensitivity of its results to the variations of different parameters.     

Mercury: Internal structure and thermal evolution

Astronomical observations and cosmochemical calculations suggest that the planet Mercury may be composed of materials which condensed at relatively high temperatures in the primitive solar nebula and may have a basaltic crust similar to parts of the moon. These findings, plus the long standing inference that Mercury is much richer in metallic iron than the other terrestrial planets, provide important constraints which we apply to models of the thermal evolution and density structure of the planet. The thermal history calculations include explicitly the differing thermal properties of iron and silicates and account for core segregation, melting and differentiation of heat sources, and simulated convection during melting. If the U and Th abundances of Mercury are taken from the cosmochemical model of Lewis, then the planet would have fully differentiated a metal core from the silicate mantle for all likely initial temperature distributions and heat transfer properties. Density distributions for the planet are calculated from the mean density and estimates of the present-day temperature. For the fully differentiated model, the moment of inertia C/MR² is 0.325 (J₂=0.302×10^?6). For models with lower heat source abundances, the planet may not yet have differentiated. The density profiles for such models give C/MR²=0.394 (J₂=0.487×10^?6). These results should be useful for preliminary interpretation of the Mariner 10 measurements of Mercury's gravitational field.     

Mariner 10 observations of hydrogen Lyman alpha emission from the venus exosphere: Evidence of complex structure

The Ultraviolet Spectrometer Experiment on the MARINER 10 spacecraft measured the hydrogen Lyman α emmission resonantly scattered in the Venus exosphere at several viewing aspects during the encounter period. Venus encounter occurred at 17:01 GMT on 5 February 1974. Exospheric emissions above the planet's limb were measured and were analyzed with a spherically symmetric, single scattering, two-temperature model. On the sunlit hemisphere the emission profile was represented by an exospheric hydrogen atmosphere with T_c = 275±50 K and n_c = 1.5 × 10⁵ cm^?3 and a non-thermal contribution represented by T_H = 1250±100 K with n_H = 500±100 cm^?3. The observations of the dark limb showed that the spherically symmetric model used for the sunlit hemisphere was inappropriate for the analysis of the antisolar hemisphere. The density of the non-thermal component had increased at low altitudes, < 12,000 km, and decreased at high altitudes, > 20,000 km, by comparison. We conclude that the non-thermal source is on the sunward side of the planet. Analysis of the dark limb crossing suggests that the exospheric temperature on the dark side is <125 K if the exospheric density remains constant over the planet; upper limits are discussed. An additional source of Lyman α emission, 70 ± 15 R, was detected on the dark side of the planet and is believed to be a planetary albedo in contrast to multiple scattering from the sunlit side. Our analysis of the MARINER 10 data is consistent when applied to the MARINER 5 data.     

Stability of Trojan planets in multi-planetary systems

Today there are more than 340 extra-solar planets in about 270 extra-solar systems confirmed. Besides the observed planets there exists also the possibility of a Trojan planet moving in the same orbit as the Jupiter-like planet. In our investigation we take also into account the habitability of a Trojan planet and whether such a terrestrial planet stays in the habitable zone. Its stability was investigated for multi-planetary systems, where one of the detected giant planets moves partly or completely in the habitable zone. By using numerical computations, we studied the orbital behaviour up to 10⁷ years and determined the size of the stable regions around the Lagrangian equilibrium points for different dynamical models for fictitious Trojans. We also examined the interaction of the Trojan planets with a second or third giant planet, by varying its semimajor axis and eccentricity. We have found two systems (HD 155358 and HD 69830) that can host habitable Trojan planets. Another aim of this work was to determine the size of the stable region around the Lagrangian equilibrium points in the restricted three body problem for small mass ratios μ of the primaries μ ≤ 0.001 (e.g. Neptune mass of the secondary and smaller masses). We established a simple relation for the size depending on μ and the eccentricity.     

An Upper Limit of Mass for a Stable Minor Planet in the Main Asteroid Belt

The stability of an imaginary planet located in the present main asteroid belt is studied with a 7-body model (Sun, Mars, Jupiter, Saturn, Uranus, Neptune and the imaginary planet). The fourth-order Hermite algorithm P(EC)³ is used, which has a very small secular energy error for the integration of periodic orbits with a constant time-step. The evolution of orbits is followed up to 10⁸ years. Our numerical results show that the low-order resonances with Jupiter can enhance the stability of the imaginary planet in some cases. The survival probability of the imaginary planet decreases with the planet mass. The upper limit of the imaginary planet's mass that can survive in the main belt is around 10²⁵ kg, i.e., about the Earth's mass.     

Neptune migration model with one extra planet

We explore conventional Neptune migration model with one additional planet of mass at 0.1-2.0M_⊕. This planet inhabited in the 3:2 mean motion resonance with Neptune during planet migration epoch, and then escaped from the Kuiper belt when jovian planets parked near the present orbits. Adding this extra planet and assuming the primordial disk truncated at about 45 AU in the conventional Neptune migration model, it is able to explain the complex structure of the observed Kuiper belt better than the usual Neptune migration model did in several respects, which are the following. (1) High-inclination Plutinos with i?15-35° are produced. (2) Generating the excitation of the classical Kuiper belt objects, which have moderate eccentricities and inclinations. (3) Producing the larger ratio of Neptune’s 3:2 to 2:1 resonant particles, and the lower ratio of particles in the 3:2 resonance to those in the classical belt, which may be more consistent with observations. (4) Finally, several Neptune’s 5:2 resonant particles are obtained. However, numerical experiments imply that this model is a low-probability event. In addition to the low probability, two features produced by this model may be inconsistent with the observations. They are small number of low-inclination particles in the classical belt, and the production of a remnant population with near-circular and low-inclination orbit within . According to our present study, including one extra planet in the conventional Neptune migration model as the scenario we explored here may be unsuitable because of the low probability, and the two drawbacks mentioned above, although this model can explain better several features which is hard to produce by the conventional Neptune migration model. The issues of low-probability event and the lack of low-inclination KBOs in the classical belt are interesting and may be studied further under a more realistic consideration.     

Analytical Solution of Coupled Perturbation of Tesseral Harmonic Terms of Mars's Non-Spherical Gravitational Potential

The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars’ tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J_2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J₂. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10−4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10⁻⁴ in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration.     

The dynamics of a high-speed Jovian jet

We present new measurements of the velocity field in the neighborhood of the high-speed jet located at approx. 24° N latitude in the Jovian atmosphere. The maximum zonal velocity is found to be 182 ± 10 m s^?1 located at 23.7 ±0.2° N and representing the largest velocity measured on the planet. The distinctive cloud markings found close to this latitude are discussed and possible dynamical consequences presented.