The photometric functions of Phobos and Deimos I. Disc-integrated photometry

We have used the integrated brightnesses from Mariner 9 high-resolution images to determine the large phase angle (20° to 80°) phase curves of Phobos and Deimos. The derived phase coefficients are β = 0.032 ± 0.001 mag/deg for Phobos and β = 0.030 ± 0.001 mag/deg for Deimos, while the corresponding phase integrals are q_Phobos = 0.52 and q_Deimos = 0.57. The predicted intrinsic phase coefficients of the surface material are β_i = 0.019 mag/deg and β_i = 0.017 mag/deg for Phobos and Deimos, respectively. The phase curves, phase coefficients and phase integrals are typical of objects whose surface layers are dark and intricate in texture, and are consistent with the presence of a regolith on both satellites. The relative reflectance of Deimos to Phobos is 1.15±0.10. The presence of several bright patches on Deimos could account for this slight difference in average reflectance.     

The photometric functions of Phobos and Deimos. III. Surface photometry of Phobos

At least three large areas on the surface of Phobos are covered by a dark material of complex texture which scatters light according to the Hapke-Irvine Law. The average 20° to 80° intrinsic and disc-integrated phase coefficients of this material are β_i = 0.020 ± 0.001 mag/deg and β = 0.033 mag/deg, respectively. These values are slightly greater than the values found for Deimos in Paper II (preceding article). On the largest scale the surface of Phobos is rougher than the surface of Deimos, perhaps accounting for the slightly greater phase coefficients. Contrary to the situation on Deimos, no definite regions of intrinsically brighter material are apparent on Phobos. This difference could account for the slightly lower average reflectance of Phobos relative to Deimos. No evidence for large exposures of solid rock has been found in the three areas studied.     

Photometric properties of the Martian satellites

New photoelectric observations yield V(1, α) = 12.95 + 0.036 α ± 0.05, BV = 0.65 ± 0.03, and UB = 0.18 ± 0.03 for Deimos and V(1, 0) = 11.9 ± 0.2 for Phobos. The derived geometric albedos of both satellites are near 0.065. Combined photometric and polarimetric results lead to the conclusion that the satellites have dusty surfaces and are possibly basaltic but more likely carbonaceous in composition.     

Secular acceleration of Phobos and Q of Mars

Reductions of Mariner 9 TV data of Phobos and Deimos tend to corroborate the existence of a secular acceleration of Phobos commensurate with two recently reported values based on a reprocessing of Earth-based data. These values of secular acceleration have been used together with Mariner 9 data on the physical size of Phobos and Earth-based photoelectric observations which infer a carbonaceous composition for Phobos to place bounds of 50 < Q < 150 on the tidal dissipation function of Mars. The corresponding bounds on the tidal lag angle are 0.19° < Φ < 0.57°.     

Phobos,Deimos, and the Moon: Size and distribution of crater ejecta blocks

The size and radial distributions of ejecta blocks around craters (D = 0.8 to 10 km) on Phobos and Deimos have been compared to those around lunar craters (D = 0.2 to 3.5 km). The radial distribution of blocks was found to be similar on Phobos and the Moon, but more dispersed on Deimos. For the best imaged crater on Deimos (D = 800 m), the size distributions of blocks and the fraction of excavated volume present as blocks are similar to those on the Moon. The wider dispersal of blocks on Deimos is consistent with other findings on the spread of finer ejecta over the satellite.     

Near-Infrared Spectrophotometry of Phobos and Deimos

We have observed the leading and trailing hemispheres of Phobos from 1.65 to 3.5 μm and Deimos from 1.65 to 3.12 μm near opposition. We find the trailing hemisphere of Phobos to be brighter than its leading hemisphere by 0.24±0.06 magnitude at 1.65 μm and brighter than Deimos by 0.98±0.07 magnitude at 1.65 μm. We see no difference larger than observational uncertainties in spectral slope between the leading and trailing hemispheres when the spectra are normalized to 1.65 μm. We find no 3-μm absorption feature due to hydrated minerals on either hemisphere to a level of ∼5-10% on Phobos and ∼20% on Deimos. When the infrared data are joined to visible and near-IR data obtained by previous workers, our data suggest the leading (Stickney-dominated) side of Phobos is best matched by T-class asteroids. The spectral slope of the trailing side of Phobos and leading side of Deimos are bracketed by the D-class asteroids. The best laboratory spectral matches to these parts of Phobos are mature lunar soils and heated carbonaceous chondrites. The lack of 3-μm absorption features on either side of Phobos argues against the presence of a large interior reservoir of water ice according to current models of Phobos' interior (F. P. Fanale and J. R. Salvail 1989, Geophys. Res. Lett.16, 287-290; Icarus88, 380-395).     

The motion of the Martian satellites

An extensive analysis of the motion of Phobos and Deimos from 1877 to 1973 has been fulfilled. The new values of the parameters of the orbital model first developed by Struve have been determined for both satellites. The new sets of the orbital parameters compete with the solutions of similar accuracy found by Wilkins and Sinclair. A secular acceleration in longitude of Phobos is found to be equal to +(0.107±0.011)×10^?7 deg day^?2. The value of the acceleration is little affected when one or another group of oppositions is omitted. The acceleration of Deimos is determined with great uncertainty: +(0.06±0.34)×10^?9 deg day^?2. Values found for the orbital parameters seem to be in good agreement since the mass, oblateness and coordinates of the pole of Mars inferred from the motion of each satellite have similar values in both cases.     

An analysis of Martian satellite photographic observations of 1967

Photographic observations of the Martian satellites were made at the opposition of 1967 with the Naval Observatory's 61-inch astrometric reflector. A small partially transparent metallic film filter was used to diminish the light from Mars in order that a measurable image for the planetary disk as well as for the satellites could be obtained. The plates were reduced by the method of plate constants using positions for the faint background stars determined from astrographic field plates. The random mean error of these observations was estimated to be not greater than ±0″.10.The main result of the orbital adjustment is a +2° correction to the zero of mean longitude for Phobos. This confirms the findings of Wilkins (1970) and is compatible with the results of the Mariner 9 observations. The scale of the orbits of both satellites gave accordant values for the mass of Mars and the combined value of 30 99 500 ± 2800 (m.e.) is in good agreement with modern determinations.The mean error for Deimos derived from the residuals after solution is ±0″.11, which agrees well with the observational error and indicates no large systematic error in either the theory or the observations. For Phobos, however, the residual error, ±0″.19, is twice the expected observational error. The implications of this discrepancy are discussed.     

Tidal rigidity of phobos

The Martian satellites Phobos and Deimos move along nearly circular coplanar, stable orbits and have created surfaces older than ～ 10⁹ years. The accretion hypothesis suggests that their primordial orbits were also very regular. However, tides raised on Mars and Phobos can substantially alter the semimajor axis a of Phobos' orbit over time. The effect of the Martian tidal torque alone on Phobos' orbit implies that the primordial e was ～0.1 to 0.2 about 4.6 × 10⁹ years ago if the present observed e = 0.015 is naively interpreted as a tidally damped remnant. Significant tidal friction in Phobos reduces the time scale for Phobos to achieve a crossing orbit with Deimos to less than 10⁹ years and permits the primodial e to approach unity. The consequences of orbital intersections cannot easily be resolved by assuming either a catastrophic origin for both satellites (namely, that both are fragments of a common parent body fractured by an impact) or that they were captured sequentially by Mars. Either hypothesis is difficult to accept, given that Deimos' orbit, which is only slightly affected by tides, is now so regular. An alternative scenario is proposed in this paper in which the observed e of Phobos results from several gravitational resonance excitations within the last 10⁹ years, assuming tidal friction in Phobos has had only a small effect on its orbit. In facr, both the primordial e and the inclination i may have been much smaller than presently observed. The constraints imposed on tidal friction in Phobos by both the apparent age of Phobos' surface (> 10⁹yrs) and the above scenario can be satisfied only of μQ > 10¹²dynes/cm². Since the Q factor is ～10², the rigidity μ > 10¹⁰dynes/cm². Thus Phobos should have substantial internal strength.     

A deep search for Martian dust rings and inner moons using the Hubble Space Telescope

It has long been suspected that Mars might be encircled by two faint rings, one originating from each of its moons Phobos and Deimos. Meteoroid impacts into these moons should release clouds of dust that quickly spread out to become rings; similar dust rings have been associated with several small inner moons of the gas giants. On May 28, 2001 Mars’ hypothetical ring plane appeared edge-on to Earth within weeks of its opposition, providing the best Earth-based opportunity to detect these rings in several decades. Using the Wide Field/Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we obtained a set of deep exposures off the east and west limbs of Mars to search for these hypothetical rings. No rings were detected. This result limits normal optical depths to ∼3×10⁻⁸ for the Phobos ring and ∼10⁻⁷ for the Deimos ring. These limits fall at the low end of prior dynamical predictions and a factor of 1000 below previous observational limits. However, our limit for the Deimos ring is more tentative because of large uncertainties about this ring's expected shape, size and orientation. Our data set is also sensitive to small, previously undetected inner moons. No moons were detected down to a radius limit of 75–125 m. Longitudinal coverage of the region near and between Phobos and Deimos is 40–80% complete. We conclude by describing a promising opportunity for further Martian ring viewing in December 2007.     

GETEMME—a mission to explore the Martian satellites and the fundamentals of solar system physics

GETEMME (Gravity, Einstein??s Theory, and Exploration of the Martian Moons?? Environment), a mission which is being proposed in ESA??s Cosmic Vision program, shall be launched for Mars on a Soyuz Fregat in 2020. The spacecraft will initially rendezvous with Phobos and Deimos in order to carry out a comprehensive mapping and characterization of the two satellites and to deploy passive Laser retro-reflectors on their surfaces. In the second stage of the mission, the spacecraft will be transferred into a lower 1500-km Mars orbit, to carry out routine Laser range measurements to the reflectors on Phobos and Deimos. Also, asynchronous two-way Laser ranging measurements between the spacecraft and stations of the ILRS (International Laser Ranging Service) on Earth are foreseen. An onboard accelerometer will ensure a high accuracy for the spacecraft orbit determination. The inversion of all range and accelerometer data will allow us to determine or improve dramatically on a host of dynamic parameters of the Martian satellite system. From the complex motion and rotation of Phobos and Deimos we will obtain clues on internal structures and the origins of the satellites. Also, crucial data on the time-varying gravity field of Mars related to climate variation and internal structure will be obtained. Ranging measurements will also be essential to improve on several parameters in fundamental physics, such as the Post-Newtonian parameter ?? as well as time-rate changes of the gravitational constant and the Lense-Thirring effect. Measurements by GETEMME will firmly embed Mars and its satellites into the Solar System reference frame.     

Speckle interferometry of asteroids: III. 511 Davida and its photometry

511 Davida was observed with the technique of speckle interferometry at Steward Observatory's 2.3-m telescope on May 3, 1982. Assuming Davida to be a featureless triaxial ellipsoid, based on five 7-min observations its triaxial ellipsoid dimensions and standard deviations were found to be (465 ± 90) × (358 ± 58) × (258 ± 356) km. This shape is close to an equilibrium figure (a gravitationally shaped “rubble pile?”) suggesting a density of 1.4 ± 0.4 g/cm³. Simultaneously with the triaxial solution for the size and shape of Davida, we found its north rotational pole to lie within 29° of RA = 19^h08^m, Dec = +15° (λ = 291°, β = +37°). If Davida is assumed to be a prolate biaxial ellipsoid, then its dimensions were found to be (512 ± 100) × (334 ± 39) km, with a north pole within 16° of RA = 10^h52^m, Dec = +16° (λ = 322°, β = +32°). We derive and apply to Davida a new simultaneous amplitude-magnitude (SAM)-aspect method, finding, from photometric data only, axial ratios of a/b = 1.25 ± .02, b/c = 1.14 ± .03, and a rotational pole within 4° of λ = 307°, β = +32°. We also derive a (weighted) linearized form of the amplitude-aspect relation to obtain axial ratios and a pole. However, amplitudes must be known to better than .01 if the b/c or a/c ratios are desired to better than 10%. Combining the speckle and SAM results, we find for the Gehrels and Tedesco phase function a geometric albedo of .033 ± .009 and for the Lumme and Bowell function .041 ± .011, for a unified model of 437 × 350 × 307 km. Differences between the photometric and speckle axial ratios and poles are probably due to the effects of albedo structure over the asteroid; details on individual lightcurves support this conclusion.     

The photometric functions of Phobos and Deimos. II. Surface photometry of Deimos

To a good approximation the face of Deimos observed by Mariner 9 is covered uniformly by a dark, texturally complex material obeying a Hapke-Irvine scattering law. The intrinsic 20° to 80° phase coefficient of this material is β_i = 0.017 ± 0.001 mag/deg, corresponding to a disc-integrated value of β = 0.030 mag/deg. There is also evidence of a slightly brighter (by ～30%) unit near some craters which may have been produced by the cratering events. Its texture appears to be identical to that of the average material. No evidence of quasi-specular reflection has been found, suggesting that large-scale exposures of unpulverized rock are absent.     

Surface features of Phobos and Deimos

Viking Orbiter images have provided nearly complete coverage of the two satellites of Mars and have been used to construct maps of the surface features of Phobos and Deimos. The satellites have radically different appearances although nearly all features on both objects were formed directly or indirectly by impact cratering. Phobos has an extensive network of linear depressions (grooves) that probably were formed indirectly by the largest impact recorded on Phobos. Deimos lacks grooves as well as the large number of ridges that occur on Phobos. Craters on Deimos have substantial sediment fill; those on Phobos have none. Evidence of downslope movement of debris is prominent on Deimos but is rare on Phobos. Many of the differences between Phobos and Deimos may be caused by modest differences in mechanical properties. However, the lack of a very large crater on Deimos may be responsible for its lack of grooves.     

Real-Time Flux Density Measurements of the 2011 Draconid Meteor Outburst

During the 2011 outburst of the Draconid meteor shower, members of the Video Meteor Network of the International Meteor Organization provided, for the first time, fully automated flux density measurements in the optical domain. The data set revealed a primary maximum at 20:09 UT ± 5 min on 8 October 2011 (195.036° solar longitude) with an equivalent meteoroid flux density of (118 ± 10) × 10^?3/km²/h at a meteor limiting magnitude of +6.5, which is thought to be caused by the 1900 dust trail. We also find that the outburst had a full width at half maximum of 80 min, a mean radiant position of α = 262.2°, δ = +56.2° (±1.3°) and geocentric velocity of v_geo = 17.4 km/s (±0.5 km/s). Finally, our data set appears to be consistent with a small sub-maximum at 19:34 UT ±7 min (195.036° solar longitude) which has earlier been reported by radio observations and may be attributed to the 1907 dust trail. We plan to implement automated real-time flux density measurements for all known meteor showers on a regular basis soon.     

Pole orientation of 16 psyche by two independent methods

Nineteen new lightcurves of 16 Psyche are presented along with a pole orientation derived using two independent methods, namely, photometric astrometry (PA) and magnitude-amplitude-shape-aspect (MASA). The pole orientations found using these two methods agree to within 4°. The results from applying photometric astrometry were prograde rotation, a sidereal period of $\text{0}\text{d}\text{dot}\text{1748143 ± 0}\text{d}\text{dot}\text{0000003}$, and a pole at longitude 223° and latitude +37°, with an uncertainty of 10°; and, from applying magnitude-amplitude-shape-aspect a pole at 220 ± 1°, +40 ± 4°, and a modeled triaxial ellipsoid shape (a > b > c) with a/b = 1.33 ± 0.02 and b/c = 1.33 ± 0.07. The discrepancy between the high pole latitude found here and the low latitudes reported by others is discussed.     

Photometric observations and modelling of the asteroid 85 Io in conjunction with data from an occultation event during the 1995–96 apparition

The asteroid 85 Io has been observed using CCD and photoelectric photometry on 18 nights during its 1995–96 and 1997 apparitions. We present the observed lightcurves, determined colour indices and modelling of the asteroid spin vector and shape. The colour indices (U-B = 0.35±0.02, B-V = 0.66±0.02, V-R = 0.34±0.02, R-I = 0.36±0.02) are as expected for a C-type asteroid. The allowed spin vector solutions have the pole co-ordinates λ₀ = 285±4°, β₀ = −52±9° or λ₀ = 108±10°, β₀ = −46±10° and λ₀ = 290±10°, β₀ = −16±10° with a retrograde sense of rotation and a sidereal period P_sid = 0^d.286463±0^d.000001. During the 1995–96 apparition the International Occultation Time Association (IOTA) observed an occultation event by 85 Io. The observations and modelling presented here were analysed together with the occultation data to develop improved constraints on the size of the asteroid. The derived value of 164 km is about 5% larger than the IRAS diameter. © 1999 Elsevier Science Ltd. All rights reserved.     

Orbital history of the Martian satellites with inferences on their origin

Recent Viking results indicate the Martian satellites are composed of carbonaceous chondritic material, suggesting that Phobos and Deimos were once asteroids captured by Mars. On the other hand, the low eccentricities and inclinations of their orbits on the equator of Mars argue against that hypothesis. This paper presents detailed calculations of the tidal evolution of Phobos and Deimos, considering dissipation in both Mars and its satellites simultaneously and using a new method applicable for any value of the eccentricity. In particular, including precession of the satellites' orbits indicates that they have always remained close to their Laplacian plane, so that the orbital planes of Phobos and Deimos switched from near the Martian orbital plane to the Martian equator once the perturbations due to the planetary oblateness dominated the solar perturbations, as they do presently. The results show that Deimos has been little affected by tides, but several billion (10⁹) years ago, Phobos was in a highly eccentric orbit lying near the common plane of the solar system. This outcome is obtained for very reasonable values of dissipation inside Mars and inside Phobos. Implications for the origin of the Martian satellites are discussed.     

Spectrophotometry of Saturn and its rings from 60 to 180 microns

We observed Saturn at far-infrared and submillimeter wavelengths during the Earth's March 1980 passage through the plane of Saturn's rings. Comparison with earlier spectroscopic observations by D. B. Ward [Icarus32, 437–442 (1977)], obtained at a time when the tilt angle of the rings was 21.8°, permits separation of the disk and ring contributions to the flux observed in this wavelength range. We present two main results: (1) The observed emission of the disk between 60 and 180 μm corresponds to a brightness temperature of 104 ± 2°K; (2) the brightness temperature of the rings drops approximately 20°K between 60 and 80 μm. Our data, in conjunction with the data obtained by other observers between 1 μm and 1 mm, permit us to derive an improved estimate for the total Saturnian surface brightness of (4.84 ± 0.32) × 10^?4W cm^?2 corresponding to an effective temperature of 96.1 ± 1.6°K. The ratio of radiated to incident power, P_R/P_I, is (1.46 ± 0.08)/(1 - A), where A is the Bond albedo. For A = 0.337 ± 0.029, P_R/P_I = 2.20 ± 0.15 and Saturn's intrinsic luminosity is L_S = (2.9 ± 0.5) × 10^?10L_⊙.     

Kinematics of the Gould Belt based on open clusters

We have redetermined the kinematic parameters of the Gould Belt using currently available data on the motion of nearby young (log t < 7.91) open clusters, OB associations, and moving stellar groups. Our modeling shows that the residual velocities reach their maximum values of ?4 km s^?1 for rotation (in the direction of Galactic rotation) and +4 km s^?1 for expansion at a distance from the kinematic center of ≈300 pc. We have taken the following parameters of the Gould Belt center: R ₀ = 150 pc and l ₀ = 128°. The whole structure is shown to move relative to the local standard of rest at a velocity of 10.7 ± 0.7 km s^?1 in the direction l = 274° ± 4° and b = ?1° ± 3°. Using the derived rotation velocity, we have estimated the virial mass of the Gould Belt to be 1.5 × 10⁶ M _⊙.