Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon

Since the continuation of an external gravity field inside topographic masses by a harmonic function results in topographic bias, geoid computation by means of global gravity models (GGMs) in terms of external-type series of spherical harmonics, at locations where the GGMs are evaluated inside the topographic masses, will be biased. Consequently, if the reference ellipsoid is defined based on the geoid, it will also be biased. In this paper, the effects of topographic bias on the geoid and reference ellipsoid of Venus, Mars, and the Moon are studied. Moreover, a thorough error analysis in the geoid and reference ellipsoid computation is presented, and it is shown that the estimated standard deviation (STD) of the geoid potential value, the geoidal heights, and the semimajor and semiminor axes of the reference ellipsoid are independent of the topographic bias. According to the results, the effects of topographic bias on the geoid potential value and the semimajor and semiminor axes of the reference ellipsoid in comparison with their estimated STDs are insignificant for Venus, Mars, and the Moon. Moreover, the effect of topographic bias on the geoidal heights of Venus as compared with the estimated STD of its geoidal heights is insignificant. However, the effects of topographic bias on the geoidal heights of Mars and the Moon can be significant, especially in high mountains such as the Tharsis volcanic region on Mars.     

Depth-diameter relation for large Martian craters determined from Mariner 9 UVS altimetry

We have determined the depth/diameter ratio for 87 craters on Mars using Mariner 9 UVS spectrometer altimetry (Barth et al., 1974). Our sample includes craters 12 to 100 km in diameter, and 0.4 to 3.3 km in depth. The largest depth/diameter ratios on Mars are comparable to those of fresh craters on Mercury (measured by Gault et al., 1975). However, more than half of our sample consists of degraded craters whose depths are significantly shallower than those of fresh craters of similar diameter on Mercury, confirming the interpretations of earlier photoanalysts.     

Mariner 9 ultraviolet spectrometer experiment: Observations of ozone on Mars

The Mariner 9 Ultraviolet Spectrometer has observed the 2550 Å ozone spectral absorption feature on Mars. This absorption was previously detected in the south polar region by Mariner 7 in 1969. Mariner 9 did not observe ozone at any time in the equatorial region, nor at the south polar cap during its summer season. However, ozone was found in the north polar region beginning at a latitude of 45°N and extending northward. Ozone later appeared in the southern hemisphere southward of 50°S as the Mars autumnal equinox approached. The presence of ozone on Mars seems to be coupled to the water vapor content of its atmosphere.     

On the accuracy of the orbit of asteroid (99942) APOPHIS at the time of its encounter with the Earth in 2029

We estimate the effect of trajectory measurement errors on the orbital parameters of asteroid Apophis determined from improvements. For this purpose, based on all of the optical and radar observations available to date, we have computed a nominal orbit of the asteroid. The scatter ellipsoid of the initial conditions of motion has been obtained by two methods. In the first, universally accepted method, the scatter ellipsoid is calculated by assuming a linear dependence of the errors in the parameters being determined on observational errors. In the second method, the scatter region of the orbital parameters around the nominal-orbit parameters is determined by the Monte Carlo method. We show that the region determined by the latter method at the initial epoch differs only slightly from the scatter ellipsoid for the linear approximation. We estimate the sizes of the projections of the corresponding regions onto the target plane at the time of the closest encounter of the asteroid with the Earth in 2029. The projections are approximated by ellipses. Our computations have shown that the ellipse has the following sizes: 389.6 km for the semimajor axis and 16.4 km for the semiminor axis in the linear case and 330.0 and 11.1 km, respectively, in the nonlinear case.     

The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C_2,2, is well determined and correlates with the equatorial shape. The S_2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J₂, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C_2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (C_m/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.     

Mariner 9 ultraviolet spectrometer experiment: Mars airglow spectroscopy and variations in Lyman alpha

Mariner 9 ultraviolet spectrometer observations show the Mars airglow consists principally of emissions that arise from the interaction of solar ultraviolet radiation with carbon dioxide, the principal constituent of the Mars atmosphere. Two minor constituents, atomic hydrogen and atomic oxygen, also produce airglow emissions. The airglow measurements show that ionized carbon dioxide is only a minor constituent of the ionosphere. Using the airglow measurements of atomic oxygen, it is possible to infer that the major ion is ionized molecular oxygen. The escape rate of atomic hydrogen measured by Mariner 9 is approximately the same as that measured two years earlier by Mariner 6 and 7. If the current escape rate has been operating for 4.5 billion years and if water vapor is the ultimate source, an amount of oxygen has been generated that is far in excess of that observed at present. Mariner 9 observations of Mars Lyman alpha emission over a period of 120 days show variations of 20%.     

Topography and Geologic Characteristics of Aeolian Grooves in the South Polar Layered Deposits of Mars

The topographic and geologic characteristics of grooves and groove-like features in the south polar layered deposits near the Mars Polar Lander/Deep Space 2 landing sites are evaluated using Mariner 9 images and their derived photoclinometry, normalized using Mars Orbiter Laser Altimeter data. Although both Mariner 9 and Viking images of the south polar layered deposits were available at the time of this study, Mariner 9 images of the grooves were selected because they were generally of higher resolution than Viking images. The dimensions and slopes of the grooves, together with orientations that nearly match the strongest winds predicted in the Martian Global Circulation Model and directions inferred from other wind indicators, suggest that they formed by aeolian scour of an easily erodible surface. Most grooves are symmetric and V-shaped in transverse profile, inconsistent with an origin involving extensional brittle deformation. Although the grooves strike along slopes and terraces of the south polar layered deposits, the variable depths and lack of terracing within the grooves themselves indicate that any stratigraphy in the uppermost 100 m of the polar layered deposits is composed of layers of similar, and relatively low, resistance. The grooves do not represent landing hazards at the scale of the Mariner 9 images (72-86 m/pixel) and therefore probably would not have affected Mars Polar Lander and Deep Space 2, had they successfully reached the surface.     

An orthographic photomap of the south pole of Mars from Marina 7

Television pictures of the south polar regions of Mars obtained by the Mariner 6 and 7 spacecraft in 1969 are rectified to a standard mapping projection using computer image processing techniques. Mosaicking of these pictures produces the first photomap of the entire south polar cap.     

Martian planetwide crater distributions: Implications for geologic history and surface processes

Population-density maps of craters in three size ranges (0.6 to 1.2 km, 4 to 10 km, and >20 km in diameter) were compiled for most of Mars from Mariner 9 imagery. These data provide: historical records of the eolian processes (0.6 to 1.2 km craters); stratigraphic, relative, and absolute timescales (4 to 10 km craters); and a history of the early postaccretional evolution of the uplands (> 20 km craters).Based on the distribution of large craters (>20 km diameters), Mars is divisible into two general classes of terrain, densely cratered and very lightly cratered—a division remarkably like the uplands-maria dichotomy of the moon. It is probable that this bimodal character in the density distribution of large craters arose from an abrupt transition in the impact flux rate from an early intense period associated with the tailing off of accretion to an extended quiescent epoch, not from a void in geological activity during much of Mars' history. Radio-isotope studies of Apollo lunar samples show that this transition occurred on the moon in a short time.The intermediate-sized craters (4 to 10 km diameter) and the small-sized craters (0.6 to 1.2 km diameter) appear to be genetically related. The smaller ones are apparently secondary impact craters generated by the former. Most of the craters in the larger of these two size classes appear fresh and uneroded, although many are partly buried by dust mantles. Poleward of the 40° parallels the small fresh craters are notably absent owing to these mantles. The density of small craters is highest in an irregular band centered at 20°S. This band coincides closely with (1) the zone of permanent low-albedo markings; (2) the “wind equator” (the latitude of zero net north or south transport at the surface); and (3) a band that includes a majority of the small dendritic channels. Situated in the southermost part of the equatorial unmantled terrain which extends from about 40°N to 40°S, this band is apparently devoid of even a thin mantle. Because this belt is also coincident with the latitutde of maximum solar insolation (periapsis occurs near summer solstice), we suggest that this band arises from the asymmetrical global wind patterns at the surface and that the band probably follows the latitude of maximum heating which migrates north and south from 25°N to 25°S within the unmantled terrain on a 50,000 year timescale.The population of intermediate-sized craters (4–10 km diameter) appears unaffected by the eolian mantles, at least within the ±45° latitudes. Hence the local density of these craters is probably a valid indicator of the relative age of surfaces generated during the period since the uplands were intensely bombarded and eroded. It now appears that the impact fluxes at Mars and the moon have been roughly the same over the last 4 b.y. because the oldest postaccretional, mare-like surfaces on Mars and the moon display about the same crater density. If so, the nearness of Mars to the asteroid belt has not generated a flux 10 to 25 times greater than the lunar flux. Whereas the lunar maria show a variation of about a factor of three in crater density from the oldest to the youngest major units, analogous surfaces on Mars show a variation between 30 and 50. This implies that periods of active eolian erosion, tectonic evolution, volcanic eruption, and possibly fluvial modification have been scattered throughout Martian history since the formation and degradation of the martian uplands and not confined to small, ancient or recent, epochs. These processes are surely active on the planet today.     

A Specific Nongravitational Effect in the Asteroid Belt

The evolution of orbits of asteroids found in the IRAS and WISE albedo databases was calculated numerically from 2005 to 2016. It follows from the analysis of the obtained results that a certain nongravitational effect (NGE) currently affects the motion of a considerable fraction of main-belt asteroids with diameters up to 40 km. This conclusion agrees with the available data regarding the axial rotation of asteroids. The NGE manifests itself in an increase in the semimajor axes of orbits of low-albedo asteroids relative to the semimajor axes of orbits of high-albedo bodies. The NGE-induced rate of elongation of semimajor axes of asteroids with albedos р_v < 0.1 may be as high as (2–8) × 10^–8 AU/year. Errors in orbital elements of asteroids (unrelated to the accuracy of observational data used to determine these orbital elements) were found in one of the MPC catalogues for 2003 in the process of estimation of the accuracy of calculations.     

Mariner 9 ultraviolet spectrometer experiment: Pressure-altitude measurements on Mars

Ultraviolet spectrometer measurements of the reflectance at 3050 Å are modeled to give pressure-altitudes for Mars assuming a quiescent atmosphere. Ultraviolet light that is Rayleigh-scattered by the Mars molecular atmosphere, with allowance for uniform turbidity, is proportional to surface pressure independent of atmospheric temperature structure. All model constants except the over-all scaling factors are found by requiring ultraviolet spectrometer pressures of 47 locations on the planet to be the same when measured at different geometries. The overall scaling factor is found by intercomparison with Mariner 9 occultation pressures. Comparison with other Mars pressure-altitude measurements show deviations from the assumption of uniform turbidity to occur over the Hesperia plateau for ultraviolet measurements obtained during the 13–26 February 1972 time period.     

Distribution of small channels on the Martian surface

The distribution of small channels on Mars has been mapped from Mariner 9 images, at the 1:5 000 000 scale, by the author. The small channels referred to here are small valleys ranging in width from the resolution limit of the Mariner 9 wide-angle images (～1 km) to about 10 km. The greatest density of small band occurs in dark cratered terrain. This dark zone forms a broad subequatorial band around the planet. The observed distribution may be the result of decreased small-channel visibility in bright areas due to obscuration by a high albedo dust or sediment mantle. Crater densities within two small-channel segments show crater size-frequency distributions consistent with those of the oldest of the heavily cratered plains units. Such crater densities coupled with the almost exclusive occurrence of small channels in old cratered terrain and the generally degraded appearance of small channels in the high-resolution images (～100 m) imply a major episode of small-channel formation early in Martian geologic history.     

Speckle interferometry of asteroids: I. 433 eros

Analytic expressions for the semimajor and semiminor axes and an orientation angle of the ellipse projected by a triaxial ellipsoid (an asteroid) and of the ellipse segment cast by a terminator across the ellipsoid as functions of the dimensions and pole of the body and the asterocenteric position of the Earth and Sun are derived. Applying these formulae to observations of the Earth-approaching asteroid 433 Eros obtained with the speckle interferometry system of Steward Observatory on December 17–18, 1981, and January 17–18, 1982, the following dimensions are derived: (40.5 ± 3.1 km) × (14.5 ± 2.3 km) × (14.1 ± 2.4 km) Eros' north pole is found to lie within 14° of RA = 0^h16^m Dec. = +43° (ecliptic longitude 23°, latitude +37°). Other than knowing the rotation period of Eros, these results are completely independent of any other data, and in the main confirm the results obtained in the 1974–1975 apparition by other methods. These dimensions, together with a lightcurve from December 18, 1981, lead to a geometric albedo of 0.156 ± 0.010. A series of two-dimensional power spectra and autocorrelation functions of the resolved asteroid clearly show it spinning in space.     

The determination of the satellite orbit of Mariner 9

This paper presents a comprehensive analysis of the Mars orbital phase of the Mariner 9 trajectory as determined from Earth based radio data. Both the method and accuracy of the orbit determination process are reviewed. Analysis is presented to show the effects of Mars gravity model and node in the plane of the sky errors on the accuracy of orbit determination. In addition the long term evolution of the orbit from insertion through the first 500 revolutions is presented, and decomposed into effects from the Mars garvity field,n-body perturbations, and solar radiation pressure. Since the orbit period is nearly commensurable with the Mars rotational period, the orbit experiences significant resonance perturbations. The primary perturbation is in-track with a maximum amplitude of 1000 km and a wavelength of 39 spacecraft revolutions.This paper was presented at the AIAA/AAS Astrodynamics Conference, Palo Alto, California, September 11 and 12, 1972. At this time Mariner 9 operations were still underway. The operational life of Mariner 9 ended October 27, 1972, when the supply of nitrogen gas, used for attitude stabilization, was depleted. This paper represents one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, under NASA Contract No. NAS 7-100.     

The frequency and intensity of comet showers from the Oort cloud

We simulate the Oort comet cloud to study the rate and properties of new comets and the intensity and frequency of comet showers. An ensemble of ∼10⁶ comets is perturbed at random times by a population of main sequence stars and white dwarfs that is described by the Bahcall-Soneira Galaxy model. A cloning procedure allows us to model a large ensemble of comets efficiently, without wasting computer time following a large number of low eccentricity orbits. For comets at semimajor axis a = 20,000 AU, about every 100 myr a star with mass in the range 1M_⊙−2M_⊙ passes within ∼10,000 AU of the Sun and triggers a shower that enhances the flux of new comets by more than a factor of 10. The time-integrated flux is dominated by the showers for comets with semimajor axes less than ∼30,000 AU. For semimajor axes greater than ∼30,000 AU the comet loss rate is roughly constant and strong showers do not occur. In some of our simulations, comets are also perturbed by the Galactic tidal field. The inclusion of tidal effects increases the loss rate of comets with semimajor axes between 10,000 and 20,000 AU by about a factor of 4. Thus the Galactic tide, rather than individual stellar perturbations, is the dominant mechanism which drives the evolution of the Oort cloud.     

On methods of graphical displaying of polar magnetic disturbances

Some simple and useful methods of mapping the field of polar magnetic disturbances are discussed. Contour maps showing the storminess in a local time-universal time plane are used to trace the variation with time of the longitudinal extent and intensity of the auroral electrojets. In effect this kind of map is a way of ascribing to each longitude an index analogous to the AE index. For the study of north-south motions of the auroral electrojets during polar magnetic substorms contour maps are used showing the disturbances of the three field components in a latitude-universal time plane.     

The Mars 1:2 resonant population

An excess of around 400 asteroids in the distribution of the semimajor axes of the asteroids is identified by means of numerical integrations as generated by a population of approximately 1000 asteroids evolving inside the exterior resonance 1:2 with Mars. Approximately 200 asteroids are librating around the asymmetric libration centers and their evolution in a time-scale of 1 million years appears stable but with a strong influence of Mars' eccentricity. The biggest Mars 1:2 resonant asteroid is (142) Polana.     

Polar wander on Mars: Evidence in the geoid

The geoid of Mars is dominated by its equilibrium figure and by the effect of the Tharsis rise. To investigate the rotational stability of Mars prior to the rise of Tharsis, we produced a residual non-hydrostatic geoid without Tharsis. First the hydrostatic component of the present-day flattening was removed. This procedure was performed using a 6% non-hydrostatic component of flattening, a value set by the spin axis precession rate of Mars. Then zonal spherical harmonics up to degree 6 centered on Tharsis were removed. Finally, the resultant residual geoid was evaluated for rotational stability by comparing polar and equatorial moments at 4050 trial pole positions. If the spin axis of ancient Mars was secularly stable, our analysis indicates that substantial polar wander has occurred with the rise of Tharsis. Stable spin axis positions on the non-hydrostatic residual figure of Mars are 15° to 90° from the present-day poles. This result is consistent with previously proposed paleopoles based on magnetic anomalies, geomorphology, and grazing impacts.     

A Mariner/MESSENGER global catalog of mercurian craters

Using MESSENGER and Mariner 10 flyby images, we have compiled a global catalog of impact structures with diameters D > 10 km. The distribution of impact structures shows a factor of 10 range in areal crater density. Most regions of low crater density are located within large impact basins, consistent with the idea that these were low-lying areas that have been filled by subsequent volcanism over an extended period.     

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.