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A strong thirteenth-order resonance has been observed in an analysis which is based on U.S. Navy tracking data regarding the slowly decaying orbit of a Diademe 2 fragment. The exact commensurability for the orbit occurred in late 1973. The major changes due to the resonance were over by late 1974. Approaches for a significant improvement of thirteenth-order geopotential terms are discussed.
Three of Uranus' satellites are involved in an interaction similar to the Laplace relation among the Galilean satellites of Jupiter. However, there are no pair-wise commensurabilities in the Uranus system as there are among the Galilean satellites. Thus analysis by Fourier expansion of disturbing functions becomes too unwieldy for practical calculation. Instead, the unexpanded perturbations are numerically averaged over a time scale short compared to the important variations in the Laplace relation. Perturbations of Miranda's orbit are estimated to be of observable magnitude for reasonable masses of Ariel and Umbriel.
A first order, semianalytical theory for the long term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal and tesseral harmonics as well as luni solar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J sub 2 and J sub 22 harmonics. Global, long term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.
Equations were derived for the perturbations on an artificial satellite when the motion of the satellite is commensurable with that of the earth. This was done by first selecting the tesseral harmonics that contribute the most to the perturbations and then by applying Hori's method by use of Lie series. Here, are introduced some modifications to the perturbations, which now result in better agreement with numerical integration.
The design of an economically viable supersonic cruise aircraft requires the lowest attainable structural-mass fraction commensurate with the selected near-term structural material technology. To achieve this goal of minimum structural-mass fraction, various combinations of promising wing and fuselage primary structure were analyzed for the load-temperature environment applicable to the arrow wing configuration. This analysis was conducted in accordance with the design criteria specified and included extensive use of computer-aided analytical methods to screen the candidate concepts and select the most promising concepts for the in-depth structural analysis.
A detailed analysis of the spiral scan was performed for antenna sizes ranging from 20 inches to 36 inches in diameter and for search angles characteristic of both the radar and the communication acquisition modes. The power budgets for passive target radar detection were calculated for antenna diameters ranging from 20 to 36 inches. Dwell times commensurate with spiral scan were used for these budget calculations. The signal design for the candidate pulse Doppler system is summarized. Ground return analysis carried out for the passive target radar mode is examined, and the details are presented. A concluding description of the proposed candidate radar/communication system configuration is given.
The Lockheed L-1011 automatic flight control systems - yaw stability augmentation and automatic landing - are described in terms of their redundancies. The reliability objectives for these systems are discussed and related to in-service experience. In general, the availability of the stability augmentation system is higher than the original design requirement, but is commensurate with early estimates. The in-service experience with automatic landing is not sufficient to provide verification of Category 3 automatic landing system estimated availability.
Second-order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. These effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly. They have the same period and phase as first-order resonance perturbations. But their amplitudes are proportional to the square of the period and dominate the first-order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18-day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this 1 arc sec (31 m) variation yields a strong fourteenth-order constraint to the geopotential field for odd degree terms. This constraint (lumped coefficient) is poorly predicted by most current models.
Reductions of Mariner 9 TV data of Phobos and Deimos tend to corroborate the existence of a secular acceleration of Phobos commensurate with two recently reported values based on a reprocessing of earth-based data. These values of secular acceleration have been used together with Mariner 9 data on the physical size of Phobos and earth-based photoelectric observations which infer a carbonaceous composition for Phobos to place upper and lower bounds of 50 and 150, respectively, on the tidal dissipation function of Mars. The corresponding upper and lower bounds on the tidal lag angle are 0.19 and 0.57 deg.
A mechanism is investigated which may provide an evolutionary explanation for the large mean eccentricity and inclination of Mercury. It is proposed that if the gravitational field of the rapidly rotating early sun had a larger second-degree harmonic, the decreasing value of this harmonic during the subsequent solar spindown would drive Mercury through two secular resonances with Venus, one involving a commensurability in the apsidal motion of the two planets and the other involving their nodal rates. An analysis is performed, showing that these resonances could increase both the inclination and eccentricity of Mercury at nearly the same time, that an initial solar rotational period of 5.5 hr or less would guarantee passage through the resonances, and that a spindown time of about 1 million years could have produced the observed inclination and eccentricity.
Sputtering and deposition rates were measured for discharge chamber components of a 30-cm diameter mercury ion thruster. It was found that sputtering rates of the screen grid and cathode baffle were strongly affected by geometry of the baffle holder. Sputtering rates of the baffle and screen grid were reduced to 80 and 125 A/hr, respectively, by combination of appropriate geometry and materials selections. Sputtering rates such as these are commensurate with thruster lifetimes of 15,000 hours or more. A semiempirical sputtering model showed good agreement with the measured values.
It is noted that the mean motions of Uranus' satellites Miranda, Ariel, and Umbriel exhibit nearly the same commensurability as that observed among the three inner Galilean satellites of Jupiter, which is referred to as the Laplace relation. The theory of the Laplace relation among the Uranian satellites is completed by generating terms due to the first-order portions of the disturbing functions, using a generalization of Souillart's approach for the Galilean satellites. The theory is compared with past observations of Miranda's mean motion to obtain an upper limit on the product of the masses of Ariel and Umbriel. This mass limit is examined in terms of implied density and albedo constraints for comparison with the bulk properties of other solar-system bodies. The results suggest that if Ariel and Umbriel both have the same geometric albedo and density, then Ariel's radius would have to be less than about 1200 km and Umbriel's, less than about 800 km.
Before the recent Pioneer probes, our knowledge of Jupiter's gravitational field was obtained from the motions of satellites and asteroids. The study of orbital perturbations of asteroids near the 2:1 commensurability yielded a value of the mass of the Jupiter system at least as precise as that obtained by the artificial probes. Precession of the inner satellites' orbits placed constraints on the harmonic coefficients J2 and J4. A correction to the satellite determination of J4 lowers its mean value closer to the Pioneer result. The orbital grouping among the outer satellites and the resonance among the Galilean satellites are described in detail, but the origins of these phenomena are not understood. However, recent research suggests that the explanation will be intimately associated with models of the origin and evolution of the planet itself.
Sputtering and deposition rates have been measured for discharge chamber components of a 30-cm diameter mercury ion thruster. It was found that sputtering rates of the screen grid and cathode baffle were strongly affected by geometry of the baffle holder. Sputtering rates of the baffle and screen grid were reduced to 80 and 125 A/hr, respectively, by combination of appropriate geometry and materials selections. Sputtering rates such as these are commensurate with thruster lifetimes of 15,000 hours or more. A semiempirical sputtering model showed good agreement with the measured values.
Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.
This paper presents a statistical estimate of the mass of Saturn's rings, determined to be (6.2 plus or minus 2.4) x 10 to the -6th masses of Saturn. This value was obtained by fitting a gravitational model of the Saturn system which included rings, satellites, and the planet to the observed secular apsidal and nodal rates of the inner satellites. The apsidal commensurability of particles in the rings of Titan was shown to produce no significant effect on the structure of the rings.
Recent advances in the theory of rotation are combined with traditional approaches to study the rotational evolution of the 33 known natural satellites. A calculation similar to that reported by Burns and Safronov (1973) is applied to each satellite to obtain the characteristic time of decay of any wobble motion to smooth rotation about the principal axis of maximum moment of inertia. Stability criteria and capture probabilities are calculated for the 3/2 spin resonance. Results show that only the regular satellites and Iapetus, Hyperion, Triton, and the moon are tidally evolved. Of these, 13 have confirmed synchronous rotation periods; capture probabilities into the 3/2 resonance indicate that none of the remaining 10 should be captured in nonsynchronous, commensurate spin states. For the most part, the irregular satellites retain their original spins except for a relaxation to principal axis rotation. Tidal evolution of the obliquities of the satellites is evaluated in the framework of the generalization of Cassini's laws for the moon. Nearly resonant, forced librations in longitude of 4.8 and 0.5 deg are calculated on the basis of the observed shapes of Phobos and Deimos, respectively.
A flat plate collector employing a mild steel, pressure-expanded absorber plate has been developed. It is capable of energy output levels commensurate with the requirements of driving an absorption refrigeration system while operating at efficiency levels in the 35-40% range. Selective absorber surfaces of black chrome over nickel and black copper over copper were analyzed and prototype collectors containing each type of absorber plating were fabricated and tested for performance. Criteria applied to the cost effectiveness analysis of the collector included both the energy output per unit area and the collector fabrication cost per unit area.