Investigations of Martian Geodesy Through Lander Tracking
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Mars Pathfinder Viking doppler radar↗
Engineering topics
Yoder, C. F.
Publications and source records attributed to Yoder, C. F..
Venusian k(sub 2) Tidal Love Number from Magellan and PVO Tracking Data
The k(sub 2) potential ove number which scales the tidal deformation of Venus by the Sun has been estimated from Doppler tracking of Magellan and Pioneer Venus Orbiter (PVO) spacecraft data. The nominal range for k(sub 2) from theoretical models is 0.23(less than or equal to)k(sub 2)(less than or equal to)0.29 for a liquid iron core and about 0.17 if the iron core has solidified. Our best estimate of this parameter is k(sub 2) = 0.295 +/- 0.662 (2X formal {delta}) and supports the hypothesis that Venus core is solid.
orbiter pvo↗
Mars Dynamics from Earth-Based Tracking of the Mars Pathfinder Lander
Measurements of Mars' rotational variations can be conducted via Earth-based radio tracking observations of the Mars Pathfinder lander during an extended mission. Two-way range measurements between an Earth antenna and the lander will enable precise monitoring of the planet's orientation and length-of-day variation, allowing details of Mars' internal structure and global surface/atmosphere interactions to be determined with precision for the first time.
two-way↗
Deep mantle viscous structure with prior estimate and satellite constraint
A radially stratified and incompressible earth model with secular variation of the second degree gravity field J-dot(2) is used here to test sensitivity of data to viscosity increases with depth and convective boundary layer structure. Prior estimates and observed nontidal J-dot(23)(-C-dot(20)) are consistent with a layered lower mantle viscosity. Details of this layering are examined by comparing predicted and observed J-dot(3), J-dot(4). Speculation that a high-velocity layer exists above D-double prime is considered. With a 650-km thick deep high-viscosity layer, the remaining lower mantle is in one of two ranges: 1.5 to 3.5 x 10 exp 20 or 3.5 to about 10 exp 22 Pa s.
Ivins, E. R.↗
The connection between Venus' free obliquity and its CMB oblateness
The most striking feature of Venus rotational state is its slow retrograde rotation which is apparently maintained by a balance between solid tidal friction and thermal tidal torques. Solid tides tend to drive the spin toward synchronous rotation while thermal tides drive it away. A balance is achieved at a specific rate because of the inverse frequency dependence of the thermal tide to the semi-diurnal heating. Atmospheric models have been constructed to estimate the thermal tidal torque based on ground heating. The solid friction dissipation factor Q approximately equal to 50 can be deduced assuming rotation has achieved steady state. The most perplexing feature of Venus orientation is its non-zero free obliquity epsilon approximately equal to 1.5 deg relative to its orbit. Although solid tides and perhaps atmospheric tides tend to increase the free obliquity on a time 1/K(sub t) approximately equal to 1 x 10(exp 8) yr, viscous friction (CMF) at a core-mantle boundary (CMB) resulting from the differential angular orientation Delta-epsilon of the core and mantle spin axes should have damped the free obliquity on a time scale as short as 10(exp 6) yr. One means of achieving a balance similar to that controlling rotation is to introduce a comparatively large CMB ellipticity e(sub c) to reduce Delta-epsilon such that there is a balance between solid-thermal tides and CMF. The balance depends not so much on the potential frequency dependence on the tides as on the quadratic dependence of CMF on Delta-epsilon if the layer is turbulent.
Yoder, C. F.↗
Phobos' gravity field and its influence on its orbit and physical librations
A model describing the physical libration in longitude and latitude for Phobos is derived. The major effect is the well-known longitude variation with the anomalistic orbital period and amplitude. Several additional meter-sized periodic librations in longitude exist. The latitude variation is dominated by the forced precession of Phobos' figure axis with the precession of Phobos' orbital plane. The contribution of Phobos' topography to its gravity field is estimated using the control network model of Duxbury and Callahan (1989).
Borderies, N.↗
Orbits and masses of Saturn's co-orbiting satellites, Janus and Epimetheus
An attempt is made to provide a constraint on the combined mass of Janus and Epimetheus from an analysis of Voyager I and Voyager 2 data and ground-based observations obtained during the 1966 and 1980 ring plane crossings. The results of the analysis presented here suggest that the total mass is 2.59 + or - 0.26 x 10 to the 21st g, the mass ratio is 3.61 + or - 0.01, and Janus' density is 0.67 + or - 0.10 g/cu cm. The low density of Janus is attributed to its porosity rather than composition.
Yoder, C. F.↗
1960 Chile - New estimate of polar motion excitation
A recent reanalysis of the International Latitude Serivce (ILS) polar motion data-day has been processed using Kalman filtering techniques to generate the polar motion excitation function over the time-span from 1960 to 1965. The resulting excitation function has been examined for the effects of 1960 Chile in an attempt to determine experimentally how large earthquake affect polar motion. The resulting upper bound of about 75 x 10 to the 22nd N-m for a 10-deg dip (about 36 x 10 to the 22nd N-m for 20-deg dip) is consistent with results obtained from previous seismic studies, including a recent normal mode excitation result. Following future great earthquakes, monitoring of polar motion by space-based techniques such as VLBI should continue at high temporal resolution for several weeks in order to directly measure the rheological parameters of the upper mantle.
Slade, M. A.↗
The dynamics of coorbital satellite systems
The dynamical behavior of N coorbital satellites moving with the same average mean motion around a primary has been studied both analytically and by numerical integrations for N from 2 to 9 satellites. Simplified dynamical equations are used to determine the different stationary configurations and their local stability against infinitesimal perturbations. The ring of equally spaced identical satellites is found to be locally unstable for N of six or less, while for N from two to eight there exists another stable compact stationary configuration with separations of 60 deg or less between adjacent satellites. For N of seven or more the equally spaced configuration becomes locally stable, and for N of nine or more it is the only stationary configuration. The motion becomes chaotic for large-amplitude perturbations. The chaotic motion fills a restricted region of phase space whose outer boundary is determined by the maximum velocity curve.
Salo, H.↗
Dynamics of coorbital satellite rings
The dynamical behavior of a coorbital satellite ring is studied for N = 2-9 satellites, in terms of a simplified dynamical description, in which the motion is reduced to the separation angles between satellites. The number and stability of different kinds of stationary configurations is explored, revealing that equally spaced rings are not stable against small perturbations for N not greater than 6, while for N = 2-8 there exists another, stable compact solution. Integrations of exact equations confirm these results. Moreover, the systems are found to display chaotic characteristics for a certain range of energy. The behavior can be interpreted in terms of maximum velocity curves, defining the allowed region of the motion in the phase space.
Salo, H.↗
Improved analytic nutation model
Models describing the earth's nutations are discussed. It is found that the simple model of Sasao et al., (1981) differs from Wahr's (1981) theory term by term by less than 0.3 marcsec if a modern earth structure model is used to evaluate the nutation structure constants. In addition, the effect of oceans is estimated.
Yoder, C. F.↗
The size of the lunar core
A 0.2 arc second phase shift in the 18.6 year forced precession of the lunar figure was inferred from analysis of lunar laser ranging data. The source of the phase shift is either viscous friction at a lunar core mantle boundary or solid friction caused by tidal flexing of the Moon by the Earth. Core mantle viscous coupling will explain the signature if the core radius R sub c approximately equals 330 km. On the other hand, solid friction can account for the signature only if the lunar solid friction 0 approximately equals 30 is abnormally small compared with that observed for, say, Mars (approximately equals 100 - 200). Although the inferred core radius is certainly within the limits imposed by the Apollo seismic experiment, it is significantly smaller than estimates of order 400-500 km from electromagnetic sounding. How accurate is the estimate of the R sub c derived from the phase shift? The effect of uncertainties in the frictional coupling mechanism, core density and ellipticity on the inferred core radius are discussed. The excitation of lunar free librations by core turbulence vis-a-vis other mechanisms (e.g., cometary or asteroidal impacts) and the influence of changes in lunar precession in the past on lunar dynamo generation are also examined.
Yoder, C. F.↗
Tidal dissipation in the Earth and Moon from lunar laser ranging
The evolution of the Moon's orbit which is governed by tidal dissipation in the Earth while the evolution of its spin is controlled by its own internal dissipation is discussed. Lunar laser ranging data from August 1969 through May 1982 yields the values of both of these parameters. It is suggested that if the Moon was orbited the Earth since its formation, this must be an anomalously high value presumably due to changes in dissipation in the oceans due to continental drift. The explanation that the dissipation occurs at the interface between the mantle and a liquid core of shell is preferred.
Yoder, C. F.↗
Secular variation of earth's gravitational harmonic J2 coefficient from Lageos and nontidal acceleration of earth rotation
Analysis of 5.5 years of Lageos satellite range data reveal significant residual nodal signatures: an acceleration and annual and semiannual periods. These signatures primarily reflect variations in the zonal gravitational harmonic J2 coefficient and hence the polar moment of inertia. The implied decrease of J2 = -3 x 10 to the -11th/yr is consistent with both historical observations of the nontidal acceleration of the earth's rotation and models of viscous rebound of the solid earth from the decrease in load due to the last deglaciation.
Yoder, C. F.↗
Theory of motion of Saturn's coorbiting satellites
A simple analytic theory describing the 1:1 orbital resonance is presented and applied to Saturn's coorbiting pair, 1980S1 and 1980S3. These satellites are very small and can approach to within 15,000 km, but are prevented from passing each other by their mutual gravitational interaction. The long-term stability of the S1-S3 orbital configuration is discussed in this paper, and a tie between the 1966 and 1980 observations is established.
Yoder, C. F.↗
Tidal rigidity of Phobos
A novel scenario is proposed in which the orbital eccentricity of Phobos results from several gravitational resonance excitations within the past one billion years, assuming that tidal friction in Phobos has had only a small effect on its orbit. Both the primordial eccentricity and inclination may have been much smaller than presently observed. Constraints imposed on tidal friction in Phobos by the apparent age of its surface, which is greater than one billion years, in addition to those of the gravitational resonance excitation scenario, can be satisfied only if the product of the rigidity and the Q factor is greater than 10 to the 12th dynes/sq cm. In view of the fact that the Q factor is only about 100, so that the rigidity must be greater than 10 to the 10th dynes/sq cm, Phobos should have substantial internal strength.
Yoder, C. F.↗
Results from lunar laser ranging data analysis
The lunar laser range data taken at McDonald Observatory between Aug. 1969 and May 1980 has been analyzed. The simple rms residual for the 2954 ranges is 31 cm. Results of the analysis include GM(earth) = 398600.45 cu km/sec sq within 0.02 cu km/sec sq and a secular acceleration of the lunar orbital mean longitude of -23.8 arcsec/sq century within 1.5 arcsec, which yields a Q of 12.3 at semidiurnal frequencies. The lunar harmonic C30 is -8.7/1,000,000 within 0.000001 and the lunar rotational dissipation of 0.0047 within 0.0005 day. Also resulting from the solution are geocentric coordinates of McDonald accurate to 30 cm, including the first value for the longitude with the new IAU constants and a dynamical equinox.
Dickey, J. O.↗
The gravitational interaction between inclined, elliptical rings
An expression for the potential for two elliptical, inclined rings is derived from a model in which the gravitational torque between two wide rings or within a ring of finite width can prevent differential precession caused by planetary oblateness. The model was proposed to explain the observed eccentricity and width variations of the Uranian epsilon ring. The stationary solutions and stability of this system are examined.
Yoder, C. F.↗