Engineering topics

Yoder, C. F.

Publications and source records attributed to Yoder, C. F..

47 records · Page 3

NASA NTRS1981

The free librations of a dissipative moon

It is noted that dissipation in the moon produces a small offset (approximately 0.23 arcsec) of the moon's rotation axis from the plane defined by the ecliptic and lunar orbit normals. Both solid body tidal friction and viscous fluid friction at a core-mantle interface are thought to be plausible mechanisms. The merits of both are discussed, and it is found that solid friction requires a low lunar tidal Q (approximately 28), whereas turbulent fluid friction requires a core with a radius of approximately 330 km to cause the signature observed by lunar laser ranging. Large (approximately 0.4-8.0 arcsec) free librations of the lunar figure have also been detected through laser ranging. Both a very recent impact on the moon and fluid turbulence in the lunar core are considered plausible mechanisms for generating these librations.

Yoder, C. F.↗

NASA NTRS1981

The tides of Io

A theory is developed for the origin and evaluation of the orbital resonances between the Galilean satellites Io, Europa and Ganymede as a result of the effects of dissipative tides in Jupiter and its satellites. Following a preliminary consideration of the consequences of tidal interaction for satellite orbits and a comprehensive Hamiltonian theory of the resonance interactions which allows terms up to third order in eccentricity to be included, a dynamic model of the origin and evolution of the resonance locks is presented in which the relative expansion of the orbits by tidal torques from Jupiter together with tidal dissipation in Io lead to the rapid driving out of Io until it is captured into a 2:1 resonance with Europa and the resonance with Ganymede is achieved. Consideration of the effects of other commensurabilities on the orbital evolution of the system reveals that second-order Laplace-like resonances would act to excite free eccentricites, while the resonances associated with the two-body 3:1 commensurability could not have been encountered. Analysis of the hypothesis that the Laplace relation is primordial shows that the bounds on the tidal dissipation of Jupiter still can not be relaxed. Recent determinations of the tidal dissipation in Jupiter are discussed, and it is noted that none is sufficiently small to be consistent with the high heat flux estimates for Io. Finally, the possibility of the observational determination of the tidal dissipation in Jupiter by the measurement of the secular acceleration of Io's main motion is considered.

Yoder, C. F.↗

NASA NTRS1981

Short period tidal variations of earth rotation

It is explained that the tidal deformation of the earth's polar moment of inertia by the moon and sun cause periodic variations in rotation. The short period oscillations give rise to a meter-sized, diurnal signature in the lunar laser ranging data obtained at McDonald Observatory. A solution is given for the scale parameter k/C at fortnightly and monthly tidal frequencies. The results are compared with those obtained by other investigators and with a theoretical estimate which includes the effect of oceans and a decoupled fluid core.

Yoder, C. F.↗

NASA NTRS1981

Tidal variations of earth rotation

The periodic variations of the earths' rotation resulting from the tidal deformation of the earth by the sun and moon were rederived including terms with amplitudes of 0.002 millisec and greater. The series applies to the mantle, crust, and oceans which rotate together for characteristic tidal periods; the scaling parameter is the ratio of the fraction of the Love number producing tidal variations in the moment of inertia of the coupled mantle and oceans (k) to the dimensionless polar moment of inertia of the coupled moments (C). The lunar laser ranging data shows that k/C at monthly and fortnightly frequencies equals 0.99 + or - 0.15 and 0.99 + or - 0.20 as compared to the theoretical value of 0.94 + or - 0.04.

Yoder, C. F.↗

NASA NTRS1980

Geophysical parameters of the earth-moon system

Doppler tracking data from Lunar Orbiter 4 have been combined with laser ranging data from lunar retroreflectors to yield a number of geophysical and geodetic parameters for the earth and moon. This joint solution gives values of (1) the lunar principal polar moment C/M R squared = 0.3905 plus or minus 0.0023, (2) GM(E) = 398600.461 plus or minus 0.026 cu km/sq s, and (3) an earth/moon mass ratio at 81.300587 plus or minus 0.000049. Also determined are the harmonics of a complete lunar gravity field through degree and order 5, the obliquity of the lunar pole, selenocentric coordinates of the lunar retroreflectors, geocentric coordinates of the McDonald Observatory, and the lunar secular acceleration. The lunar potential Love number is weakly determined at 0.022 plus or minus 0.013, and a suprisingly large dissipation of rotational energy is inferred, though either solid body tidal dissipation or liquid core mantle interactions could be causes.

Ferrari, A. J.↗

NASA NTRS1979

Notes on the origin of the Trojan asteroids

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.

Yoder, C. F.↗

NASA NTRS1979

Does Venus wobble

The free wobble damping time for Venus due to solar tides and rotational flexing is found to be approximately 700,000 times Q sub omega years, where Q sub omega is the dissipation function associated with the wobble frequency. The slow spin and expected small (nonhydrostatic) J2 predict a very long wobble period of about 100,000 years. As a result, a simple scaling of the earth's Chandler wobble excitation rate to that of Venus suggests that an appreciable wobble could exist. Detection (or lack thereof) of a free wobble may thus place constraints on the dynamic activity (e.g., mantle convection, Venusquakes, etc.) of the Venus interior.

Yoder, C. F.↗

NASA NTRS1979

How tidal heating in Io drives the Galilean orbital resonance locks

The mechanisms by which orbital resonance locks are maintained among Io, Europa and Ganymede are analyzed, and the effects of the dissipative tides in Jupiter and Io on their establishment and evolution are considered. According to the proposed model, initially all three satellites are in orbits far from the 2:1 commensurabilities or the three body lock. The tide raised on Io damps down the free eccentricity; only modest tidal heating occurs. Subsequently the dissipative tide raised on Jupiter by Io causes Io's orbit to spiral outwards; Io approaches the 2:1 commensurability with Europa. Io's forced eccentricity increases rapidly to a critical value, and thereafter the resonant interaction causes Europa's orbit to expand at half that of Io's orbit. A fluid core is probably formed as the result of tidal heating. Finally Europa approaches the 2:1 commensurability, angular momentum is transferred from Europa's orbit to Ganymede's, and a steady state is attained. On the basis of the observed three-body resonance amplitude (0.066 deg), it is concluded that three-body resonance may have formed less than 500 million years ago; a measurement of the rate of tidal heating in Io may determine the Q value of both Io and Jupiter. Upper and lower limits for the Jovian Q value of 2 million and 20,000 are suggested.

Yoder, C. F.↗

NASA NTRS1979

Diagrammatic theory of transition of pendulum like systems

Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.

Yoder, C. F.↗

NASA NTRS1978

Tidal acceleration of the moon

The analysis of eight years of lunar laser ranging data yields a value for the tidally induced secular acceleration of the lunar orbital longitude of -23.8 + or - 4 arcsec/century per century. For semidiurnal tidal frequencies this corresponds to a terrestrial Q = 12 + or - 2. The error in n is dominated by noise in the data and its modeling. The error is expected to decrease significantly as future data become available and it may become possible to detect an 18.6-yr periodic modulation of the acceleration which would allow the separation of the effects of diurnal and semidiurnal tides. Comparison of the secular acceleration with values published from the analysis of classical astronomical observations does not show a significant difference which can be attributed to a changing gravitational constant.

Williams, J. G.↗

NASA NTRS1973

On the establishment and evolution of orbit-orbit resonances

A theory which suggests that in the case of planetary satellites, a tidally induced torque acting on the satellites may play an essential role on the evolution of the observed resonances is investigated as it applies to the three resonances among pairs of satellites of Saturn. Three stages are investigated: a theoretical description of transition is developed for a simple time dependent pendulum plus constant applied torque; the two body gravitational interaction is expanded and reduced to a one dimensional time independent Hamiltonion; and the model is applied to Saturn resonances. Although the theory proves successful in the Saturn case, it is less successful in the Tital-Hyperion case in providing a resonable time scale for the damping of the amplitude of liberation.

Yoder, C. F.↗