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.     

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.     

Worldwide photometry and lightcurve observations of 16 Psyche during the 1975–1976 apparition

We present 26 lightcurves of 16 Psyche from 1975 and 1976. The synodic period during this apparition was 4^h.1958. Combining photometric data from this opposition with those from previous apparitions allowed us to derive a mean phase coefficient in V of 0.026 ± 0.002 mag/deg and to establish that Psyche's absolute V₀ magnitude and rotational amplitude vary with aspect; at 90° aspect, V₀(1, 0) = 6.27 ± 0.05 and the lightcurve amplitude is 0.30 mag, while at 0° or 180° aspect, V₀(1, 0) = 6.02 ± 0.02 and the amplitude is ?0.03 mag. This behavior is accounted for if, to first order, Psyche's shape is that of a triaxial ellipsoid with axial ratios near 5:4:3. Colors at zero phase are U-B = 0.26 ± 0.01 and B-V = 0.71 ± 0.01. Color phase coefficients are <0.001 mag/deg in U-B and 0.0010 ± 0.0004 mag/deg in B-V.     

Voyager disk-integrated photometry of Io

Voyager full-disk images of Io, available at solar phase angle of α = 2?29° and 101?159°, allow comparisons of the satellite's near-opposition photometric behavior with Earth-based results and the determination of the phase curve out to very high phase angles. The near-opposition data were reduced iteratively for self-consistent phase and rotation curves in each Voyager filter; the resulting phase coefficients, geometric albedos, and rotational lightcurves are consistent with Earth-based findings, except for a previously noted tendency for Voyager to yield somewhat redder spectral information. The derived near-opposition phase coefficients, ranging between 0.016 and 0.024 mag/ deg, decrease with increasing wavelength, a trend weakly noted in some Earth-based observations. The full, α = 2?159° phase curves allow the first direct determination of the phase integral of Io at several wavelengths: q rises from ≈0.7 in the ultraviolet to ≈0.8 in the orange. Combination of the Voyager phase integrals with Earth-based albedo information leads to a best estimate of the bolometric Bond albedo of 0.50 ± 0.10, a value consistent with, but slightly below, previous estimates.     

Mariner 9 polarimetry of Phobos and Deimos

We have used the Mariner 9 A-camera system to measure the polarization (P) of Phobos and Deimos at large phase angles (α). For Deimos, P = +22 ± 4% at α = 74°; for Phobos P = +20.5 ± 4% at α = 77°, and P = +24.5 ± 4% at α = 81°. These measurements refer to orange light at about 0.57 μm. A comparison with laboratory measurements of powdered rock samples indicates that the observations are consistent with the presence of regoliths on the satellites.     

Pole coordinates of the asteroids 9 metis, 22 kalliope,and 44 Nysa

By means of new photoelectric observations made in 1974 an attempt to determine the poles of asteroids 9 and 44 was made. Following a method based upon the magnitude-aspect and amplitude-aspect relations, the coordinates of the poles for 9 and 44 were found to be, respectively, λ₀ = 191° ± 5°, β₀ = 56° ± 6° and λ₀ = 100° ± 10°, β₀ = 50° ± 10°. The previously published pole for asteroid 22, λ₀ = 215° ± 10°, β₀ = 45° ± 15°, was confirmed. From its phase relation we determined the phase coefficient of 44 Nysa, a very high albedo object (p_v = 0.377). The very low phase coefficient obtained (β_v = 0.018 mag/deg) agrees very well with an inverse relation between geometrical albedo and phase coefficient. The results are summarized in a table.     

Worldwide photometry and lightcurve observations of 1 Ceres during the 1975–1976 apparition

We present 19 lightcurves of asteroid 1 Ceres obtained during a global campaign in 1975–1976. The synodic period is 0.37812 ± 0.00004 day. The mean absolute V magnitude is 3.61 ± 0.03 and the phase coefficient is 0.40 ± 0.001 mag/deg. The U-B and B-V phase coefficients are +0.0015 ± 0.0007 and +0.0006 ± 0.0003 mag/deg, respectively. The colors at zero phase are B-V = +0.70 ± 0.01 and U-B = +0.41 ± 0.01.     

UBV photometry of asteroid 433 Eros

UBV observations of asteroid 433 Eros were conducted on 17 nights during the winter of 1974/75. The peak-to-peak amplitude of the lightcurve varied from about 0.3 mag to nearly 1.4mmag. The absolute V mag at maximum light, extrapolated to zero phase, is 10.85. Phase coefficients of 0.0233 mag/degree, 0.0009 mag/degree and 0.0004 mag/degree were derived for V, B-V, and U-B, respectively. The zero-phase color of Eros (B?V = 0.88, U?B = 0.50) is representative of an S (silicaceous) compositional type asteroid. The color does not vary with rotation. The photometric behavior of Eros can be modeled by a cylinder with rounded ends having an axial ratio of about 2.3:1. The asteroid is rotating about a short axis with the north pole at λ₀ = 15° and β₀ = 9°.     

Voyager photometry of Rhea,Dione, Tethys,Enceladus and Mimas

Voyager imaging observations provide new photometric data on Saturn's satellites at large phase angles (up to 133° in the case of Mimas) not observable from Earth. Significant new results include the determination of phase integrals ranging from 0.7 in the case of Rhea to 0.9 for Enceladus. For Enceladus we find an average geometric albedo p_v = 1.04 ± 0.15 and Bond albedo of 0.9 ± 0.1. The data indicate an orbital lightcurve with an amplitude of 0.2 mag, the trailing side being the brighter. For Mimas, the lightcurve amplitude is probably less than 0.1 mag. The value of the geometric albedo of Mimas reported here, p_v = 0.77 ± 0.15 (corresponding to a mean opposition magnitude V₀ = +12.5) is definitely higher than the currently accepted value of about 0.5. For Dione, the Voyager data show a well-defined orbital lightcurve of amplitude about 0.6 mag, with the leading hemisphere brighter than the trailing one.     

Lightcurves and the axis of rotation of 433 Eros

Ten lightcurves and UBV photometry of 433 Eros were obtained between August 1972 and May 1975. The absolute magnitude of the lightcurve maximum is 10.75 and the phase coefficient is 0.025 mag/deg. There may be a small difference in B-V color between the northern and southern hemispheres. The pole of the axis of rotation is directed toward λ₀ = 16°, β₀ = 12°, ecliptic longitude and latitude, respectively, and the rotation is direct with a sidereal period of 0.^d219599 or 5^h16^m13^s4 ± 0.^s2. The dimensions derived from the polarimetric albedo and the lightcurve amplitudes are 12km × 12km × 31km for a smooth cylinder with hemispherical ends.     

Lightcurves and phase relation of asteroid 324 Bamberga

A worldwide photometric investigation of the asteroid 324 Bamberga was conducted during the period September–November 1978. The full-cycle lightcurve shows two maxima and two minima with a maximum amplitude of 0.075 mag; the rotation period was found to be P_syn = 29.^h42 ± 0.^h01. A linear least-squares solution of the phase relation gives β_y = (0.334 ± 0.001) mag/degree and V₀ (1, 0) = (7.17 ± 0.01) mag. The color indices measured are B-V = 0.69, U-B=0.36, in agreement with the C taxonomic type given for 324 Bamberga. The very long period indicates 324 Bamberga is an unusual object among asteroids with diameters greater than 200 km.     

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°.     

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.     

A photometric study of the minor planet 63 Ausonia

Photoelectric observations of the minor planet 63 Ausonia were obtained on 12 nights during the 1976 opposition at the Astronomical Observatory of Torino. A complete lightcurve with two maxima and two minima was observed with a maximum amplitude of 0.47 mag. The synodic period of rotation, never before determined photoelectrically, was found to be 9^h17^m48^s ± 5^s. The absolute magnitude of the primary maximum, V₀(1, 0) = 7.49 mag, and the phase coefficient, β_v = 0.035 mag/deg, were deduced by the magnitude-phase relation. Comparison with other observations is briefly discussed and a mean radius is determined from a previous value of the geometric albedo.     

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.     

Photoelectric lightcurves of the asteroid 1862 Apollo

Photoelectric lightcurves of the asteroid 1862 Apollo were obtained in November–December 1980 and in April–May 1982. The period of rotation is unambiguously determined to be 3.0655 ± 0.0008 hr. The 1980 observations span a range of solar phase angle from 30° to 90°, and the 1982 observations, 0.°2 to 90°. The Lumme-Bowell-Harris phase relation can be fit to the absolute magnitudes at maximum light with an RMS scatter of 0.06 magnitude over the entire range of phase angle. The constants of the solution are absolute V magnitude at zero phase angle and at maximum light, 16.23 ± 0.02; slope parameter, 0.23 ± 0.01. These constant corresponds to values in the linear phase coefficient system of V(1, 0) = 16.50 ± 0.02 and a phase coefficient of β_v = 0.0305 ± 0.0012 mag/degree in the phase range 10°–20°. The slope of the phase curve is typical for a moderate albedo asteroid. The absolute magnitudes observed in 1980 and 1982 fall along a common phase curve. That is, Apollo was not intrinsically brighter at one apparition than the other. This is not surprising, since the two apparitions were almost exactly opposite one another in the sky. A pole position was calculated from the observed deviation of the lightcurve from constant periodicity (synodic-sidereal difference) during both apparitions. The computed 1950 ecliptic coordinates of the pole are: longitude = 56°, latitude = −26°. This is the “north” pole with respect to right-handed (counter-clockwise) rotation. The formal uncertainty of the solution for the pole position is less than 10°, but realistically may be several times that, or even completely wrong. The sidereal period of rotation asscociated with this pole solution is 3.065436 ± 0.000012 hr.     

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.     

The lightcurve and phase relation of the asteroid 133 Cyrene

The asteroid 133 Cyrene was observed photometrically on 17 nights during oppositions in 1979 and 1980. The synodic period of rotation was found to be 12.^h708 ± 0.^h001 with an amplitude of ～0.^m30 during both oppositions. At large phase angles, the phase relation is quite ordinary (β_v ≈ 0.025 mag/degree); however, the low phase angle observations reveal a dramatic opposition brightening, ～0.2 mag/degree near zero phase angle. The absolute magnitude, V(1,0), extrapolated with the above linear phase coefficient, is 8.40. The following color indicates were also measured: B- V = 0.90, U-B = 0.51.     

A photometric study of BO Canum Venaticorum

Photometric BV light curves of BO CVn obtained in 1992 and new times of minima are presented. The primary minimum shows a transit, whereas the secondary minimum, shows an occultation. The system may be classified as an A‐type W UMa system. A complete study of minima allows one to detect a possibly increasing period by about 0.037 s/yr. This indicates that the conservative mass transfer rate from the less massive component to the more massive one is 1.57 10^—10M_⊙ /yr. Because of the variable period, the new ephemeris is determined for future observations. Using the Wilson‐Devinney code a simultaneous solution of the B and V light curves is also performed. The analysis shows that the system is in a contact configuration with q = 0.205 ± 0.001 and fillout factor (f) = 0.18, T₁ = 7240 K (fixed), T₂ = 7150± 10 K. The high orbital inclination i = 87°.54 ± 0.26 was con firmed by photometric observations of the secondary minimum.     

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.