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NASA NTRS1972

Equivalent gravity modes - An interim evaluation

The behavior of the main solar semidiurnal tidal mode in a dissipative atmosphere is studied both in a rotating spherical atmosphere and by means of the equivalent gravity mode approximation. Coefficients are chosen to crudely simulate the effects of molecular viscosity and conductivity. Major findings are: (1) Below 130 km, where friction is unimportant, equivalent gravity mode results are, for all practical purposes, identical to those at the equator obtained from a spherical calculation. (2) Above 130 km amplitudes over the equator obtained from the spherical calculation are about 30 percent smaller than those obtained from the equivalent gravity mode calculations. Also, there is a 15 deg (1/2 hour) difference in phase. (3) The amplitude reduction over the equator, is associated with a broadening of the latitude distribution of amplitude for the oscillatory pressure and temperature fields within the thermosphere. There is also significant variation of phase with latitude within the thermosphere. Associated with the above variations are significant changes in the latitude distribution of horizontal velocity within the thermosphere.

Lindzen, R. S.↗

NASA NTRS2019

Deviation of the Shape of Bennu from Rotational Figures of Stability

Images of asteroid (101955) Bennu acquired by the OSIRIS-REx mission reveal a rocky world covered in rubble; Shape deviates from hydrostatic surface; Internal friction and/or cohesion even if no tensile strength; Understanding the deviation of the surface from idealized shape may help constrain mechanical properties of the interior; Geologic evolution of Bennu is driven by downslope migration of surface material and rubble; May be caused by YORP-induced spin-up, re-accumulation, impact-induced seismic shaking, thermal stresses, or tidal disruption by close encounters to larger bodies.

Roberts, J. H.↗

NASA NTRS1984

A reappraisal of Darwin's fission hypothesis and a possible limit to the primordial angular momentum of the Earth

G. H. Darwin proposed that the primordial Earth may have rotated fast enough that the solar tidal period was nearly resonant with the fundamental free oscillation period of a fluid Earth and that a large and unstable tidal oscillation split off to become the moon. Jeffreys argumented that dissipation during resonance would be sufficient to prevent such an unstable oscillation greater than the tidal frequency (period - 2.68 hr). It is considered that solar tides have extracted angular momentum from the Earth-Moon system over 4.5 b.y. The correspondence of the primordial tidal and resonant frequencies is nearly exact. (The effect of central condensation of the proto earth is to increase both frequencies by a similar amount, though the resonance is not precisely known. This result, was unknown to Darwin or Jeffreys. The effects of resonance were evaluated. The resonance is likely to be too damped for fission. This argument is more general than Jeffreys', who considered friction between the oscillating mantle and a rigid core. It is argued that the fact that Q must be so great for fission that equilibrium can not be maintained; the fluid proto Earth passes so quickly through resonance that maximum amplitude is not reached. It is suggested that solar resonant tides acted as a brake on the spin of the primordial partially molten Earth. Certain proposed origins for the Moon do not necessarily involve addition of substantial amounts of angular momentum to the Earth-Moon system. The primordial Earth-Moon system may have had nearly the same angular momentum as it has today.

Mckinnon, W. B.↗

NASA NTRS1989

Thermal state of an ice shell on Europa

The thickness of the ice shell presently hypothesized for Europa, which is decoupled from a silicate core by a liquid water layer, is calculated as a function of colatitude and longitude under suitable assumptions for two plausible ice rheology behaviors: that of Maxwell type, and that of generalized flow-law rheology. Due to the dissipation rate's pronounced temperature dependence, virtually all tidal dissipation is found to concentrate in the lowest few kilometers of the shell. While for some parameter choices an insulating regolith that raises the near-surface temperature by more than a few tens of degrees C may stabilize the shell against polar wander, a modest regolith may enhance the probability of such wander's occurrence through the reduction of the shell's retarding friction.

Ojakangas, Gregory W.↗

NASA NTRS1989

A complete spherical harmonic approach to luni-solar tides

In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni-solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides - for any theory - appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.

Dickman, S. R.↗

NASA NTRS1978

On the accelerations of the moon and sun, the constant of gravitation, and the origin of mountains

On the assumption of a constant value for the gravitational constant G, the lunar and solar tidal couples and the rate of change of angular velocity of the earth are recalculated on the basis of the improved values for the apparent accelerations of the moon and sun arrived at by Muller and Stephenson (1977). These new values are then used to derive general dynamical equations with a changing moment of inertia and changing G connecting the apparent accelerations to the lunar and solar couples. The effect of a changing G is considered, and a value of (dG/dt)/G = -3 times 10 to the -11th power per yr can be reconciled only weakly with the improved accelerations, especially for the case of linear friction. For quadratic friction the situation is more favorable. The new accelerations, however, are best reconciled with a nonchanging G, and certainly cannot be reconciled with a value of (dG/dt)/G = -6 times 10 to the -11th power per yr.

Lyttleton, R. A.↗