The topography of Janus

A topographic model of Saturn's larger co-orbital satellite Janus was derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The model is presented here in tabular and graphic form, including the first detailed shaded relief maps of the satellite. The shape is approximated by a triaxial ellipsoid with axes of 196, 192 and 150 km. The volume is estimated to be 3.0 ± 0.5 × 10⁶ km³, leading to a density estimate of 0.67 ± 0.10 g/cm³. The surface is heavily cratered. Several possible crater chains of uncertain significance are observed, but few prominent linear ridges and no narrow grooves.     

The topography of Epimetheus

A topographic model of Saturn's smaller co-orbital satellite Epimetheus was derived from the shapes of limbs, terminators and shadows of the F Ring in Voyager images, modified locally to accommodate large craters and ridges. The model is presented here in tabular and graphic form, including the first detailed shaded relief maps of the satellite. The shape is approximated by a triaxial ellipsoid with axes of 144, 108 and 98 km. The volume is estimated to be 8 ± 1 × 10⁵ km³. A prominent valley and several grooves are found on the heavily cratered surface.     

The surfaces of Larissa and Proteus

Topographic models of Neptune's small inner satellites Larissa and Proteus were derived from the shapes of limbs and terminators in Voyager images, modified locally to accomodate large craters and ridges. The models are presented here in tabular and graphic form, including the first map of Larissa and the first detailed relief map of Proteus. The shape of Larissa is approximated by a triaxial ellipsoid with axes of 208, 192 and 178 km, but is only weakly constrained by the single available view. The volume is estimated to be 3.5 ± 1.0 × 10⁶ km³. The surface is heavily cratered and may be crossed by one or two poorly seen linear ridges. Proteus is approximated by a triaxial ellipsoid with axes of 424, 390 and 396 km (the latter being the rotation axis dimension). The volume is estimated to be 3.4 ± 0.4 × 10⁷ km³. Its surface appears to be very heavily cratered and extensive evidence for linear fractures is observed despite very low image quality.     

Density and stress distribution in the moon

A model is presented for the lateral variations of density within the Moon. The model gives rise to a gravitational potential which is equal to the observed potential at the lunar surface, moreover, it minimizes the total shear-strain energy of the Moon. The model exhibits lateral variations of about ±0.25 g cc^–1 within 50 km depth. The variations, however, reduce to ±0.06 and ±0.008 g cc^–1 within layers at 50–135 and 135–235 km respectively, and they become negligible below this region. The associated stress differences are found to be about 50 bar within 600 km depth, having their maximum values of about 90 bars at a depth of about 250 km. On the basis of these stress differences a strength of about 100 bar is concluded for the upper 400 km of the lunar interior for the last 3.3 b.y.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration. This paper is Lunar Science Institute Contribution No. 117.     

The cosmic distance scale

Summary The status of the cosmic distance scale problem in early 1989 is reviewed. Internally consistent distances to Local Group galaxies are given in Tables 5 and 6. Within the Local Group the distance scale is found to be 11±5% smaller than that previously adopted by Sandage and Tammann. Distances to nearby galaxies are used as stepping stones to the Virgo cluster. The interpretation of the Tully-Fisher observations of Virgo spirals is found to be ambiguous because it is not yet clear which spirals are cluster members and which are background objects. Distance estimates of the Virgo cluster obtained by different techniques are listed in Table 11. The distance modulus of the Virgo cluster is found to be 31.5±0.2, corresponding to a distance of 20±2 Mpc. The elliptical galaxies in the core of the Virgo cluster haveV ₀=1200±46 kms^–1, which corresponds toV _LG=1082±48 km s^–1. With an infall velocity of 250±50 km s^–1 this yields a cosmological redshiftV=1332±69 km s^–1, from which a Hubble parameter H₀=67±8 km s^–1 Mpc^–1 is obtained. Space Telescope observations of distant Cepheids, Tully-Fisher observations of spirals in the Hercules eluster, and interference filter observations of Virgo planetary nebulae in the light of [O_III], should soon result in a major improvement in the accuracy with which H₀ is known.     

On the CN (0, 0) spectrum of Comet Mrkos 1957d

We have carried out an analysis of the (0, 0) vibrational band of the CN molecule in Comet Mrkos 1957d, including the effect of collisions. We found that the sum of the squares of the residuals can be reduced by a factor of ten, if collisions account for 46±3% of the population of the lower level. A rotational temperature can be assigned to the cometary gas. The best value found was 410±40 K. The best fit for the constantR ₁ was (1.07±0.10)×10^–4. The velocity of the comet was left as a free parameter. We found for it a value of 34.38±0.10 km s^–1. This result is in disagreement with the nuclear orbital velocity of 34.74 km s^–1. The discrepancy can be explained, if the CN molecules are ejected from the cometary nucleus preferentially in the sunward direction, with a mean velocity that corresponds to the above temperature.     

The photospheric velocity field of Procyon

BUSS observations of the profiles of two well observed spectral lines in the ultraviolet spectrum of CMi (Procyon; F5 IV–V) are analysed with a Fourier transform method in order to determine values of various parameters of the velocity field of the upper photosphere. We find a microturbulent line-of-sight velocity componentL = 0.9 ± 0.4 km s^–1, a macroturbulent velocity componentL _M = 5.3 ± 0.2 km s^–1, and a rotational velocity componentv _R sini=10.0±1.2 km s^–1. In these calculations a single-moded sinusoidal isotropic macroturbulent velocity function was assumed. The result appears to be sensitive to the assumed shape of the macroturbulence function: for an assumed Gaussian shape the observations can be described withv _R sini=4 km s^–1 andL _M = 11.6 ± 2.7 km s^–1. A comparison is made with other results and theoretical predictions.     

Mass and density of Asteroid 121 Hermione from an analysis of its companion orbit

We report on Adaptive Optics observations of the satellite of Asteroid 121 Hermione with the ESO-Paranal UT4 VLT and the Keck AO telescopes. The binary system, belonging to the Cybele family, was observed during two observing campaigns in January 2003 and January 2004 aiming to confirm its trajectory and accurately determine its orbital elements. A precessing Keplerian model was used to describe the motion of S/2002 (121) 1. We find that the satellite of Hermione revolves at a=768±11 km from the primary in P=2.582±0.002 days with a roughly circular and prograde orbit (e=0.001±0.001, i=3±2° w.r.t. equator primary). These extensive astrometric measurements enable us to determine the mass of Hermione to be 0.54±0.03×¹⁰¹⁹ kg and its pole solution (λ₀=1.5°±2.00, β₀=10°±2.0 in ecliptic J2000). Additional Keck AO observations taken close to the asteroid opposition in December 2003 give us direct insight into the structure of the primary which presents a bilobated shape. Since the angular resolution is limited to the theoretical angular resolution of the telescope (43 mas corresponding to a spatial resolution of 80 km), two shape models (called snowman and peanut) are proposed based on the images which were deconvolved with MISTRAL deconvolution process. Assuming a purely synchronous orbit and knowing the mass of the primary, the peanut shape composed of two separated components is quite unlikely. Additionally the J₂ calculated from the analysis of the secondary orbit is not in agreement with the peanut model, but close to the snowman shape. The bulk density of the primary as derived from the observed size of the snowman shape is estimated to ρ∼1.8±0.2 g/cm³ implying a porosity ∼14% for this C-type asteroid, corresponding to a fractured asteroid. Considering the IRAS diameter, the density is lower (ρ=1.1±0.3 g/cm³) leading to a high porosity (p=30-60%) with a nominal value of p=48%, which indicates a completely loose rubble-pile structure for the primary. Further work is necessary to better constrain the size, shape, and then internal structure of Hermione's primary.     

The shapes and surface features of Prometheus and Pandora

Topographic models of Saturn's F-Ring shepherd satellites Prometheus and Pandora were derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The models are presented here in tabular and graphic form, including the first published maps of the satellites. The shape of Prometheus is approximated by a triaxial ellipsoid with axes of 145, 85 and 60 km. The volume is estimated to be 3.9 ± 1.0 × 10⁵ km³, significantly smaller than previous estimates. A system of prominent ridges and valleys cross the north polar region. Prometheus appears to be less heavily cratered than the other small satellites near the edge of the rings, though this may be an artifact of the low resolution of available images. Pandora is approximated by a triaxial ellipsoid with axes of 114, 84 and 62 km. The volume is estimated to be 3.1 ± 1.0 × 10⁵ km³. Its surface appears to be very heavily cratered.     

Figure of the double Asteroid 90 Antiope from adaptive optics and lightcurve observations

A long-term adaptive optics (AO) campaign of observing the double Asteroid (90) Antiope has been carried out in 2003-2005 using 8-10-m class telescopes, allowing prediction of the circumstances of mutual events occurring during the July 2005 opposition [Marchis, F., Descamps, P., Hestroffer, D., Berthier, J., de Pater, I., 2004. Bull. Am. Astron. Soc. 36, 1180]. This is the first opportunity to use complementary lightcurve and AO observations to extensively study the (90) Antiope system, an interesting visualized binary doublet system located in the main belt. The orbital parameters derived from the AO observations have served as input quantities for the derivation of a whole set of other physical parameters (namely shapes, surface scattering, bulk density, and internal properties) from analysis of collected lightcurves. To completely model the observed lightcurves, we employed Roche figures to construct an overall shape solution. The combination of these complementary observations has enabled us to derive a reliable physical and orbital solution for the system. Our model is consistent with a system of slightly non-spherical components, having a size ratio of 0.95 (with Ravg=42.9±0.5 km, separation=171±1 km), and exhibiting equilibrium figures for homogeneous rotating bodies. A comparison with grazing occultation event lightcurves suggests that the real shapes of the components do not depart from Roche equilibrium figures by more than 10%. The J2000 ecliptic coordinates of the pole of the system are λn=200°±2° and αn=38°±2°. The orbital period was refined to P=16.5051±0.0001 h, and the density is found to be slightly lower than previous determinations, with a value of 1.25±0.05 g/cm³, leading to a significant macro-porosity of 30%. Possible scenarios for the origin of the system are also discussed.     

The far UV spectrum of the Be star AX Monocerotis

In this paper we study the main features of the far UV spectrum of the binary star AX Mon, observed with the IUE satellite at phase 0.568.Ions indicating a large range of ionization stages, going fromCi,Oi,Ni toSiv,Civ,Nv are present.The spectrum is dominated by shell absorption lines of Feii, Feiii, Siiii,Cii, Alii, Mgii and Niii.Two satellite components are clearly indicated in all these lines except for Niii which presents only one. Their mean velocities are +10±5 km s^–1, –75±10 km s^–1, and –260±15 km s^–1.Red emission wings are observed in the Mgii resonant doublet at 2800 Å, which shows a P Cygni profile. Each of the absorption lines of the Mgii doublet is formed by a narrow component, which is blended with the Mgii interstellar line and a broad component, which shows a complex structure.Broad and asymmetrical profiles are observed for the Siiv,Civ, andNv resonance lines with blue edge velocities about –700±30 km s^–1.     

The strength of the lunar lithosphere

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m³ within the crustal layers, reducing rapidly to less than ±20 kg/m³ at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8-10 MPa within the lower lithosphere (150-270 km) of Model A and maximums of 12-16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.     

New optical measurements of planetary diameters— Part IV: Planet Mars

Optical measurements of the diameter of Mars were made using a double-image micrometer with large refractors from 1952 to 1971. Discussion of the 90 independent series of measurements gives nine determinations of radius with an accuracy of ±7–8km for different latitudes from pole to equator. The Mariner 4, 6 and 7 occultation results and the radar results availble in 1970 added seven further determinations of comparable accuracy. All these values, within the accuracy of measurement, fit an ellipsoid with R_eq=3398±3km and R_po1=3371±4km. The mean density of Mars is thus 3940±0.012g cm⁻³. The resulting optical oblateness of 0.0079, larger than the dynamical value of 0.0052, results in an equatorial radius excess of 9±5 km which presumably comes about by internal stresses.     

The application of a Bessel transform to the determination of stellar rotational velocities

A method for analysing line profiles by means of a transform using Bessel functions is described. This yields the stellar rotational velocityv sini, to an accuracy of about ±1 km s^–1 for rotational velocities greater than about 5 km s^–1, provided that rotation is the major source of line broadening. The theory of the method is a special case of a general theory of linear transforms in data analysis, which is outlined in an appendix.     

Direct measurement of the size, shape, and pole of 511 Davida with Keck AO in a single night

Using the high-quality data set of 165 images taken at 11 epochs over the 5.13 h rotation of the large C-type Asteroid 511 Davida, we find the dimensions of its triaxial ellipsoid model to be 357±2×294±2×231±50 km. The images were acquired with the adaptive optics system on the 10 m Keck II telescope on December 27, 2002. The a and b diameters are much better determined than previously estimated from speckle interferometry and indirect measurements, and our mean diameter, (abc)^1/3=289±21 km, is 19% below previous estimates. We find the pole to lie within 2° of [RA=295°; Dec=0°] or in Ecliptic coordinates [λ=297°; β=+21°], a significant improvement to the pole direction. Otherwise, previous determinations of the axial ratios agree with our new results. These observations illustrate that our technique of finding the dimensions and pole of an asteroid from its changing projected size and shape is very powerful because it can be done in essentially one night as opposed to decades of lightcurves. Average departures of 3% (5 km) of the asteroid's mean radius from a smooth outline are detected, with at least two local positive-relief features and at least one flat facet showing approximately 15 km deviations from the reference best-fit ellipsoid. The facet is reminiscent of large global-scale craters on Asteroid 253 Mathilde (also a C-type) when seen edge-on in close-up images from the NEAR mission flyby. We show that giant craters (up to 150 km diameter, the size of the largest facets seen on Davida) can be expected from the impactor size distribution, without likelihood of catastrophic disruption of Davida.     

A study of weak molecular and atomic lines in the photospheric spectrum

An attempt is made to detect the lines of Mg²⁵H and Mg²⁶H in the photospheric spectrum, using calculated isotope shifts. From comparisons with the Mg²⁴H lines of the ² –² transition in the (0, 0) band the ratios Mg²⁵/Mg²⁴ = 0.12 ± 0.04 and Mg²⁶/Mg²⁴ = 0.12 ± 0.02 are derived. These are essentially the same as the terrestrial ratios. The profile of one line of Mgi confirms these values.The wavelengths of MgH and C₂ lines, when corrected for the gravitational red shift, indicate that macroturbulent (or streaming) velocities die out near log ₀ = – 1.0. From the equivalent widths of the MgH lines a rotational temperature of 5132 ± 200 K is obtained and compared to predictions from various model atmospheres. The band oscillator strength is found to be 0.024 ± 0.002, in serious disagreement with the single laboratory determination.The profiles of MgH, C₂, CN and some weak atomic lines are used to derive the variation of the radial component of microturbulence with optical depth, on the assumption of streaming velocities of 2.5–3.0 km/sec. A slow increase with increasing height in the photosphere is found, over the range –1.5 < log₀< 0.2.The center-limb variation of the equivalent widths of MgH and C₂ lines for a wholly inhomogeneous model is found to be the same as for a model which is homogeneous above log ₀ = - 1.0. With such a model as the latter, the center-limb variation of the profiles of the selected molecular and atomic lines is moderately-well reproduced by an anisotropic microturbulent velocity with a tangential component of 3 km/sec which seems to be constant with height over the range considered.     

CN, C2 radicals and dust in Comets Shoemaker-Levy 1991 T2 and P/deVico 1995 S1

The results of the multiaperture photometry of Comet Shoemaker-Levy 1991 T2 in the pre-perihelion and P/deVico in the post-perihelion period with the narrowband CN, C₂ and Blue Continuum (BC) IHW filters are presented. A Haser model of the molecular coma was used for the determination of the parent and daughter scale-lengths and production rates of the radicals. The comets showed some substantial differences between their parent scale-lengths. The CN parent scale-length (at 1.0 AU) was 16×¹⁰³ km for Comet Shoemaker-Levy and 39×¹⁰³ for P/deVico, the C₂ parent scale-lengths were respectively 29×¹⁰³ and 54×¹⁰³ km. Such divergences could be interpreted in the frame of different scenarios of emission of cometary parents, either from a nucleus or from a volume source. The daughter scale-lengths for these comets were quite similar, namely: 306×¹⁰³ and 318×¹⁰³ km for CN and 69×¹⁰³ and 66×¹⁰³ km for C₂. We determined the Afρ parameter for apertures of different radii. A Monte Carlo model of the dust coma was used to obtain the dust ejection velocity. It was of the order of 0.1 km s⁻¹ for both comets. The power index of the distribution of the β-parameter of dust particles (ratio of light pressure to the solar gravitation) was of the order of 3 for C/Shoemaker-Levy and close to 2 for P/deVico. The dependence on heliocentric distance (rh) of the radical and dust production rates for P/deVico in the range of 0.7-1.0 AU was described by the power law function with a power index equal to: 5.55±0.14 for CN, 5.70±0.24 for C₂ and 5.22±0.19 for dust. Relative abundances of the dynamically new Comet Shoemaker-Levy and short-period P/deVico were quite similar with an enhancement of C₂ comparing with standard values taken from A'Hearn et al. (1995).     

Topography and geology of Hyperion

I have mapped the Saturnian satellite Hyperion using Voyager 2 images obtained in 1981 and a shape model derived from the results of Thomas et al. (1995). The results are presented in tabular and graphic form, including detailed shaded relief maps of the satellite. The shape is approximated by a triaxial ellipsoid with axes of 270, 201 and 336 km. The volume is estimated to be 9.5 ± 2.0 × 10⁶ km³. Geological interpretations were augmented by the use of super-resolution image composites. The surface is heavily cratered. A system of scarps and an isolated mountain are interpreted as the rim and central peak of an impact crater with a diameter similar to the mean diameter of the satellite itself, the largest crater with recognizable impact morphology in relation to the size of the body yet observed in the solar system. The crater density dates that impact, not the formation of Hyperion. Grooves are identified in several images, and form part of a zone of fracturing radial to a prominent crater.University of Western Ontario     

Bias-corrected population, size distribution, and impact hazard for the near-Earth objects

Utilizing the largest available data sets for the observed taxonomic (Binzel et al., 2004, Icarus 170, 259-294) and albedo (Delbo et al., 2003, Icarus 166, 116-130) distributions of the near-Earth object population, we model the bias-corrected population. Diameter-limited fractional abundances of the taxonomic complexes are A-0.2%; C-10%, D-17%, O-0.5%, Q-14%, R-0.1%, S-22%, U-0.4%, V-1%, X-34%. In a diameter-limited sample, ∼30% of the NEO population has jovian Tisserand parameter less than 3, where the D-types and X-types dominate. The large contribution from the X-types is surprising and highlights the need to better understand this group with more albedo measurements. Combining the C, D, and X complexes into a “dark” group and the others into a “bright” group yields a debiased dark-to-bright ratio of ∼1.6. Overall, the bias-corrected mean albedo for the NEO population is 0.14±0.02, for which an H magnitude of 17.8±0.1 translates to a diameter of 1 km, in close agreement with Morbidelli et al. (2002, Icarus 158 (2), 329-342). Coupling this bias corrected taxonomic and albedo model with the H magnitude dependent size distribution of (Stuart, 2001, Science 294, 1691-1693) yields a diameter distribution with 1090±180 NEOs with diameters larger than 1 km. As of 2004 June, the Spaceguard Survey has discovered 56% of the NEOs larger than 1 km. Using our size distribution model, and orbital distribution of (Stuart, 2001, Science 294, 1691-1693) we calculate the frequency of impacts into the Earth and the Moon. Globally destructive collisions (∼10²¹ J) of asteroids 1 km or larger strike the Earth once every 0.60±0.1 Myr on average. Regionally destructive collisions with impact energy greater than 4×10¹⁸ J (∼200 m diameter) strike the Earth every 56,000±6000 yr. Collisions in the range of the Tunguska event (4-8×10¹⁶ J) occur every 2000-3000 yr. These values represent the average time between randomly spaced impacts; actual impacts could occur more or less closely spaced solely by chance. As a verification of these impact rates, the crater production function of Shoemaker et al. (1990, Geological Society of American Special Paper 247) has been updated by combining this new population model with a crater formation model to find that the observed crater production function on both the Earth and Moon agrees with the rate of crater production expected from the current population of NEOs.     

New determination of the size and bulk density of the binary Asteroid 22 Kalliope from observations of mutual eclipses

In 2007, the M-type binary Asteroid 22 Kalliope reached one of its annual equinoxes. As a consequence, the orbit plane of its small moon, Linus, was aligned closely to the Sun's line of sight, giving rise to a mutual eclipse season. A dedicated international campaign of photometric observations, based on amateur-professional collaboration, was organized and coordinated by the IMCCE in order to catch several of these events. The set of the compiled observations is released in this work. We developed a relevant model of these events, including a topographic shape model of Kalliope refined in the present work, the orbit solution of Linus as well as the photometric effect of the shadow of one component falling on the other. By fitting this model to the only two full recorded events, we derived a new estimation of the equivalent diameter of Kalliope of 166.2±2.8 km, 8% smaller than its IRAS diameter. As to the diameter of Linus, considered as purely spherical, it is estimated to 28±2 km. This substantial “shortening” of Kalliope, gives a bulk density of 3.35±0.33 g/cm³, significantly higher than past determinations but more consistent with its taxonomic type. Some constraints can be inferred on the composition.