Analysis of the orbit of ariel 1, 1962-15A,near 15th-order resonance

Ariel 1, the first international satellite, was launched on 26 April 1962, into an orbit inclined at 53.85° to the equator, with an initial perigee height near 390 km. On 8 May 1973 the orbit passed through 15th-order resonance and has been determined, with the RAE orbit refinement program PROP, at eight epochs between February and August 1973 using 500 observations.The orbital inclinations during the time of 15th-order resonance, as given by these eight orbits and 31 U.S. Navy orbits, were fitted with a theoretical curve using the THROE computer program, the best fit giving $\text{10}{}^9\text{C}\text{?}{}_{15}\text{= ?370 ± 14}$ and 10⁹S₁₅ = ?114 ± 31.The values of eccentricity were also successfully fitted using THROE, and the results are discussed.     

Photometry of Saturn's satellites: The opposition effect of Iapetus at maximum light and the variability of Titan

We present photometry, V and (B - V), of Iapetus at six western elongations (the phase of maximum brightness) that span a range in solar phase, α, from ≈6° to <0°.4, and we find that a substantial opposition effect, >0.12 mag (V), is present. We make a few cautious remarks about the possible relevance of the use of this result to interpret the phase curve of Saturn's ring. We also give a few measures of Rhea and Hyperion, at $\text{α ? 0.3°}$, and more of Titan, which indicate that the latter has been anomalously bright during much of 1973 and 1974, sometimes by nearly 0.1 mag (V).     

Titan: Far-infrared and microwave remote sensing of methane clouds and organic haze

It is shown that Titan's surface and plausible atmospheric thermal opacity sources—gaseous N₂, CH₄, and H₂, CH₄ cloud, and organic haze—are sufficient to match available Earth-based and Voyager observations of Titan's thermal emission spectrum. Dominant sources of thermal emission are the surface for wavelenghts λ ? 1 cm, atmospheric N₂ for 1 cm ? λ ? 200 μm,, condensed and gaseous CH₄ for 200 μm ? λ ? 20 μm, and molecular bands and organic haze for λ ? 20 μm. Matching computed spectra to the observed Voyager IRIS spectra at 7.3 and 52.7° emission angles yields the following abundances and locations of opacity sources: CH₄ clouds: 0.1 g cm^? at a planetocentric radius of 2610–2625 km, 0.3 g cm^?2 at 2590–2610 km, total 0.4 ± 0.1 g cm^–2 above 2590 km; organic haze: $\text{4 ± 2 × 10}{}^{\mathrm{?6}}\text{,}\text{g cm}\text{,}{}^{\mathrm{?2}}$ above 2750 km; tropospheric H₂: 0.3 ± 0.1 mol%. This is the first quantitative estimate of the column density of condensed methane (or CH₄/C₂H₆) on Titan. Maximum transparency in the middle to far IR occurs at 19 μm where the atmospheric vertical absorption optical depth is $\text{?0.6}$ A particle radius $\text{r}\text{? 2 μ}\text{m}$ in the upper portion of the CH₄ cloud is indicated by the apparent absence of scattering effects.     

Analysis of the orbit of cosmos 395 rocket (1971-13B) near 15th-order resonance

Cosmos 395 rocket (1971-13B) is moving in a near-circular orbit inclined at 74° to the equator. Its average height, near 540 km after launch in February 1971, slowly decreased under the action of air drag and on 24 March 1972 it experienced exact 15th-order resonance, with the successive equator crossings 24° apart in longitude. Its orbit has been determined at 21 epochs between September 1971 and September 1972 using 1100 observations, including 55 from the Malvern Hewitt camera: the mean S.D. in inclination is 0.001° and in eccentricity 0.00001.The variations in inclination i, eccentricity e, right ascension of the node $\text{Ω}$, and argument of perigee ω, near 15th-order resonance are analysed to determine values of lumped 15th-order harmonic coefficients in the geopotential. The inclination yields equations accurate to 4 per cent for coefficients of order 15 and degree 15,17,19..., which are in excellent agreement with those from Cosmos 387 (1970-111A) in an orbit of similar inclination but different resonant longitude. Analysis of the variations in e gives two pairs of equations for the coefficients of order 15 and degree 16, 18..., which are used to obtain tentative values of the (16,15) coefficients. For the first time the resonant variation of other elements ($\text{Ω}\text{and}\text{ω}$) has also been analysed with partial success.     

Optical constants of organic tholins produced in a simulated Titanian atmosphere: From soft x-ray to microwave frequencies

As part of a continuing series of experiments on the production of dark reddish organic solids, called tholins, by irradiation of cosmically abundant reducing gases, the synthesis from a simulated Titanian atmosphere of a tholin with a visible reflection spectrum similar to that of the high altitude aerosols responsible for the albedo and reddish color of Titan has been reported Sagan and Khare, 1981, Sagan and Khare, 1982, Orig. Life. 12, 280) and [C. Sagan, B. N. Khare, and J. Lewis, in press. In Saturn (M. S. Matthews and T. Gehrels, Eds.), Univ. of Arizona Press, Tucson]. The determination of the real (n) and imaginary (k) parts of the complex refractive index of thin films of such tholin prepared by continuous D.C. discharge through a 0.9 N₂/0.1 CH₄ gas mixture at 0.2 mb are reported. For $\text{250}\text{A}\text{?}\text{≤ γ ≤ 1000 μ}\text{m}\text{, n}\text{and}\text{k}$ have been determined from a combination of transmittance, specular reflectance, interferometric, Brewster angle, and ellipsometric polarization measurements; experimental uncertainties in n are estimated to be ±0.5, and in k ± 30%. Values of n(?1.65) and k (?0.004 to 0.08) in the visible range are consistent with deductions made by ground-based and spacecraft observations of Titan. Maximum values of k (?0.8) are near 1000 Å, and minimum values (?4 × 10^?4) are near 1.5 μm. Many infrared absorption features are present in k(γ), including the 4.6-μm nitrile band.     

Numerical experiment applicable to the latest stage of planet growth

A three-dimensional numerical model was developed with the goal of studying limited dynamical problems relevant to the latest stage of planet growth in the accretion theory. A small number of large protoplanets (～ Moon size) of different masses, moving around the Sun, are considered. The dynamical evolution and growth of the population is studied under mutual gravitational perturbations, accretion, and collisional fragmentation processes. Gravitational encounters are treated exactly by numerical integration of the N-body problem. Outcomes of collisional fragmentation are modeled according to the results of R. Greenberg et al. (1978, Icarus, 35, 1–26). In the present work, we consider 25 protoplanets with uniform mass distribution in the range 2 × 10²⁵?4 × 10²⁶ g on heliocentric orbits in the Earth zone. These bodies are initially confined to a small volume of space to permit gravitational perturbations by close approaches and collisions within a finite length of integration time. The dynamical evolution of the swarm is followed for four different sets of initial ranges in semimajor axis, eccentricity, and inclination: Δa=0.01, 0.02, 0.04, 0.08 AU; Δe= 0.005, 0.01, 0.02, 0.04; Δi=0°3, 0°6, 1°2, 2°4. Among other results, it is found that average eccentricities and inclinations evolve toward a steady state such that $\text{i}\text{?}\text{1}\text{2}\text{,}\text{e}$; it is also found that, whatever the initial conditions, the population evolves toward a quasi-equilibrium relative velocity distribution corresponding to a Safronov parameter value $\text{θ?10}$. Moreover, the growth process of the growing planet presents very similar behavior in the four cases considered, except for the time scale of evolution, which increases with the initial range of orbital elements. Earlier works of this kind have been presented by L.P. Cox and J.S. Lewis (1980, Icarus, 44, 706–721) and by G.N. Wetherill (1980b, In Geol. Soc. Canad. Spec. Publ., p. 20), although a number of differences exist between the three approaches.     

The asteroids as outcomes of catastrophic collisions

The role of catastrophic collisions in the evolution of the asteroids is discussed in detail, employing extrapolations of experimental results on the outcomrs of high-velocity impacts. We determine the range of the probable largest collision for target asteroids of different sizes during the solar system's lifetime, and we conclude that all the asteroids have undergone collisional events capable of overcoming the material's solid-state cohesion. Such events do not lead inescapably to complete disruption of the targets, because (i) for a previously unfractured target, experiments show that fragments of significant size can survive breakup, depending on the energy and geometry of the collision; (ii) self-gravitation can easily cause a reaccumulation of fragments for targets exceeding a critical size, which seems to be of the order of 100 km. In the intermediate diameter range 100?D ?300 km, where formation of gravitationally bound “rubble piles” is frequent, the transfer of angular momentum can be large enough to produce objects with triaxial equilibrium shapes (Jacobi ellipsoids) or to cause fission into binary systems. In the same size range, low-velocity escape of collisional fragments can also occur, leading to the formation of dynamical families. Asteroids smaller than ～100 km are mostly multigeneration fragments, while for $\text{D?300}\text{km}$ the collisional process produces nearly spheroidal objects covered by megaregoliths; whether their rotation is “primordial” or collisionally generated depends critically on the past flux of colliders. The complex and size-dependent phenomenology predicted by the theory compares satisfactorily with the observational evidence, as derived both by a classification of asteroids in terms of their size, spin rate, and lightcurve amplitude, and by a comparison between the rotational properties of family and nonfamily asteroids. The fundamental result of this investigation is that almost all asteroids are outcomes of catastrophic collisions, and that these events cause either complete fragmentation of the target bodies or, at least, drastic readjustments of their internal structure, shape, and spin rate.     

Production and condensation of organic gases in the atmosphere of Titan

The rates and altitudes for the dissociation of atmospheric constituents of Titan are calculated for solar UV, solar wind protons, interplanetary electrons, Saturn magnetospheric particles, and cosmic rays. The resulting integrated synthesis rates of organic products range from 10²–10³ g cm^?2 over 4.5 × 10⁹ years for high-energy particle sources to 1.3 × 10⁴ g cm^?2 for UV at $\text{λ < 1550}\text{A}\text{?}$, and to 5.0 × 10⁵ g cm^?2 if $\text{λ > 1550}\text{A}\text{?}$ (acting primarily on C₂H₂, C₂H₄, and C₄H₂) is included. The production rate curves show no localized maxima corresponding to observed altitudes of Titan's hazes and clouds. For simple to moderately complex organic gases in the Titanian atmosphere, condensation occurs below the top of the main cloud deck at 2825 km. Such condensates comprise the principal cloud mass, with molecules of greater complexity condensing at higher altitudes. The scattering optical depths of the condensates of molecules produced in the Titanian mesosphere are as great as ～ 10²/(particulate radius, μm) if column densities of condensed and gas phases are comparable. Visible condensation hazes of more complex organic compounds may occur at altitudes up to ～ 3060 km provided only that the abundance of organic products declines with molecular mass no faster than laboratory experiments indicate. Typical organics condensing at 2900 km have molecular masses = 100–150 Da. At current rates of production the integrated depth of precipitated organic liquids, ices, and tholins produced over 4.5 × 10⁹ years ranges from a minimum ～ 100 m to kilometers if UV at $\text{λ > 1550}\text{A}\text{?}$ is important. The organic nitrogen content of this layer is expected to be ～ 10^?1?10^?3 by mass.     

Analysis of the orbital inclination of Tansei 3 rocket 1977-12B

The orbit of Tansei 3rocket(1977-12B) has been determined at 47 epochs between 1 October 1977 and 19 March 1979 using over 1700 observations and the RAE orbit refinement program PROP6. The rate of change of the inclination was examined to evaluate values of the atmospheric rotation rate, Λ rev day^?1. Analysis yielded the value Λ = 1.1 ± 0.05 at height 315 ± 30 km, average conditions; or alternatively Λ = 1.1 ± 0.1 at height 347 ± 12 km, slight winter bias and Λ = 1.07 ± 0.1 at height 270 ± 18 km, average conditions, supplying further evidence of a decrease in rotation rates from the 1960s to the 1970s.Analysis of the inclination at 15th-order resonance yielded the lumped harmonic values

$\text{10}{}^9\text{C}{}^{\mathrm{0,1}}{}_{15}\text{= 13.4 ± 6.2, 10}{}^9\text{S}{}^{\mathrm{0,1}}{}_{15}\text{= 0.7 ± 13.3}$

for inclination 65.485°.     

Observations of Saturn's outer ring and new satellites during the 1980 edge-on presentation

Observations of Saturn's satellites and external rings during the 1980 edge-on presentation were obtained with a focal coronograph. A faint satellite traveling in the orbit of Dione and leading it by 72° has been detected, together with the two inner satellites already suspected (cf. J. W. Fountain and S. M. Larson, 1978,Icarus36, 92–106). The external ring has been observed on both east and west sides; it may extend up to $\text{?8.3}$ Saturn radii, and appears structured.     

Direct measurement of conjugate photoelectrons and predawn 630 nm airglow

A sounding rocket was flown during the predawn on 17 January, 1976 from Uchinoura, Japan, to measure directly the behaviour of the conjugate photoelectrons at magnetically low latitudes. On board the rocket were an electron energy analyzer, 630 nm airglow photometer, and plasma probes to measure electron density and temperature. The incoming flux of the photoelectrons was measured in the altitude range between 210 and 340 km. The differential flux at the top of the atmosphere was determined to be $\text{F = (1.3 ± 0.4) × 10}{}^{11}\text{exp}\text{[?}\text{E(}\text{eV}\text{)}\text{12}\text{]}$ electron · m^?2 · sr^?1 · s^?1 in the energy range 10 ? E ? 50 eV. The emission rate of the 630 nm airglow was observed in the altitude range between 90 and 360 km. The apparent emission rate observed at 80 km was 32 ± 5 R. From a theoretical calculation of the optical excitation rate using the observed electron flux data along with a model distribution of atomic oxygen, it was estimated that more than 65% of the emission could be produced by direct impact of the photoelectrons with atomic oxygen in the thermosphere between 200 and 360 km. Using the observed electron density and the model distribution of oxygen molecules the residual of the emission was ascribed to the excitation of O(¹D) through dissociative recombination, $\text{O}{}_2{}^{\mathrm{+}}\text{+}\text{e}\text{→}\text{O}{}^1\text{+}\text{O}{}^7$. The direct collisional excitation by ambient electrons is estimated to be negligibly small at the level of observed electron temperature.     

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.     

Secular resonance,solar spin down,and the orbit of Mercury

A mechanism capable of accounting for the large mean eccentricity (0.175) and inclination (7°.2) of Mercury is discussed. Provided the gravitational field of the rapidly rotating primordial Sun had a sufficiently large second degree harmonic (i.e., J₂ ? order 10^?3), subsequent solar spin down would drive the orbit of Mercury through two secular resonances with Venus, one involving the precession of the line of apsides, the other one involving the regression of the nodal line. Resonance passage generates contributions to the eccentricity and inclination that are proportional to the square root of the characteristic solar spin down time. We find that an initial solar rotation l period of $\text{P ? 5}\text{1}\text{2}\text{hr}$ guarantees passage through resonance and that a spin down time of $\text{τ = Ω|dΩ/dt|}{}^{\mathrm{?1}}$ of order 10⁶ years could have produced the observed eccentricity and inclination. Such a primordial rotation rate is comparable to the measured rotations of very young stars and the spin down time appears consistent with the time scale derived for magnetic braking of the Sun's rotation by an intense solar wind during a T-Tauri stage of solar evolution.     

Io's sodium emission cloud and the voyager 1 encounter

Io's neutral sodium emission cloud was monitored during the period of Voyager 1 encounter from two independent ground-based sites. Observations from Table Mountain Observatory verified the continued existence of the “near-Io cloud” (d < 1.5 × 10⁵ km, for 4πI > 1 kR; R denotes Rayleigh) while those from Wise Observatory showed a deficiency in the weaker emission at greater distances from Io. The sodium cloud has been monitored from both observatories for several years. These and other observations demonstrate that the behavior of the cloud is complex since it undergoes a variety of changes, both systematic and secular, which can have both time and spatial dependencies. The cloud also displays some characteristics of stability. Table Mountain images and high-dispersion spectra (resolution $\text{～0.2}\text{A}\text{?}$) indicate that the basic shape and intensity of the “near cloud” have remained relatively constant at least since imaging observations began in 1976. Wise Observatory low-dispersion spectra (resolution $\text{～1}\text{A}\text{?}$) which have been obtained since 1974 demonstrate substantial variability of the size and intensity of the “far cloud” (d ? 1.5 × 10⁵ km) on a time scale of months or less. Corresponding changes in the state of the plasma associated with the Io torus are suggested, with the period of Voyager 1 encounter represented as a time of unusually high plasma temperature and/or density. Dynamic models of the sodium cloud employing Voyager 1 plasma data provide a reasonable fit to the Table Mountain encounter images. The modeling assumptions of anisotropic ejection of neutral sodium atoms from the leading, inner hemisphere of Io with a velocity distribution characteristic of sputtering adequately explain the overall intensity distribution of the “near cloud”. During the Voyager 1 encounter period there appeared a region of enhanced intensity projecting outward from Io's orbit and inclined to the orbital plane. This region is clearly distinguished from the sodium emission normally aligned with the plane of Io's orbit. The process responsible for this phenomenon is not yet understood. Similar but less pronounced features are also present in several Table Mountain images obtained over the past few years.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

The orbit of the Dhajala meteorite

Observations of the trail caused by the meteorite which fell around Dhajala, Gujarat (India), on 28 January 1976 have been used to compute the probable orbit of the meteoroid in space. The cosmic ray effects in the meteorite fragments indicate high mass ablation (?90%), suggesting a high velocity (?20 km/sec) of entry into the Earth's atmosphere. The atmospheric trajectory is reasonably well documented and its deviation from the projected ground fallout can be understood in terms of the ambient wind pattern. The apparent radiant of the trail was at a point in the sky with right ascension 165°, declination +60°. Considering the errors in estimating the radiant, we get a range of orbits with a = 2.3 ± 0.8 AU, e = 0.6 ± 0.1, and i = 28 ± 4° with the constraints of a ? 1.5 AU and V_∞ < 25 km/sec (which causes nearly complete evaporation of the meteoroid). Taking V_∞ = 21.5 lm/sec as indicated by the measured mass ablation of the meteorite, the orbital elements are deduced to be $\text{a = 1.8}\text{AU}\text{, e = 0.59, i = 27°.6, ω = 109°.1, Ω = 307°.8,}\text{and}\text{q = 0.74}$.     

The 63 μm radiation field in the earth's thermosphere and its influence on the atomic hydrogen temperature

The thermal escape of hydrogen from the Earth's atmosphere is strongly affected by its temperature at the exobase. It has been suggested recently that the hydrogen temperature might be significantly lower than the thermospheric temperature as a result of a collisional exchange of energy with atomic oxygen. The tendency is to cool the hydrogen since the energy of the excited ${}^3\text{P}{}_1$ level of oxygen can be lost from the atmosphere via magnetic dipole emission of the 63 μm line (${}^3\text{P}{}_2\text{?}{}^3\text{P}{}_1$). We present here a detailed calculation of the net cooling effect as a function of altitude throughout the thermosphere. The calculations have been performed for both day and night conditions and for periods of maximum and minimum solar activity conditions. It is found that its effect on ΔT/T varies from a very small value to a maximum of ～3%. We also provide the theoretical framework for describing deviations of the 63 μm emission from local thermodynamic equilibrium and show that these effects can cause the emission to be reduced by as much as 40% near 500 km.     

On fourier-analysis of geomagnetic pulsations pc-1, “two-fold” and “three-fold” pulsations pc-1 and fundamental frequencies of the magnetospheric cavity—I

The paper gives the results of detailed studies of the frequency spectra $\text{S}{}_{\mathrm{s}}\text{(?)}$ of the chain of the wave packets F_s(t) of geomagnetic pulsations PC-1 recorded at the Novolazarevskaya station. The bulk of the energy of F_s(t) is concentrated in the vicinity of the central frequencies $\text{?}{}_{\mathrm{s0}}$ of spectra—the carrier frequencies of the signals. The velocity $\text{V}{}_0\text{≌ 6.10}{}^3\text{km s}{}^{\mathrm{?1}}$ of the flux of protons generating these signals correspond to them. The spectra of the signals have oscillations—“satellites” irregularly distributed in frequency. These satellites, as the authors believe, testify to the presence of the individual groups of protons of low concentration whose velocities vary within 10³–10⁴ km s^?1.Their energy is only of the order of 10^?2–10^?3 of the energy of the main proton flux. Clearly pronounced maxima on double and triple frequencies $\text{? = 2?}{}_{\mathrm{s0}}\text{and}\text{3?}{}_{\mathrm{s0}}$ are detected. They show that the generation of pulsations PC-1 is accompanied by the generation on the overtones of wave packets called in this paper “two-fold” and “three-fold” pulsations PC-1. Intensive symmetrical satellites of a modulation character have been discovered on frequencies $\text{?}{}^{\mathrm{\pm }}{}_{\mathrm{sK}}$. Frequency differences $\text{Δ?}{}_{\mathrm{sK}}{}^{\mathrm{\pm }}\text{=}\text{¦?}{}_{\mathrm{s0}}\text{? ?}{}_{\mathrm{sK}}{}^{\mathrm{\pm }}\text{¦}\text{= (0.011,0.022}\text{and}\text{0.035)}\text{Hz}$ correspond to them. The authors believe that the values of Δ?^±_sK are resonance frequencies of the magnetospheric cavity in which geomagnetic pulsations PC-1 are generated. It is established that the values of Δ?^±_sK coincide closely with the carrier frequencies of geomagnetic pulsations PC-3 and PC-4 generated in the magnetosphere. This leads to the conclusion that the resonance oscillations of the magnetospheric cavity are their source. Thus, the generation of geomagnetic pulsations of different types and resonance oscillations in the magnetosphere are integrated into a unified process. The importance of the results obtained and the necessity to check further their trustworthiness and universality, using experimental data gathered in different conditions, is stressed.     

The angular momenta of solar system bodies: Implications for asteroid strengths

The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [Icarus18, 285–293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [Icarus7, 251–256 (1967]) and W. K. Hartmann and S. M. Larson [Icarus7, 257–260 (1967)], H is approximately proportional to $\text{M}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects.The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm^?3. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.     

Estimates of quasipolar absorption by methane in the atmosphere of Titan

The basis for “quasipolar” absorption (QPA) by CH₄ is the existence of a small electric dipole moment in its ground state. The integrated intensity α_QPA at a temperature of 90K is calculated to be between 4.8 × 10^?5 and 1.9 × 10^?2 cm^?2 atm^?1. With an assumed mean pressure of 0.1 atm and a relative abundance of $\text{[}\text{CH}{}_4\text{]}\text{[}\text{H}{}_2\text{]}\text{= 1}$, it is estimated that the ratio of quasipolar to pressure-induced absorption (PIA) is 0.05 ? α_QPA/α_PIA ? 18 for the spectral range from 0 to 300 cm^?1. This result suggests that quasipolar absorption may contribute to a weak, CH₄-induced greenhouse in the atmosphere of Titan.