Recent radar observations of asteroid 1566 Icarus

We report Doppler-only radar observations of Icarus at Goldstone at a transmitter frequency of 8510 MHz (3.5 cm wavelength) during 8–10 June 1996, the first radar detection of the object since 1968. Optimally filtered and folded spectra achieve a maximum opposite-circular (OC) polarization signal-to-noise ratio of about 10 and help to constrain Icarus physical properties. We obtain an OC radar cross section of 0.05 km² (with a 35% uncertainty), which is less than values estimated by Goldstein, 1969and by Pettengill et al., 1969, and a circular polarization (SC⧸OC) ratio of 0.5±0.2. We analyze the echo power spectrum with a model incorporating the echo bandwidth B and a spectral shape parameter n, yielding a coupled constraint between B and n. We adopt 25 Hz as the lower bound on B, which gives a lower bound on the maximum pole-on breadth of about 0.6 km and upper bounds on the radar and optical albedos that are consistent with Icarus tentative QS classification. The observed circular polarization ratio indicates a very rough near-surface at spatial scales of the order of the radar wavelength.     

Saturn's rings: Particle composition and size distribution as constrained by microwave observations: I. Radar observations

We have calculated the radar backscattering characteristics of a variety of compositional and structural models of Saturn's rings and compared them with observations of the absolute value, wavelength dependence, and degree of depolarization of the rings' radar cross section (reflectivity). In the treatment of particles of size comparable to the wavelength of observation, allowance is made for the nonspherical shape of the particles by use of a new semiempirical theory based on laboratory experiments and simple physical principles to describe the particles' single scattering behavior. The doubling method is used to calculate reflectivities for systems that are many particles thick using optical depths derived from observations at visible wavelengths. If the rings are many particles thick, irregular centimeter- to meter-sized particles composed primarily of water ice attain sufficiently high albedos and scattering efficiencies to explain the radar observations. In that case, the wavelength independence of radar reflectivity implies the existence of a broad particle size distribution that is well characterized over the range 1 cm ? r ? m by n(r)dr = n₀r^?3dr. A narrower size distribution with $\text{a}\text{～ 6}\text{cm}$ is also a possibility. Particles of primarily silicate composition are ruled out by the radar observations. Purely metallic particles, either in the above size range and distributed within a many-particle-thick layer or very much larger in size and restricted to a monolayer, may not be ruled out on the basis of existing radar observations. A monolayer of very large ice “particle” that exhibit multiple internal scattering may not yet be ruled out. Observations of the variation of radar reflectivity with the opening angle of the rings will permit further discrimination between ring models that are many particles thick and ring models that are one “particle” thick.     

The rings of Saturn: Two-frequency radar observations

Observations of 3.5- and 12.6-cm radar echoes from the rings of Saturn suggest that no significant difference in scattering properties exists in this wavelength interval. The echoes are largely unpolarized at both wavelengths, and yield a radar cross section at 3.5 cm of 7.32 ± 0.84 × 10⁹ km² for each polarization. The combined radar cross sections for both polarizations correspond to 1.37 ± 0.16 times the optically observed projected A- and B-ring areas (excluding that part of the rings shadowed by the planet). The shape of the echo spectrum is compatible with a homogeneous ring scattering model, except in having excess power at frequencies near the center of the spectrum. A number of possible explanations for the observed scattering properties are explored.     

70-cm radar observations of 433 Eros

Radar observations of 433 Eros were made at the Arecibo Observatory using a wavelength of 70 cm during the close approach of Eros to Earth in mid-January, 1975. A peak radar cross section of 39 ± 15 km² was observed. The spectral broadening obtained was approximately 30 Hz, which is consistent with a value of 16 km for the maximum radius of the asteroid. The surface of Eros appears to be relatively rough at the scale of a wavelength as compared to the surfaces of the terrestrial planets and the Moon. The composition of the surface is not well determined, except that it cannot be a highly conducting metal. A single measurement each of round-trip echo times delay and doppler shift was made.     

Radar observations of asteroid 1580 Betulia

Radar observations of the asteroid 1580 Betulia, made at a wavelength of 12.6 cm, show a mean radar cross section of 2.2 ± 0.8 km² and a total spectral bandwidth of 26.5 ± 1.5 Hz. Combining our bandwidth measurements with the optically determined rotation period sets a lower limit to the asteroid's radius of 2.9 ± 0.2 km.     

Radar detectability of asteroids: A survey of opportunities for 1977 through 1987

The capability of Earth-based radar to study asteroids is assessed with respect to determining the number of detectible objects and the number of detectable events during the next 10 years. Bar graphs have been prepared showing the number of events and objects falling into 5-db detectability slots based both on estimates of minimum distance and on direct calculations using known orbital elements. These indicate that the Goldstone radar system operating at 3.5-cm wavelength should be able to detect roughly 18 different asteroids at 34 favorable opportunities during the next 10 years. The Arecibo radar system operating at 12.5-cm wavelength may be able to detect 60 asteroids at approximately 97 favorable opportunities in the 10-year period. This sample is sufficiently large that classification of types and correlation with optical data should be possible. The detectability margin for many objects should be large enough to permit more refined analysis of the radar spectrograms. Estimates of the average surface roughness, rotation rate, and direction of the polar axis, as well as estimates of range and Doppler frequency offsets, which can be used to refine the orbital elements, should be otainable for many objects. Equations are given which indicate the variances expected for measurements of cross section, center frequency, and bandwidth measured either singly or jointly. These are functions of the noise-to-signal ratio and other physical parameters such as the backscattering law. Curves are given based on backscattering functions of the form cosⁿθ.     

Radar detection of Vesta

Asteroid 4 Vesta was detected on 1979 November 6 with the Arecibo Observatory's S-band (12.6-cm-wavelength) radar. The echo power spectrum, received in the circular polarization opposite to that transmmited,, yields a radar cross section of (0.2 ± 0.1)πa², for a = 272 km. The data are too noisy to permit derivation of Vesta's rotation period.     

Radar studies of the Martian surface at centimeter wavelengths: The 1975 opposition

The Goldstone radar system was operated at wavelengths of 3.5 and 12.6 cm to probe the Martian surface during the 1975 opposition. Regions studied in detail by range-Doppler techniques are Syrtis Major, Sinus Meridiani, and the crater Schiaparelli. Average rms slopes of 1.6° and 1.1° were measured in Syrtis Major at 3.5 and 12.6 cm, respectively, while the average reflectivity was 0.064 ± 0.02 at both wavelengths. No wavelength dependence of surface roughness was seen in Sinus Meridiani, where rms surface slopes averaged 1.8° and the reflectivity was 0.08 ± 0.02. The regions around Schiaparelli were probed at a 12.6-cm wavelength. The echo from the bottom of the crater was undetectable. Hence _ρ0C < 25, where _ρ0 is the reflectivity and C is the Hagfors roughness parameter. Operating at 3.5 cm during May and June of 1976, 149 continous-wave echo spectra were obtained near latitude 18°, sampling most longitudes including the early Viking landing sites A1 and A2. The average total radar cross section is 4.8% of the geometrical cross section. The diffuse component was estimated to be 1.9%, leaving 2.9% to the average quasi-specular component. The average rms slope is 4.1°. Six spectra obtained at site A1 indicate that rms slopes are 5 to 9° between latitudes 17 and 19°. Three spectra obtained at s site A2 indicate an rms slope of 3.9°.     

Upper limit on the radar cross section of the comet Kohoutek

An attempt to observe radar echoes from the comet Kohoutek was made at a radio frequency of 7840 MHz (λ ～- 3.8 cm) on 12 January 1974 using the Haystack Observatory radar in Massachusetts. A search for an echo over a range of band-widths covering 2Hz to 66kHz yielded no positive result. The upper limit on the radar cross section is therefore approximately $\text{10}{}^4\text{B}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{km}{}^2$, where B is the (unknown) bandwidth of the echo in Hertz. For $\text{B ? 100}\text{Hz}$, it follows that (i) the nucleus, if a perfect spherical reflector, must be less than 250 km in diameter, and (ii) the density of any millimeter-sized particles must be less than 1m^?3 for a coma of diameter 10⁴km.     

Radar detection of Asteroid 2002 AA29

Radar echoes from Earth co-orbital Asteroid 2002 AA29 yield a total-power radar cross section of 2.9×10⁻⁵ km² ±25%, a circular polarization ratio of SC/OC=0.26±0.07, and an echo bandwidth of at least 1.5 Hz. Combining these results with the estimate of its visual absolute magnitude, H_V=25.23±0.24, from reported Spacewatch photometry indicates an effective diameter of 25±5 m, a rotation period no longer than 33 min, and an average surface bulk density no larger than 2.0 g cm⁻³; the asteroid is radar dark and optically bright, and its statistically most likely spectral class is S. The H_V estimate from LINEAR photometry (23.58±0.38) is not compatible with either Spacewatch's H_V or our radar results. If a bias this large were generally present in LINEAR's estimates of H_V for asteroids it has discovered or observed, then estimates of the current completeness of the Spaceguard Survey would have to be revised downward.     

High resolution absorption cross section measurements of SO2 at 213 K in the wavelength region 172–240 nm

Laboratory measurements at high resolution of the absorption cross section of SO₂ at the temperature 213 K have been performed in the wavelength region 172–240 nm with a 6.65 m scanning spectrometer/spectrograph operated at an instrumental width of 0.002 nm. The measured cross sections are presented graphically in representative wavelength regions and are available throughout the region 172–240 nm at wavenumber intervals of 0.4–0.1 cm^?1 as a numerical tabulation stored on magnetic tape from the National Space Science Data Center, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A. The measured cross sections, which are relevant to the photochemistry of planetary atmospheres, possess significantly more spectroscopic structure, and are more accurate, than previous measurements made at lower resolution.     

Ceres’ spectral link to carbonaceous chondrites—Analysis of the dark background materials

Ceres’ surface has commonly been linked with carbonaceous chondrites (CCs) by ground‐based telescopic observations, because of its low albedo, flat to red‐sloped spectra in the visible and near‐infrared (VIS/NIR) wavelength region, and the absence of distinct absorption bands, though no currently known meteorites provide complete spectral matches to Ceres. Spatially resolved data of the Dawn Framing Camera (FC) reveal a generally dark surface covered with bright spots exhibiting reflectance values several times higher than Ceres’ background. In this work, we investigated FC data from High Altitude Mapping Orbit (HAMO) and Ceres eXtended Juling (CXJ) orbit (~140 m/pixel) for global spectral variations. We found that the cerean surface mainly differs by spectral slope over the whole FC wavelength region (0.4–1.0 μm). Areas exhibiting slopes ?1 constitute only ~3% of the cerean surface and mainly occur in the bright material in and around young craters, whereas slopes ≥?10% μm^?1 occur on more than 90% of the cerean surface; the latter being denoted as Ceres’ background material in this work. FC and Visible and Infrared Spectrometer (VIR) spectra of this background material were compared to the suite of CCs spectrally investigated so far regarding their VIS/NIR region and 2.7 μm absorption, as well as their reflectance at 0.653 μm. This resulted in a good match to heated CI Ivuna (heated to 200–300 °C) and a better match for CM1 meteorites, especially Moapa Valley. This possibly indicates that the alteration of CM2 to CM1 took place on Ceres.     

Theory of radio occultation by Saturn's rings

The radio occultation technique is developed here as a new method for the study of the physical properties of planetary ring systems. Particular reference is made to geometrical and system characteristics of the Voyager dual-wavelength (13 and 3.6 cm) experiment at Saturn. The rings are studied based on the perturbations they introduce in the spectrum of coherent sinusoidal radio signals transmitted through the rings from a spacecraft in the vicinity of the planet to Earth. Two separate signal components are identified in a perturbed spectrum: a sinusoidal component that remains coherent with the incident signal but is reduced in intensity and possibly changed in phase, and a Doppler-broadened incoherent component whose spectral shape and strength are determined by the occultation geometry and the radial variation of the near-forward radar cross section of illuminated ringlets. Both components are derived in terms of the physical ring properties starting from a conventional radar formulation of the problem of single scattering on ensembles of discrete scatterers, which is then generalized to include near-forward multiple scattering. The latter is accomplished through special solutions of the equation of transfer for particles that are larger than the wavelength. When the occultation geometry is optimized, contributions of an individual ringlet to a perturbed spectrum can be identified with radial resolution on the order of a few kilometers for the coherent component and a few hundred kilometers for the incoherent one, thus permitting high-resolution reconstruction of the radial profile of the optical depth, as well as reconstruction of the radar cross section of resolved ringlets. Simultaneous estimates of the optical depth and radar cross section of a ringlet at 3.6 cm-gl allow separation of its aerial density and particle size, if the particles are of known material and form a narrow size distibution with radii greater than several tens of centimeters. This separation is also achieved for radii ?10 cm from differential effects on the coherent signal parameters at 3.6- and 13-cm wavelengths. For the more general case of a broad size distribution modeled by a power law, the absence of differential effects on the coherent signal binds the minimum size to be ?10 cm. In this case, the radius inferred from an estimate of the radar cross section represents an equivalent radius, which is strongly controlled by the maximum size of the distribution provided that the power index is in the range 3 to 4. On the other hand, detection of differential coherent signal extinction determines an upper bound on the maximum size and a lower bound on the power index, assuming water-ice particles. These bounds, together with an inferred equivalent size, constrain the size distribution at both its small and large ends.     

Radar measurements of Mercury’s north pole at 70 cm wavelength

We present radar imaging of Mercury using the Arecibo Observatory’s 70-cm wavelength radar system during the inferior conjunction of July 1999. At that time the sub-Earth latitude was ∼11°N and the highly reflective region at Mercury’s north pole that was first identified in radar images at the shorter wavelengths of 3.6 cm [Slade, M.A., Butler, B.J., Muhleman, D.O., 1992. Science 258, 635-640] and 13 cm [Harmon, J.K., Slade, M.A., 1992. Science 258, 640-643] was again clearly detected. The reflectivity averaged over a 75,000 km² region including the pole is similar to that measured at the other wavelengths over a comparable area, and the 70 cm circular polarization ratio of μ_C∼0.87 is possibly slightly lower. If this strong backscattering results from volume scattering in low absorption layers, the persistence of this effect over more than an order of magnitude change in wavelength scale has implications for the depth and thickness of the deposits responsible. The resolution of the radar maps at this wavelength is not sufficient to resolve individual craters, nor to discern features at other latitudes, but the planet’s total reflectivity is consistent with previous work and the scattering function suggests a surface roughness at this wavelength similar to the lunar highlands.     

Radar and photoelectric observations of asteroid 2100 Ra-Shalom

Results of 13-cm-wavelength radar observations and V-filter photoelectric observations of Ra- Shalom during its 1981 Aug–Sep apparition are reported. The radar data yid detections of echoes in the same sense of circular polarization as transmitted (i.e., the SC sense) as well as in the opposite (OC) sense. The estimate of the ratio of SC to OC echo power, μ_c = 0.14 ± 0.02, indicates that most, but certainly not all, of the backscattering is due to single reflections from surface elements that are fairly smooth at decimeter scales. The value obtained for the OC radar cross section on Aug 26 (1.2 ± 0.3 km²) is about three times larger than those obtained on Aug 23, 24, and 25. The echo bandwidth appears to be within about 1.5 Hz of 5.0 Hz on each date. The photoelectric data suggest a value, P_syn = 19.79 hr, for the synodic rotation period, and yield a composite lightcurve with two pairs of extrema. Combining this value for P_syn with a firm lower bound (4 Hz) on the maximum echo bandwidth yields a lower bound of 1.4 km on the maximum distance between Ra-Shalom's spin axis and any point on its surface.     

Effective field theory calculation of two-deuteron radiative capture reaction at astrophysical energies

Two-deuteron radiative capture reaction is one of the deuterium-burning processes that the cross section is not well known at very low-energies. We develop the formalism based on pionless Effective Field Theory (EFT) for deuteron–deuteron (dd) scattering to derive the cross section of two-deuteron radiative capture. Within this formalism the two- and three-body forces, should also be included in the capture cross section calculations. The aim of the present work is to calculate the observables of the low-energy dd photonuclear reactions. The cross section and the astrophysical S-factor for the ²H(d,γ)⁴He reaction have been calculated. The ⁴He is studied as four-body bound states in the pionless EFT. The theoretical uncertainties for observables are estimated based on the variation of the cutoffs. The astrophysical S-factor is accurately determined to be 6.9×10^?6 keV?b (6.1×10^?6 keV?b) for two-body (two- and three-body) at zero energy. A satisfactory agreement between theory and experiment for dd radiative capture observables up to order of calculation has been found by insertion of three-body force.     

Generation and emplacement of fine-grained ejecta in planetary impacts

We report here on a survey of distal fine-grained ejecta deposits on the Moon, Mars, and Venus. On all three planets, fine-grained ejecta form circular haloes that extend beyond the continuous ejecta and other types of distal deposits such as run-out lobes or ramparts. Using Earth-based radar images, we find that lunar fine-grained ejecta haloes represent meters-thick deposits with abrupt margins, and are depleted in rocks ?1 cm in diameter. Martian haloes show low nighttime thermal IR temperatures and thermal inertia, indicating the presence of fine particles estimated to range from ∼10 μm to 10 mm. Using the large sample sizes afforded by global datasets for Venus and Mars, and a complete nearside radar map for the Moon, we establish statistically robust scaling relationships between crater radius R and fine-grained ejecta run-out r^* for all three planets. On the Moon, r^* ∼ R^−0.18 for craters 5-640 km in diameter. For Venus, radar-dark haloes are larger than those on the Moon, but scale as r^* ∼ R^−0.49, consistent with ejecta entrainment in Venus’ dense atmosphere. On Mars, fine-ejecta haloes are larger than lunar haloes for a given crater size, indicating entrainment of ejecta by the atmosphere or vaporized subsurface volatiles, but scale as R^−0.13, similar to the ballistic lunar scaling. Ejecta suspension in vortices generated by passage of the ejecta curtain is predicted to result in ejecta run-out that scales with crater size as R^1/2, and the wind speeds so generated may be insufficient to transport particles at the larger end of the calculated range. The observed scaling and morphology of the low-temperature haloes leads us rather to favor winds generated by early-stage vapor plume expansion as the emplacement mechanism for low-temperature halo materials.     

Radar observations of asteroid 1999 JM8

Abstract— We report results of delay‐Doppler observations of 1999 JM8 with the Goldstone 8560 MHz (3.5 cm) and Arecibo 2380 MHz (13 cm) radars over 18 days in July‐August 1999. The images place thousands of pixels on the asteroid and achieve range resolutions as fine as 15 m/pixel. The images reveal an asymmetric, irregularly shaped object with a typical overall dimension within 20% of 7 km. If we assume that 1999 JM8's effective diameter is 7 km, then the absolute magnitude, 15.15, and the average Goldstone radar cross section, 2.49 km², correspond to optical and radar albedos of 0.02 and 0.06, establishing that 1999 JM8 is a dark object at optical and radar wavelengths. The asteroid is in a non‐principal axis spin state that, although not yet well determined, has a dominant periodicity of ?7 days. However, images obtained between July 31 and August 9 show apparent regular rotation of features from day to day, suggesting that the rotation state is not far from principal axis rotation. 1999 JM8 has regions of pronounced topographic relief, prominent facets several kilometers in extent, numerous crater‐like features between ?100 m and 1.5 km in diameter, and features whose structural nature is peculiar. Arecibo images provide the strongest evidence to date for a circular polarization ratio feature on any asteroid. Combined optical and radar observations from April 1990 to December 2000 permit computation of planetary close approach times to within ± 10 days over the interval from 293 to at least 2907, one of the longest spans for any potentially hazardous asteroid. Integration of the orbit into the past and future shows close approaches to Earth, Mars, Ceres, and Vesta, but the probability of the object impacting Earth is zero for at least the next nine centuries.     

On the dissociation of nitrogen by electron impact and by E.U.V. photo-absorption

The dissociation of N₂ by electron impact and by e.u.v. photo-absorption is studied, and it is shown that the forbidden predissociation of the numerous ¹Π_u and ¹Σ_u⁺ valence and Rydberg states of N₂ in the 11–24eV energy range is the dominant mechanism for N atom production. By measuring the absolute emission cross sections for the e.u.v. singlet bands of N₂ and by using the generalized oscillator strength data of Lassettre (1974), it has been possible to construct a detailed model of the total N₂ dissociation cross section which is in good agreement with the measurements of Winters (1966) and Niehaus (1967) and provides some insights into the maximum possible $\text{N(}{}^2\text{D)}$ yield from dissociative excitation. The total cross section for exciting N₂ e.u.v. radiation in the 800Å–1100Å wavelength range has been measured and found to have a value of 3.4 ×10^?17 cm² at 100 eV under optically thin conditions. Although this result implies that large fluxes of e.u.v. photons should be excited in auroral substorms and in the airglow, they are not observed, and we show that this development is a consequence of radiation entrapment and predissociation. The total cross section for dissociating N₂ by electron impact is given for optically thin and thick media. And some questions concerning the energy budget of a magnetospheric storm which are raised by these results, are discussed.     

Plasmatrough ion mass densities determined from ULF pulsation eigenperiods

Auroral radar studies of ULF pulsations have proved useful in determining the spatial characteristics of resonant oscillations. A particular class of ringing or transient pulsations has been identified in the radar data as toroidal mode eigenoscillations. We have considered a total of 64 events of this type recorded by either the STARE radar in Scandinavia, or the Slope Point radar in New Zealand, giving a combined latitudinal coverage of approx. 12°. These events are interpreted as toroidal mode eigenoscillations; the periods for individual events and the mean periods increase with geomagnetic latitude. Use of hydromagnetic resonance theory allows the equatorial ion mass density to be determined. The densities obtained are appropriate to the plasmatrough and range from ～ 10 to 100 a.m.u. cm^?3 near geosynchronous orbit. The radial variation in the equatorial plane is typically R^?5 in the midnight-noon sector and R^?3 in the noon-midnight sector. To reconcile these pulsation periods with in situ electron density measurements implies that H⁺ ion densities in the range ～ 1–10 cm^?3 and ～50% O⁺ ions are required.