Photometric properties of zodiacal light particles

From published ground-base, spacecraft, and rocket photometry and polarimetry of the zodiacal light, a number of optical and physical parameters have been derived. It was assumed that the number density, mean particle size, and albedo vary with heliocentric distance, and shown that average individual interplanetary particles have a small but definite opposition effect, a mean single-scattering albedo in the V band at 1-AU heliocentric distance of 0.09 ± 0.01, and a zero-phase geometric albedo of 0.04. Modeled by a power law, both albedos decrease with increasing heliocentric distance as r^?0.54. The corresponding exponents for changes in mean particle size and number density are related in a simple way. The median orbital inclination of zodiacal light particles with respect to the ecliptic is 12°, close to the observed median value for faint asteroids and short-period comets. Furthermore, the color of dust particles and its variation with solar phase angle closely resemble those of C asteroids. These findings are, at least, consistent with the zodiacal cloud originating primarily from collisions among asteroids. Finally, a value of ?10¹⁸?_ErmE g was derived for the mass of the zodiacal cloud, where ?_E is the mean particle radius (in micrometers) at 1-AU-heliocentric distance. For extinction in the ecliptic, $\text{Δm = 10}{}^{\mathrm{?5}}\text{?}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{mag}$ was obtained, where ? is the solar elongation in degrees.     

Planetary impact probabilities for long-period comets

Planetary impact probabilities for long-period (near-parabolic) comets are determined by averaging Öpik's equations over inclination and perihelion distance for each planet. These averaged values compare well with the results of more elaborate Monte Carlo calculations. The impact probabilities are proportional to the square of the normalized capture radius of each planet, which in turn is a function of the planet's radius and mass, so that the major planets have the highest impact probabilities. Encounter velocities have an average value of $\text{3}\text{1}\text{2}$ times the planetary orbital velocity but the most probable encounter velocities are slightly higher than this for the terrestrial planets and slightly lower for the major planets. Comparison of the impact probabilities with the cratering record, corrected for gravity and velocity effects, indicates that long-period comets may account for 3 to 9% of the observed large crattes (diameter > 10 km) on the terrestrial planets. The inclination and perihelion properties of the impact probabilities obtained from numerical averaging provide a simple method for determining the impact probabilities for nonuniform distributions. The perihelion distribution of long period comets from J. A. Fernandez ((1981) Astron. Astrophys.96, 26–35) results in a crater production rate quite similar throughout the solar system, unlike that of a uniform perihelion distribution.     

Particle size distributions in Saturn's rings from voyager 1 radio occultation

Observations of microwave opacity τ[λ] and near forward scatter from Saturn's rings at wavelengths λ of 3.6 and 13 cm from the Voyager 1 ring occultation experiment contain information regarding ring particle sizes in the range of about a = 0.01 to 15 m radius. The opacity measurements τ[3.6] and τ[13] are sufficient to constrain the scale factor n(a₀) and index q of a power law incremental size distribution n(a) = n(a₀)[a₀/a]^q, assuming known minimum and maximum sizes and a many-particle-thick model. The families of such distributions are highly convergent in the centimeter-size range. Forward scatter at 3.6 cm can be used to solve for a general distribution over the radius range $\text{1 ? a ? 15}\text{m}$ by integral inversion and inverse scattering methods, again assuming a many-particle-thick slab-type radiative transfer model. Distributions n(a) valid over $\text{0.01 ? a ? 15}\text{m}$ are obtained by combining the results from the two types of measurements above. Mass distributions may be computed directly from n(a). Such distributions, partly measured and partly synthesized, have been obtained for four features in the ring system centered at 1.35, 1.51, 2.01, and 2.12 Saturn radii (R_s). The size and mass distributions both cut off sharply at a ? 4–5 m; the mass distribution peaks over the narrow size range $\text{3 ? a ? 4}\text{m}$ for all four locations. No single power law distribution is consistent with the data over the entire interval $\text{0.01 ? a ? 5}\text{m}$, although a power law-type model is consistent with the data over a limited size range of $\text{0.01 ? a ? 1}\text{m}$, where the indices q = 3.4 and 3.3 are obtained from the slab model for the features located at 1.51 and 2.01 R_s. The fractional contribution of the suprameter particles to the microwave opacity in each feature appears to be about $\text{1}\text{3}\text{,}\text{1}\text{3}\text{,}\text{2}\text{3}\text{,}\text{and}\text{1}$, respectively, with the fraction at 2.12 R_s being the least certain. The cumulative surface mass per unit area obtained for the classical slab model is approximately 11, 16, 41, and 132 g/cm² for the four features, respectively, if the particles are solid H₂O ice. Both the fractional opacity and the mass density estimates represent upper bounds implied by the assumption of a uniformly mixed set of particles in a many-particle-thick vertical profile; lower estimates would result if the rings were assumed to be nearly a monolayer or if the vertical distribution of particles were size dependent.     

An Einstein search for X-ray emission from comet Bradfield (1979l)

X-radiation may result from active plasma phenomena in the interactions of comets with the solar wind. We have carried out a limited but sensitive search for soft X-radiation from Comet Bradfield (1979$\text{l}$), on 1980 Feb. 5. No X-radiation was detected at a level (3σ) of 1.7 × 10^?13 erg(cm²sec keV)^?1 in the 0.2 – 4.0 kev range. This corresponds to a limit on the power dissipated in the comet by non-thermal electrons of approximately 10¹⁹ ergs sec^?1, averaged over the 2568-sec exposure to the comet. This energy deposition is near the magnitude suggested by simple theoretical ideas, and further searches of appropriate comets both in soft X-radiation and at radio wavelengths seem warranted.     

Evolution of comet orbits under the perturbing influence of the giant planets and nearby stars

The orbital evolution of 500 hypothetical comets during 10⁹ years is studied numerically. It is assumed that the birthplace of such comets was the region of Uranus and Neptune from where they were deflected into very elongated orbits by perturbations of these planets. Then, we adopted the following initial orbital elements: perihelion distances between 20 and 30 AU, inclinations to the ecliptic plane smaller than 20°, and semimajor axes from 5 × 10³ to 5 × 10⁴ AU. Gravitational perturbations by the four giant planets and by hypothetical stars passing at distances from the Sun smaller than 5 × 10⁵ AU are considered. During the simulation, somewhat more than 50% of the comets were lost from the solar system due to planetary or stellar perturbations. The survivors were removed from the planetary region and left as members of what is generally known as the cometary cloud. At the end of the studied period, the semimajor axes of the surviving comets tend to be concentrated in the interval 2 × 10⁴ < a < 3 × 10⁴ AU. The orbital planes of the comets with initial $\text{a ≧ 3 × 10}{}^4\text{AU}$ acquired a complete randomization while the others still maintain a slight predominance of direct orbits. In addition, comet orbits with final a < 6 × 10⁴AU preserve high eccentricities with an average value greater than 0.8 Most “new” comets from the sample entering the region interior to Jupiter's orbit had already registered earlier passages through the planetary region. By scaling up the rate of paritions of hypothetical new comets with the observed one, the number of members of the cometary cloud is estimated to be about 7 × 10¹⁰ and the conclusion is drawn that Uranus and Neptune had to remove a number of comets ten times greater.     

Ultraviolet absorption studies of H2O and other species in comet comae with satellite telescope-spectrometers

Ultraviolet absorption by H₂O and other species in the comae of comets could be detected by studying, with satellite telescope-spectrometers, the occultation of hot stars by comets. Such observations could produce the first direct detection of H₂O, the fundamental parent molecule in comet comae, and give measures of molecular level populations. The first instrument suitable for such observations will be the High Resolution Spectrograph on Space Telescope and, therefore, we consider its capabilities. We have used a Haser model to estimate the molecular column densities and to predict equivalent widths for lines of H₂O, OH, CO, and O as functions of time and angular distance from a comet with a high H₂O production rate. We have determined the minimum detectable equivalent widths, and therefore, the maximum angular separation from such a comet at which H₂O, OH, and CO could be studied. A conservative, statistical estimate shows that comets with high water production rates should pass near enough to about 10 to 100 stars suitable for absorption studies of the $\text{C}\text{}\text{X}$ band of H₂O (1240 Å). Estimated equivalent widths for CO, OH, and the resonance lines of C and O indicate that these species may also be detected.     

Radiation forces on small particles in the solar system

We present a new and more accurate expression for the radiation pressure and Poynting-Robertson drag forces; it is more complete than previous ones, which considered only perfectly absorbing particles or artificial scattering laws. Using a simple heuristic derivation, the equation of motion for a particle of mass m and geometrical cross section A, moving with velocity v through a radiation field of energy flux density S, is found to be (to terms of order $\text{v}\text{c}$)

$\text{m}\text{v}\text{?}\text{= (}\text{SA}\text{c}\text{)Q}{}_{\mathrm{<mtext>pr</mtext>}}\text{[(1 ?}\text{r}\text{?}\text{c}\text{)}\text{S}\text{?}\text{?}\text{v}\text{c}\text{]}$

, where ? is a unit vector in the direction of the incident radiation, $\text{r}\text{?}$ is the particle's radial velocity, and c is the speed of light; the radiation pressure efficiency factor Q_pr ≡ Q_abs + Q_sca(1 ? 〈cos α〉), where Q_abs and Q_sca are the efficiency factors for absorption and scattering, and 〈cos α〉 accounts for the asymmetry of the scattered radiation. This result is confirmed by a new formal derivation applying special relativistic transformations for the incoming and outgoing energy and momentum as seen in the particle and solar frames of reference. Q_pr is evaluated from Mie theory for small spherical particles with measured optical properties, irradiated by the actual solar spectrum. Of the eight materials studied, only for iron, magnetite , and graphite grains does the radiation pressure force exceed gravity and then just for sizes around 0.1 μm; very small particles are not easily blown out of the solar system nor are they rapidly dragged into the Sun by the Poynting-Robertson effect. The solar wind counterpart of the Poynting-Robertson drag may be effective, however, for these particles. The orbital consequences of these radiation forces-including ejection from the solar system by relatively small radiation pressures-and of the Poynting-Robertson drag are considered both for heliocentric and planetocentric orbiting particles. We discuss the coupling between the dynamics of particles and their sizes (which diminish due to sputtering and sublimation). A qualitative derivation is given for the differential Doppler effect, which occurs because the light received by an orbiting particle is slightly red-shifted by the solar rotation velocity when coming from the eastern hemisphere of the Sun but blue-shifted when from the western hemisphere; the ratio of this force to the Poynting-Robertson force is $\text{(}\text{R}{}_{\mathrm{\odot }}\text{r}\text{)}{}^2\text{[(}\text{w}{}_{\mathrm{\odot }}\text{n}\text{) ? 1]}$, where R_⊙ and w_⊙ are the solar radius and spin rate, and n is the particle's mean motion. The Yarkovsky effect, caused by the asymmetry in the reradiated thermal emission of a rotating body, is also developed relying on new physical arguments. Throughout the paper, representative calculations use the physical and orbital properties of interplanetary dust, as known from various recent measurements.     

A Monte Carlo investigation of Jovian perturbations on short-period comet orbits

We present statistical distributions of Jovian perturbations on short-period comet orbits resulting from accurate numerical integrations. Our sample of 60, 000 cometary orbits with low inclinations and random orientations is characterized by perihelia between 0 and 7 AU and aphelia between 4 and 13 AU. The perturbations considered are those experienced because of Jupiter's gravitation per orbital revolution by the comets. Regularization and accurate step-length control in the numerical integration gives statistical results appreciably different from those computed by Rickman and Vaghi (1978). Their use of a crude method of integration led to erroneous results for close encounters. Strong asymmetries of the $\text{δ(}\text{1}\text{a}\text{)}$ distributions, in particular for the extreme tails, are observed for perihelion- or aphelion-tangent orbits. These orbits are also shown to experience the strongest energy perturbations on the average. Some results concerning the perturbations of Tisserand parameters are indicated. The perturbation distributions for the angular elements are described and discussed. The role of the minimum distance from Jupiter as an indicator of perturbations is investigated.     

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.     

Residence time heating effect in auroral conic generation

It is pointed out that, in addition to previously considered microscopic aspects of ion perpendicular heating in the auroral region, the effect of mass-dependent resident times in a finite-length perpendicular heating region may be important. In a simple illustrative model, particles are assumed to enter upward into an auroral acceleration region of finite extent along B, in which both parallel electric fields and perpendicular heating exist. In this situation, the particle residence times vary with particle mass as $\text{M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, so that, in addition to effects associated with species-dependent heating rates, the resultant perpendicular energization associated with residence time also varies as $\text{M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The residence time effect thus favors heating of heavier particles, and may therefore be of some importance in understanding the greater energization of oxygen over hydrogen that has been observed, and also why no electron conics have been observed.     

Laboratory measurement on impact ionization by neutrals and floating potential of a spacecraft during encounter with Halley's Comet

A spacecraft penetrating into the dense cloud of ambient gas and dust particles in the coma of Halley's Comet, is exposed to a bombardment by these particles having a high kinetic energy due to the large velocity of the spacecraft relative to the cometary coma. The interaction of the spacecraft and cometary neutral particles was simulated by using neutral beams of different species directed towards various target materials such as aluminium, gold and the white conductive paint PCB-Z. The kinetic energy of the primary beam covered, depending on the species, the range from about 700 eV up to more than 3 keV and contained, except for H₂O, the expected specific ram energy of $\text{24}\text{eV}\text{amu}$. The highest achievable density corresponded to a distance of slightly less than 10⁴ km off the nucleus. Upon impact on the surface of the target, emission of charged as well as neutral secondary particles was initiated. The yields of the charged particles were derived from measurements of the electrical current produced by secondary ions or electrons. The obtained results for the yields complement other measurements performed in parallel to this work. The derived floating potentials show somewhat lower voltages than obtained by model calculations. It was found that for the metallic targets, the acquired charging potential due to neutral gas impact lies between 4 and 6 V. In the case of PCB-Z, the averaged floating potential amounts to about 14 V.     

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.     

Transport,charge exchange and loss of energetic heavy ions in the earth's radiation belts: Applicability and limitations of theory

Ions in the trapping region of the earth's magnetosphere are subject to physical and chemical interactions which control their absolute and relative abundances. Charge exchange reactions act to establish a distribution of ionic states that is largely determined by the chemical properties of the individual species. Convection (“drift”) mechanisms and cross-L diffusion cause ions to be distributed over the entire trapping region with flux intensities determined by the nature and strength of the ion source, transport and loss mechanisms which in general are dependent on energy, mass and charge. Current theories describe ion transport through path tracing for individual particles or by radial diffusion for a population as a whole based on stochastic analysis; a comprehensive treatment of the combined convection and diffusion for trapped and non-trapped ions is yet to be developed. Even in studies where diffusion is the sole transport mechanism considered, only equatorially mirroring particles ($\text{α}{}_0\text{=}\text{π}\text{2}$) have been theoretically treated. There are clearly both upper and lower bounds on the ion energy beyond which diffusion theory ceases to be valid: at high energies where the ion gyroradius becomes too large for the adiabatic approximations to be valid and at low energies where convective drift is a dominant process. In spite of the known shortcomings of the diffusion theory and associated modeling, intriguing theoretical predictions of the relative ionic composition of the radiation belts have been made and some of them are now confirmed by direct observation. Among them is the predicted importance of ions heavier than protons at ring current energies of tens of keV which follows from the charge exchange chemistry.     

Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. We present the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. The disks are represented by a distribution of about 6 × 10⁴ point masses on a two-dimensional (r, φ) grid. The motions of the particles in the self-consistent gravity field are calculated, and the evolving density distributions are examined for instabilities. Two parameters that have major influences on stability are varied: the initial temperature of the disk (represented by an imposed velocity dispersion), and the mass of the protostar relative to that of the disk. It is found that a disk as massive as 1M_⊙, surrounding a 1M_⊙ protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300°K or greater. Stability of a cooler disk requires that it be less massive, but even at 100°K a stable disk can have an appreciable fraction ($\text{～}\text{1}\text{3}$) of a solar mass.     

Venus mesosphere and thermosphere temperature structure: II. Day-night variations

A two-dimensional nonlinear hydrodynamic model has been developed for studying the global scale winds, temperature, and compositional structure of the mesosphere and thermosphere of Venus. The model is driven by absorption of solar radiation. Ultraviolet radiation produces both heating and photodissociation. Infrared solar heating and thermal cooling are also included with an accurate NLTE treatment. The most crucial uncertainty in determining the solar drive is the efficiency by which $\text{λ < 1080}\text{A}\text{?}$ solar radiation is converted to heat. This question was analyzed in Part I, where it was concluded that essentially all hot atom and O(¹D) energy may be transferred to vibrational-rotational energy of CO₂ molecules. If this is so, the minimum possible euv heating occurs and is determined by the quenching of the resulting excess rotational energy. The hydrodynamic model is integrated with this minimum heating and neglecting any small-scale vertical eddy mixing. The results are compared with predictions of another model with the same physics except that it assumes that 30% of $\text{λ < 1080}\text{A}\text{?}$ radiation goes into heat and that the heating from longer-wavelength radiation includes the O(¹D) energy. For the low-efficiency model, exospheric temperatures are ?300°K on the dayside and drop to < 180°K at the antisolar point. For the higher-efficiency model, the day-to-night temperature variation is from ?600°K to ?250°K. Both versions of the model predict a wind of several hundred meters per second blowing across the terminator and abruptly weakening to small values on the nightside with the mass flow consequently going into a strong tongue of downward motion on the nightside of the terminator. The presence of this circulation could be tested observationally by seeing if its signature can be found in temperature measurements. Both versions of the model indicate that a self-consistent large-scale circulation would maintain oxygen concentrations with ?5% mixing ratios near the dayside F-1 ionospheric peak but ?40% at the antisolar point at the same pressure level.     

Satellite resonance with longitude-dependent gravity—III. Inclination changes for close satellites

The longitude-dependent part of the geopotential can give rise to significant changes in inclination for a close satellite when its mean motion is commensurable with the Earth's rotation. For a decaying satellite passing through resonance, the total change in inclination depends on the value of a resonant variable at exact commensurability, which is an essentially random quantity. Many different gravity coefficients may contribute significantly, with relative amplitudes which are highly dependent on inclination. The equations for general $\text{β}\text{α}$ resonance also reveal a basic distinction between (βt- α) even and odd.When the drag significantly exceeds the resonance forces, an approximate solution can be found in terms of Fresnel integrals. This shows that the inclination is almost equally likely to increase or decrease, and that the total change is proportional to (drag)${}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, i.e. to the time taken to pass through resonance.The effect offers a way of deriving gravity coefficients of medium order (e.g. m=15) from the observed magnitude and shape of the variation in inclination. The magnitudes of even higher order gravity coefficients obtained from some resonance with α=2 (e.g. $\text{29}\text{2}$) or even with α=3 (e.g. $\text{44}\text{3}$) might yield information on the depth of the sources of the high order gravity field.The effect is also of special interest in deriving upper-atmosphere mean winds from the changes in inclination of decaying satellite orbits since the satellite may pass through a strong resonance.     

Determination of magnetic field direction in a comet's head

The Stokes parameters of resonance radiation scattered by a Na atom with the angular momentum F aligned by directed unpolarized radiation in a magnetic field H ～ 10^?5?10^?1 Oe are presented. An influence of the orientation of the magnetic field on these parameters are studied; the intensity ratio $\text{I(D}{}_2\text{)}\text{I(D}{}_1\text{)}$ changes within ±5%, and the polarization degree P(D₂) within ±25%. Measurements of $\text{I(D}{}_2\text{)}\text{I(D}{}_1\text{)}$ and P(D₂), if the geometry of scattering is known, may give information on the direction of the magnetic field in the sodium atmospheres of comets, as well as Io's sodium cloud or man-made cosmic clouds.