With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes the measurement of the seasonal changes in the gravity coefficients (e.g., (J) over bar (2), (J) over bar (3), (C) over bar (21), (C) over bar (21), (S) over bar (21), (C) over bar (31), (S) over bar (31) ) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Mars' spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of (C) over bar (21) and (S) over bar (21). A strong annual signature is observed in (C) over bar (21), and this is it Mixture of polar motion and ice mass redistribution. The Love number Solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data [Yoder et a]., 2003. Science 300, 299-303], giving a combined solution of k(2) = 0. 152 +/- 0.009 using MGS and Odyssey tracking data. The solutions for the masses of the Mars' moons show consistency between MGS, Odyssey, and Viking data sets; Phobos GM = (7.16 +/- 0.005) x 10(-4) km(3)/s(2) and Deimos GM = (0.98 +/- 0.07) x 10(-4) km(3)/s(2). Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga. (c) 2006 Elsevier Inc. All rights reserved.

The predicted orientation of Venus' rotation axis relative to its orbit can be uniquely determined given knowledge of its J(2) gravity coefficient and polar moment of inertia C if its free obliquity is fully damped. This assumption seems warranted given the dominant damping mechanism: turbulent fluid friction at a core mantle boundary (CMB). This skin friction results from differential obliquity of mantle and core spin axes, and the associated damping rare could be as short as 1/10(6) year. However, the observed pole orientation indicates a free obliquity amplitude epsilon similar or equal to 2.1 degrees compared with a nominal forced amplitude of 0.5 degrees. There are two plausible explanations. The most likely is that the observed obliquity is a tidally evolved end state in which core friction, modulated by CMB ellipticity and core obliquity amplitude, counterbalances solid and atmospheric tidal torques. This concept is similar to the explanation for the retrograde spin omega as an end state in which solid and atmospheric thermal tidal torques balance at the present spin rate because of the omega(-1) dependence of the axial thermal torque. Large core ellipticity e(c) drop (C-c - 1/2(A(c) + B-c))/C-c (C-c greater than or equal to B-c greater than or equal to A(c) are core moments of inertia) can substantially increase fluid friction damping time if e(c) is significantly larger than the whole body ellipticity e(o) = J(2)MR(2)/C similar or equal to 1.3 x 10(-5) by reducing the relative obliquity of core and mantle spin vectors. Note that the hydrostatic contribution to oblateness similar to 1.7 x 10(-7) is presently negligible. Weaker effects such as solid and thermal tides can then compete with core friction and for plausible models, their sum tends to increase free obliquity. The obliquity balance is controlled by the nonlinear (and nearly quadratic) dependence of the CMB turbulent ''skin friction'' torque on obliquity. I find that a steady state is achieved for e(c) similar or equal to 29e(o) similar or equal to 4 x 10(-4). If the CMB topography is dynamically supported, then the necessary bottom density anomaly is constrained to the bottom similar to 10% of the mantle.An alternative model is that the obliquity results from resonant excitation due to small amplitude (less than or equal to 0.002 degrees), prograde oscillations in Venus' orbit, one of which happens nearly to match Venus' precession rate sigma. This mechanism can account for the obliquity even if the iron core has solidified, but also requires a tectonically quiescent planet (d\J(2)/dt\ < 10(-15) year(-1)). This model has been explored numerically for a wide range of initial conditions, tidal parameters, temporal J(2) variations, and chaotic wander of the driving frequencies for the orbit. Only four frequencies, in or near the predicted band for sigma, have a significant effect and also have a narrow range of effectiveness. I estimate the polar moment to be in the range 0.0341. (C/MR(2)) less than or equal to 0.331 and hence the precession rate a to be in the range 44.1 less than or equal to sigma less than or equal to 45.8('') year(-1) based on construction of a suite of density profiles in which mantle composition and core size have theoretically limited variations. Comparing resonance widths to the a uncertainty, I find that the resonance hypothesis has about a 30% chance of being correct.Core ellipticity also has a profound effect on tidal evolution of Venus obliquity. The ratio of turbulent core and solid tidal friction scales like omega(-4), implying that core friction ''turns on'' only as the spin omega approaches its end state. I also find that the semiannual atmospheric tide can have a dramatic effect on evolution, allowing for inversion of spin orientation from prograde to retrograde if the initial obliquity is sufficiently large (greater than or equal to 45 degrees).Potential measurements which have a bearing on these models including precession rate, tidal Love number k(2), and semidiurnal variation in atmospheric pressure at Venus' surface. Perhaps the most useful parameter is k(2), which is detectable from orbit, requires only a modest improvement in the tracking accuracy and spacecraft stability over that provided by Magellan, and is an excellent proxy for core fluidity and if fluid, core size and composition. (C) 1995 Academic Press, Inc.

The dynamic plausibility of various ideas on the origin of the Trojans is briefly discussed. We take the point of view that the present, tightly bound population has secularly evolved through some mechanism from less to more tightly bound orbit configurations. The mechanisms considered are changes in the Jovian mass or semimajor axis during planetary formation, collisional interactions with external, asteroidal material, and cometary outgassing.

The structure of planet Earth and the dynamics of its constiruent parts have received the intel- lectual attention of natural philosophers since ancient times. Only in the present century has the quantitative, physics-oriented approach led to a deeper and more profound understanding of the subject, and only in the past two decades has the role of satellite data become both well established and centrally important. As we strive to leam more about geodesy from satellite data we are compelled to take into account that the data contain the effects of the atmosphere, noise and bias to the geode- sist but signal to the meteorologist. Thus, it is not su¡prising that branches of geophysics other than geodesy are directly involved in the properinterpretation of satellite data. The relation between atmospheric angular momentum and the length of day, for example, compels geophysicists to understand the fluid dynamics of the eafh's cores and atmosphere, and the coupling between them. Coupling occurs throughout the âisciplines of geophysics, including geodesy, and is the theme of this chapter. Beyond the Earth we realize that geophysical techniques, particularly those based on a¡tificial satellites, allow us to study the other planets in the sola¡ system. In less than one year after the meeting in Erice that led to this report the planet Neprune will have been visited by a spacecraft. Interesting as such "flybys" may be, future studies of the other planets would benefit considerably from satellite data, one of the subjects treated in this chapter. Ca¡eful design of inteqplaneta,ry space probes can convert the sola¡ system into a huge iaboratory for experimental physics. Gravity is the subject of primary interest. The most enigmatic force in Nature, it is the focus of experiments on all scales, from antiproton experi- ments th-rough geophysical investigations of the Newtonian constant to the large scale pro- jects proposed and discussed in this chapter. The interaction betwe'.,n satellite geodesy and fundamental physics is intriguing and represents the breadth and depth of geophysics.