The Dynamical Environment of Dawn at Vesta

Dawn is the first NASA mission to operate in the vicinity of the two most massive asteroids in the main belt, Ceres and Vesta. This double-rendezvous mission is enabled by the use of low-thrust solar electric propulsion. Dawn will arrive at Vesta in 2011 and will operate in its vicinity for approximately one year. Vesta's mass and non-spherical shape, coupled with its rotational period, presents very interesting challenges to a spacecraft that depends principally upon low-thrust propulsion for trajectory-changing maneuvers. The details of Vesta's high-order gravitational terms will not be determined until after Dawn's arrival at Vesta, but it is clear that their effect on Dawn operations creates the most complex operational environment for a NASA mission to date. Gravitational perturbations give rise to oscillations in Dawn's orbital radius, and it is found that trapping of the spacecraft is possible near the 1:1 resonance between Dawn's orbital period and Vesta's rotational period, located approximately between 520 and 580 km orbital radius.This resonant trapping can be escaped by thrusting at the appropriate orbital phase. Having passed through the 1:1 resonance, gravitational perturbations ultimately limit the minimum radius for low-altitude operations to about 400 km,in order to safely prevent surface impact. The lowest practical orbit is desirable in order to maximize signal-to-noise and spatial resolution of the Gamma-Ray and Neutron Detector and to provide the highest spatial resolution observations by Dawn's Framing Camera and Visible InfraRed mapping spectrometer. Dawn dynamical behavior is modeled in the context of a wide range of Vesta gravity models. Many of these models are distinguishable during Dawn's High Altitude Mapping Orbit and the remainder are resolved during Dawn's Low Altitude Mapping Orbit, providing insight into Vesta's interior structure.Comment: Corrected normalization coefficients; updated table text and reference

The JPL Mars gravity field, Mars50c, based upon Viking and Mariner 9 Doppler tracking data

This report summarizes the current JPL efforts of generating a Mars gravity field from Viking 1 and 2 and Mariner 9 Doppler tracking data. The Mars 50c solution is a complete gravity field to degree and order 50 with solutions as well for the gravitational mass of Mars, Phobos, and Deimos. The constants and models used to obtain the solution are given and the method for determining the gravity field is presented. The gravity field is compared to the best current gravity GMM1 of Goddard Space Flight Center

About the various contributions in Venus rotation rate and LOD

% context heading (optional) {Thanks to the Venus Express Mission, new data on the properties of Venus could be obtained in particular concerning its rotation.} % aims heading (mandatory) {In view of these upcoming results, the purpose of this paper is to determine and compare the major physical processes influencing the rotation of Venus, and more particularly the angular rotation rate.} % methods heading (mandatory) {Applying models already used for the Earth, the effect of the triaxiality of a rigid Venus on its period of rotation are computed. Then the variations of Venus rotation caused by the elasticity, the atmosphere and the core of the planet are evaluated.} % results heading (mandatory) {Although the largest irregularities of the rotation rate of the Earth at short time scales are caused by its atmosphere and elastic deformations, we show that the Venus ones are dominated by the tidal torque exerted by the Sun on its solid body. Indeed, as Venus has a slow rotation, these effects have a large amplitude of 2 minutes of time (mn). These variations of the rotation rate are larger than the one induced by atmospheric wind variations that can reach 25-50 seconds of time (s), depending on the simulation used. The variations due to the core effects which vary with its size between 3 and 20s are smaller. Compared to these effects, the influence of the elastic deformation cause by the zonal tidal potential is negligible.} % conclusions heading (optional), leave it empty if necessary {As the variations of the rotation of Venus reported here are of the order 3mn peak to peak, they should influence past, present and future observations providing further constraints on the planet internal structure and atmosphere.}Comment: 12 pages, 10 figures, Accepted in A&

Venus Gravity Handbook

This report documents the Venus gravity methods and results to date (model MGNP90LSAAP). It is called a handbook in that it contains many useful plots (such as geometry and orbit behavior) that are useful in evaluating the tracking data. We discuss the models that are used in processing the Doppler data and the estimation method for determining the gravity field. With Pioneer Venus Orbiter and Magellan tracking data, the Venus gravity field was determined complete to degree and order 90 with the use of the JPL Cray T3D Supercomputer. The gravity field shows unprecedented high correlation with topography and resolution of features to the 2OOkm resolution. In the procedure for solving the gravity field, other information is gained as well, and, for example, we discuss results for the Venus ephemeris, Love number, pole orientation of Venus, and atmospheric densities. Of significance is the Love number solution which indicates a liquid core for Venus. The ephemeris of Venus is determined to an accuracy of 0.02 mm/s (tens of meters in position), and the rotation period to 243.0194 +/- 0.0002 days

Four problems in stratified flows

We extend the vorticity-based modeling approach of Borden & Meiburg (2013) to non-Boussinesq gravity currents and derive an analytical expression for the Froude number without the need for an energy closure. Via detailed comparisons with simulation results, we assess the validity of three key assumptions underlying both our as well as earlier models, viz. i) steady-state flow in the moving reference frame; ii) inviscid flow; and iii) horizontal flow sufficiently far in front of and behind the current. The current approach does not require an assumption of zero velocity in the current.Double-diffusive lock-exchange gravity currents in the fingering regime are explored via two- and three-dimensional Navier-Stokes simulations in the Boussinesq limit. The front velocity of these currents exhibits a nonmonotonic dependence on the diffusivity ratio and the initial stability ratio due to the competing effects of increased buoyancy and increased drag. Scaling arguments based on the simulation results suggest that even low Reynolds number double-diffusive gravity currents are governed by a balance of buoyancy and turbulent drag.The stability of an interface separating less dense, clear salt water above from more dense, sediment-laden fresh water below is explored via direct numerical simulations. We find that the destabilizing effects of double-diffusion and particle settling amplify each other above the diffusive interface, whereas they tend to cancel each other below. For large settling velocities, plume formation below the interface is suppressed. We identify the dimensionless parameter that determines in which regime a given flow takes place.The effects of shear on double-diffusive fingering and on the settling-driven instability are assessed by means of a transient growth analysis. Shear is seen to dampen both instabilities, which is consistent with previous findings by other authors. The shear damping is more pronounced for parameter values that produce larger unsheared growth. These trends can be explained in terms of instantaneous linear stability results for the unsheared case. For both double-diffusive and settling-driven instabilities, low Pr-values result in less damping and an increased importance of the Orr mechanism, for which a quantitative scaling law is obtained

Geophysical Exploration of Vesta

Dawn’s year-long stay at Vesta allows comprehensive mapping of the shape, topography, geology, mineralogy, elemental abundances, and gravity field using it’s three instruments and highprecision spacecraft navigation. In the current Low Altitude Mapping Orbit (LAMO), tracking data is being acquired to develop a gravity field expected to be accurate to degree and order ~20 [1, 2]. Multi-angle imaging in the Survey and High Altitude Mapping Orbit (HAMO) has provided adequate stereo coverage to develop a shape model accurate to ~10 m at 100 m horizontal spatial resolution. Accurate mass determination combined with the shape yields a more precise value of bulk density, albeit with some uncertainty resulting from the unmeasured seasonally-dark north polar region. The shape and gravity of Vesta can be used to infer the interior density structure and investigate the nature of the crust, informing models for Vesta’s formation and evolution

An Atmospheric Variability Model for Venus Aerobraking Missions

Aerobraking has proven to be an enabling technology for planetary missions to Mars and has been proposed to enable low cost missions to Venus. Aerobraking saves a significant amount of propulsion fuel mass by exploiting atmospheric drag to reduce the eccentricity of the initial orbit. The solar arrays have been used as the primary drag surface and only minor modifications have been made in the vehicle design to accommodate the relatively modest aerothermal loads. However, if atmospheric density is highly variable from orbit to orbit, the mission must either accept higher aerothermal risk, a slower pace for aerobraking, or a tighter corridor likely with increased propulsive cost. Hence, knowledge of atmospheric variability is of great interest for the design of aerobraking missions. The first planetary aerobraking was at Venus during the Magellan mission. After the primary Magellan science mission was completed, aerobraking was used to provide a more circular orbit to enhance gravity field recovery. Magellan aerobraking took place between local solar times of 1100 and 1800 hrs, and it was found that the Venusian atmospheric density during the aerobraking phase had less than 10% 1 sigma orbit to orbit variability. On the other hand, at some latitudes and seasons, Martian variability can be as high as 40% 1 sigmaFrom both the MGN and PVO mission it was known that the atmosphere, above aerobraking altitudes, showed greater variability at night, but this variability was never quantified in a systematic manner. This paper proposes a model for atmospheric variability that can be used for aerobraking mission design until more complete data sets become available

The impact of the Kuiper Belt Objects and of the asteroid ring on future high-precision relativistic Solar System tests

We preliminarily investigate the impact of the Kuiper Belt Objects (KBOs) and of the asteroid ring on some proposed high-precision tests of Newtonian and post-Newtonian gravity to be performed in the Solar System by means of spacecraft in heliocentric \approx 1 AU orbits and accurate orbit determination of some of the inner planets. It turns out that the Classical KBOSs (CKBOS), which amount to \approx 70% of the observed population of Trans-Neptunian bodies, induce a systematic secular error of about 1 m after one year in the transverse direction T of the orbit of a test particle orbiting at 1 AU from the Sun. For Mercury the ratios of the secular perihelion precessions induced by CKBOs to the ones induced by the general relativity and the solar oblateness J_2 amount to 6 10^-7 and 8 10^-4, respectively. The secular transverse perturbation induced on a \approx 1 AU orbit by the asteroid ring, which globally accounts for the action of the minor asteroids whose mass is about 5 10^-10 solar masses, is 10 m yr^-1; the bias on the relativistic and J_2 Mercury perihelion precessions is 6.1 10^-6 and 1 10^-2, respectively. Given the very ambitious goals of many expensive and complex missions aimed to testing gravitational theories to unprecedented levels of accuracy, these notes may suggest further and more accurate investigations of such sources of potentially insidious systematic bias.Comment: Latex2e, Elsevier macros, 5 pages, no figures, 1 table. To appear in Planetary Space Science. Small change in table's captio

Determination of Ceres mass based on the most gravitationally efficient close encounters

Here is presented recalculated value of the mass of Ceres, based on explicit tracking of its gravitational influence on orbits evolution of 21 selected asteroids during their mutual close encounters (CE). It was applied a new modified method (MM) for mass determination, based on the connecting of pre-encounter observations to the orbit determined from post-encounter ones. The calculated weighted mean value of Ceres mass, based on modified method, is $(4.54\pm0.07)\,10^{-10}M_{\odot}$ while standard procedure (SM) provided result of $(4.70\pm0.04)\,10^{-10}M_{\odot}$. We found that correlation between individual estimated masses based on modified and standard method is 0.78, which confirms reliability of using modified method.Comment: MNRAS:Accepted 2011 September 28. Received 2011 September 28; in original form 2011 January 2

Orbital effects of spatial variations of fundamental coupling constants

We deal with the effects induced on the orbit of a test particle revolving around a central body by putative spatial variations of fundamental coupling constants $\zeta$. In particular, we assume a dipole gradient for \zeta(\bds r)/\bar{\zeta} along a generic direction \bds{\hat{k}} in space. We analytically work out the long-term variations of all the six standard Keplerian orbital elements parameterizing the orbit of a test particle in a gravitationally bound two-body system. It turns out that, apart from the semi-major axis $a$, the eccentricity $e$, the inclination $I$, the longitude of the ascending node $\Omega$, the longitude of pericenter $\pi$ and the mean anomaly $\mathcal{M}$ undergo non-zero long-term changes. By using the usual decomposition along the radial ($R$), transverse ($T$) and normal ($N$) directions, we also analytically work out the long-term changes $\Delta R,\Delta T,\Delta N$ and $\Delta v_R,\Delta v_T,\Delta v_N$ experienced by the position and the velocity vectors \bds r and \bds v of the test particle. It turns out that, apart from $\Delta N$, all the other five shifts do not vanish over one full orbital revolution. In the calculation we do not use \textit{a-priori} simplifying assumptions concerning $e$ and $I$. Thus, our results are valid for a generic orbital geometry; moreover, they hold for any gradient direction (abridged).Comment: Latex2e, 20 pages, 1 figure, 7 tables. Version accepted by Monthly Notices of the Royal Astronomical Society (MNRAS). Error in the caption of Table 5 corrected. References update