G33A-01 INVITED 13:40h
Current and Future Applications of Laser Altimetry to Planetary Geodesy
Planetary orbital lidar mapping, first used by the Apollo Orbiters in 1971-72, achieved a new status with the mapping of Mars by the MOLA instrument aboard Mars Global Surveyor, 1998-2001. A new geodetic control network has been tied to MOLA altimetry, providing the basis for subsequent missions, and the crustal and lithospheric structure of Mars has been resolved. Further applications included measurement of seasonally-varying polar topography, atmospheric properties, orbital decay of Phobos due to tidal dissipation, and surface modifications produced by volatiles. The MLA instrument on the MESSENGER mission will measure the shape of Mercury and determine the amplitude of forced libration from orbit. Lidar instruments on earlier missions to the Moon and asteroid 433 Eros, in combination with radio tracking, have also revealed internal structure. We summarize the state of the art of lidar mapping and discuss advances in determination of gravity potential of solid bodies using altimetric crossovers.
G33A-02 INVITED 13:55h
Earth-based Measurements of Planetary Rotational States
The rotational response of planetary bodies to a variety of forcings provides fundamental insights into their interior structure and rheology. High-precision rotation measurements of the solid planets can be obtained with an Earth-based radar technique originally proposed by Green (1962, 1968) and also studied by Holin (1988, 1992). We have devised a practical implementation of this technique using the radio telescopes at Goldstone, Green Bank, and Arecibo. Initial data have been obtained for Mercury, Venus, and Mars. Our observations of Mercury provide instantaneous spin measurements with a fractional precision of 10$^{-5}$, a level that is sufficient to characterize the amplitude of the 88-day librations in longitude with 10% uncertainties. A dozen measurements obtained over the past two years strikingly trace the phase of the expected libration signature derived from the torque equation, yielding considerable confidence that the librations have been unambiguously detected. Least-squares fits to the data accumulated to date indicate a libration amplitude of $\sim$60 arcseconds. Peale (1976) showed that the measurement of the amplitude of those librations, the obliquity, and the $C_{20}$ and $C_{22}$ gravitational harmonic coefficients can provide important information about the state and size of the core of Mercury. One can use the Mariner 10 determination of the gravitational harmonics (Anderson et al., 1987) to estimate the libration amplitude. If the core was solid and coupled to the mantle, the amplitude of the 88-day librations would be within 50% of 20 arcseconds. Our measurements reveal librations with an amplitude that is three times larger than that, indicating that an outer shell only participates in the librations. The mantle of Mercury must therefore be decoupled from a core that is liquid, with profound implications for the thermal evolution and magnetic field generation of the planet. The observational evidence for a liquid core at Mercury strengthens the hypothesis that a dynamo may generate the magnetic field, even though a remanent crustal field can still explain the Mariner 10 magnetic field data (Stephenson 1976, Aharonson et al., 2004). Our measurements cannot provide a precise constraint on the size of the core until improved values of the gravitational harmonic coefficients are obtained by the MESSENGER and BepiColombo spacecraft.
G33A-03 14:10h
Free Rotational Motions of Mercury
If free rotational modes of significant amplitude are found in the precise measurements of Mercury's obliquity and the libration in longitude by radar speckle displacement interferometry (RSDI), and the MESSENGER and BepiColombo spacecraft, sources of excitation of the free modes will be constrained by the time scales for damping their amplitudes. The free modes consist of libration in longitude (10 year period), precession of the spin about the Cassini state (1000 year period), and wobble (500 year period), where the term free means the modes can have arbitrary amplitude and phase. The amplitude of the physical libration in longitude and the obliquity of the Cassini state together with the gravitational coefficients $J_2$ and $C_{22}$ determine the state and constrain the geometry of Mercury's core (e.g. Peale, et al. 2002). A free libration in longitude does not compromise the determination the 88 day forced libration, since the latter is simply superposed and its amplitude easily determined. But a free precession will make the determination of the obliquity of the Cassini state somewhat uncertain. The latter obliquity is crucial in constraining $C/MR^2$, where $C,M,R$ are moment of inertia, mass and radius of Mercury. The signature of a free precession would be finding the spin axis displaced from the plane determined by the orbit normal and the normal to the Laplacian plane and thereby not occupying the Cassini state. A free wobble will be hard to detect with the proposed measurements, but it should not compromise the determination of the core properties. Already RSDI has determined that $C_m/C<0.7$ with 95% confidence by measuring a large physical libration amplitude of $60\pm 5$ arcsec (Margot {\it et al.} 2004), which is consistent with Mercury having a molten core. $C_m$ is the moment of inertia of the mantle alone. That means we must add the dissipation at the core-mantle interface to the traditional tidal friction in determining the damping times of the free modes. We model the torque between a liquid core and solid mantle as being simply proportional to the difference in the angular velocities and relate the constant of proportionality to the kinematic viscosity of the core material by comparing with known spin-up time scales. Representative time scales in years for damping the free modes are as follows with subscripts $\ell,p,w$ indicating longitude, precession and wobble respectively, and $T,C$ indicating tide and core: $\tau_{\ell T}=9.3e5,\; \tau_{\ell C}=2.1e5$ ($1.7e5$ for tides and core acting together), $\tau_{pT}=6.4e6,\;\tau_{pC}=1.0e5,\;\tau_{wT}=3.7e6,\; \tau_{wC}=3.5e8$. The damping times of all the free modes with both tidal and core-mantle dissipation acting together are short compared with the age of the solar system, so we would expect all such amplitudes to be undetectable, at least for the near future, and the state and geometry of the core to be discernible with the radar and spacecraft measurements. Otherwise, we must seek still unspecified processes for their excitation. The obvious choice of a relatively recent collision by an asteroid or comet is improbable because of the short damping time scales.
G33A-04 INVITED 14:25h
Mars Geodesy and Cartography
A review of the history of the Mars geodesy and cartography is given leading up to the production of the landing site map of Meridiani for MER, produced before landing and having an absolute accuracy to about 100 meters.
G33A-05 14:40h
Improved Estimate of Phobos Secular Acceleration from MOLA Observations
We report on new observations of the orbital position of Phobos, and use them to obtain a new and improved estimate of the rate of secular acceleration in longitude due to tidal dissipation within Mars. Phobos is the inner-most natural satellite of Mars, and one of the few natural satellites in the solar system with orbital period shorter than the rotation period of its primary. As a result, any departure from a perfect elastic response by Mars in the tides raised on it by Phobos will cause a transfer of angular momentum from the orbit of Phobos to the spin of Mars. Since its discovery in 1877, Phobos has completed over 145,500 orbits, and has one of the best studied orbits in the solar system, with over 6000 earth-based astrometric observations, and over 300 spacecraft observations. As early as 1945, Sharpless noted that there is a secular acceleration in mean longitude, with rate (1.88 $\pm$ 0.25) 10$^{-3}$ deg/yr$^{2}$. In preparation for the 1989 Russian spacecraft mission to Phobos, considerable work was done compiling past observations, and refining the orbital model. All of the published estimates from that era are in good agreement. A typical solution (Jacobson et al., 1989) yields (1.249 $\pm$ 0.018) 10$^{-3}$ deg/yr$^{2}$. The MOLA instrument on MGS is a laser altimeter, and was designed to measure the topography of Mars. However, it has also been used to make observations of the position of Phobos. In 1998, a direct range measurement was made, which indicated that Phobos was slightly ahead of the predicted position. The MOLA detector views the surface of Mars in a narrow field of view, at 1064 nm wavelength, and can detect shadows cast by Phobos on the surface of Mars. We have found 15 such serendipitous shadow transit events over the interval from April 1999 to July 2004, and all of them show Phobos to be "ahead of schedule", and getting progressively farther ahead of the predicted position. In contrast, the cross-track positions are quite close to the predicted values. Assuming that the along-track discrepancy is small enough that we can linearize the corrections, we model the mean orbital longitude as a quadratic function of time, and solve for corrections to the constant, linear, and quadratic terms. The time span of the recent observations is insufficient to properly resolve this issue alone, but when the 127 years of prior observations are added, we find a solution which reduces misfit to the new observations considerably, and makes no significant change to the fit to earlier observations. Our estimate for the secular acceleration term is (1.367 $\pm$ 0.006) 10$^{-3}$ deg/yr$^{2}$. The corresponding rate of energy dissipation is 3.34 MW. From a geophysical perspective, a more interesting parameter than the secular acceleration itself is the tidal lag angle, or tidal quality factor Q, for Mars. Unfortunately, the limiting error source in that determination is remaining uncertainty in the tidal Love numbers at harmonic degrees 2, 3, and even 4. Until those parameters are better constrained, improvement in the orbital model of Phobos will not provide corresponding benefits for understanding the interior of Mars.
G33A-06 INVITED 14:55h
Recent advances in planetary gravity modeling: From global to local analysis.
One method of deciphering the near surface interior structure of a planet is through the joint analysis of its gravity and topography fields. Countless such studies have been undertaken for the Earth, and for a large portion of these, the analysis was performed in the spectral domain. Given the high spatial resolution of the measurements, and the generally small scale of the regions of interest in these studies, it was often appropriate to neglect the Earth's curvature and to utilize the assumption of Cartesian geometry. In doing so, many powerful methods become available to the analyst, such as multitaper spectral estimation methods and wavelet analysis techniques. In contrast, when analyzing the gravity fields of the other terrestrial planets, the assumptions of Cartesian geometry are no longer tenable. The primary gravity models for these bodies are often expressed in terms of global spherical harmonic coefficients, and these all have a much lower spatial resolution than that of the Earth. While localized spectral analysis techniques in Cartesian geometry have reached a certain level of maturity, analogous techniques in the spherical domain are still in their infancy. The purpose of this talk is to address the fundamental question of how one can obtain spectral estimates of a function expressed on a sphere that are localized to a certain "geographic" region. Using these localized spectral estimates, one can then calculate localized admittance and coherence functions, and then compare these with the predictions from a similarly localized model. Examples of this methodology will be applied to the planet Mars, showing how localized estimates of elastic thickness and load density can be obtained. The method described here is the spherical analog to Slepian's Cartesian concentration problem and Thomson's multitaper spectral estimation method. The first aspect of this method is to find a suitable windowing function in order to "localize" a geographic province on the sphere. By solving an optimization problem, a family of orthogonal functions are obtained. Next, localized spectral estimates can be obtained by multiply the data by these functions, and then expanding the resulting field in spherical harmonics. For the simple case when the input spectra is "white" we show that the localized spectral estimates are nearly unbiased. However, when the input spectra is "red" (which is the case of gravity of topography fields), the spectral bias can be significant. We show that the spectral estimates associated with a single localizing window are in general a poor approximation of the true localized spectra. However, by employing multiple data tapers, the multitaper spectral estimate becomes increasing robust as the number of windows increases.
http://geoweb.princeton.edu/people/resstaff/simons/Wieczorek+2004-GJI.html
G33A-07 15:10h
The Gravity Fields and Masses of Mars' Seasonal Icecaps
The atmosphere of Mars deposits CO2 on the polar caps during the fall and winter seasons, which is sublimed back into the atmosphere during spring and summer. This exchange of mass between the surface and the atmosphere is large enough to perturb spacecraft in orbit about the planet. These perturbations are seen as changes in the low degree gravity field of Mars, particularly the C3,0 term. However, obtaining reliable estimates of the seasonal masses from the gravity coefficients has proved difficult because of the correlations between the coefficients. We have developed an approach to estimating these seasonal masses from the tacking data by utilizing an icecap model in which we estimate the masses directly. This approach involves assuming a seasonal cap of given shape and depth, deriving the mass and gravity field of that cap for an assumed density, and adding that delta gravity field multiplied by a scale factor to the a priori static field, then solving for the scale factor that best fits the orbital data. In this approach, all the gravity coefficients are effectively included in the estimation for the adopted model. This approach has been applied to nearly 5 years of MGS tracking, using disks and cones to represent the seasonal caps, and has permitted the estimation of the seasonal caps with better confidence.
G33A-08 15:25h
Lunar Rotation, Orientation and Science
The Moon is the most familiar example of the many satellites that exhibit synchronous rotation. For the Moon there is Lunar Laser Ranging measurements of tides and three-dimensional rotation variations plus supporting theoretical understanding of both effects. Compared to uniform rotation and precession the lunar rotational variations are up to 1 km, while tidal variations are about 0.1 m. Analysis of the lunar variations in pole direction and rotation about the pole gives moment of inertia differences, third-degree gravity harmonics, tidal Love number k$_{2}$, tidal dissipation Q vs. frequency, dissipation at the fluid-core/solid-mantle boundary, and emerging evidence for an oblate boundary. The last two indicate a fluid core, but a solid inner core is not ruled out. Four retroreflectors provide very accurate positions on the Moon. The experience with the Moon is a starting point for exploring the tides, rotation and orientation of the other synchronous bodies of the solar system.