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Comparison of analytical relative motion theory with numerical solution for equations of planar motion for two satellites of oblate planet
Dicke-Goldenberg solar oblateness measurement explained by equatorial temperature excess smoothly distributed
Robertson metric beta and gamma coefficients and solar dynamic oblateness determination from probe motion under relativistic effects
Spherical harmonic expansion of nonhomogeneous oblate spheroid mass distribution potential, giving convergence criterion
Low thrust vehicle optimal takeoff calculations from orbit about oblate planet, using two variable asymptotic expansion technique
Motion of a space probe about a spherical center of attraction is considered, applying the general theory of relativity. Motion of a probe under the influence of the sun's oblateness is also discussed. Estimates of beta, gamma, and J20 using solar probe motion are presented. It is concluded that such measurements are possible if the unknown long-period perturbing acceleration is of the order of 10 to the -11th or -12th power m/sec. sq.
The general theory of the method of averaging is used to study the effect of the oblateness of the earth on the motion of an artificial satellite. The first-order harmonic J2 and the second-order harmonics J3 and J4 are included in the analysis. The first-order, periodic variations together with the second-order, averaged and secular variations are derived for all the six orbital elements. Alternative orbital elements and necessary relations are introduced to deal with circular orbits, orbits at critical inclination and equatorial orbits. Essential transformations and initialization procedures are also outlined.
Two yellow and two blue photometric plates of Mars obtained on the near-opposition date of November 21/22, 1958 were studied with a microdensitometer. The plates were provided with a photometric tube scale. The measurements were converted into absolute normalized intensities with the aid of integrated magnitudes of the planet adopted from other sources. Exposures, coordinates and isophotic points are discussed together with the normalization of isophotic radii, standard distributions of brightness, reduced radii, atmospheric levels, and apparent oblateness.
Second order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. Results show that: (1) these effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly; (2) they have the same period and phase as first order resonance perturbations; and (3) 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 one arc second (31m) variation yielded a strong 14th order constraint to the geopotential for odd degree terms. This constraint is poorly predicted by current models.
The frequency limit below which sound scattering by a microphone body is sufficiently small to permit accurate pressure gradient measurements was determined. The sound pressure was measured at various points on the surface of a rigid oblate spheroid illuminated by spherical waves generated by a point source at a large distance from the spheroid, insuring an essentially plane sound field. The measurements were made with small pressure microphones flush mounted from the inside of the spheroid model. Numerical solutions were obtained for a variety of spheroid shapes, including that of the experimental model. Very good agreement was achieved between the experimental and theoretical results. It was found that scattering effects are insignificant if the ratio of the major circumference of the spheroid to the wavelength of the incident sound is less than about 0.7, this number being dependent upon the shape of the spheroid. This finding can be utilized in the design of pressure gradient microphones.
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.
A new analytical state transition matrix is presented. This transition matrix contains the two-body terms and the secular and short periodic terms due to the J2 oblateness perturbation. The matrix is derived from a satellite theory which uses a set of 8 canonical elements with the true anomaly as the independent variable. This theory was chosen because of its accuracy and concise formulation. It presents no problems concerning the accuracy of the mean motion, which is typical for classical satellite theories. Numerical experiments show the J2 transition matrix to be superior to the simple two-body matrix.
The ratio of the mass of the sun to that of Mercury deduced from the first and third flybys of Mercury by Mariner 10 is 6,023,600 plus or minus 600 and 6,023,700 plus or minus 300, respectively. Additional analysis should improve these uncertainties by a factor of 2 to 5. Assuming an equatorial radius of 2439 km, the mean density of the planet is 5.44 g/cu cm. The gravitational oblateness deduced from the first encounter is discussed. Data received from the third encounter are better suited for this determination and yield J2 of 0.00008 plus or minus 0.00006. In addition, the third-encounter data are sensitive to local gravity effects or anomalies.
The paper considers photographs of Uranus obtained by the Stratoscope II balloon-borne telescope in 1970. These data have been redigitized and reanalyzed, and the geometric oblateness of Uranus was determined from the isophotes near the limb using an expression in terms of the equatorial and polar radii.
Brouwer and Brouwer-Lyddanes' use of the Von Zeipel-Delaunay method is employed to develop an efficient analytical orbit theory suitable for microcomputers. A succinctly simple pseudo-phenomenologically conceptualized algorithm is introduced which accurately and economically synthesizes modeling of drag effects. The method epitomizes and manifests effortless efficient computer mechanization. Simulated trajectory data is employed to illustrate the theory's ability to accurately accommodate oblateness and drag effects for microcomputer ground based or onboard predicted orbital representation. Real tracking data is used to demonstrate that the theory's orbit determination and orbit prediction capabilities are favorably adaptable to and are comparable with results obtained utilizing complex definitive Cowell method solutions on satellites experiencing significant drag effects.
In most real cases requiring simple null optics, the optical path difference cannot be reduced to zero but can be kept at a fractional wavelength level so that interferometric data reduction can be used to account for the residual error. In other cases, computer-generated holograms may be used to obtain apparently straight fringes when the desired surface is obtained. Two examples, one involving an f/2.5 concave oblate spheroid and the other a Paul-Baker secondary, are examined. It is shown that although the null tests are not generally perfect, the residual error is small and the tests are simple.
Two surveys of dynamical models of E6 elliptical galaxies were constructed with de Vaucouleurs'surface-brightness distributions. One set of models has a constant mass-to-light ratio. The other set consists of models embedded in oblate isothermal gravitational potentials. In both sets, the observed axis ratio of the models is 0.55 when viewed edge-on. When viewed edge-on, it is possible to construct models in either potential that have velocity-dispersion profiles that increase or decrease with radius along either or both principal axes. The observational data seem to indicate that dispersion profiles decrease or remain constant as function of radius. The most surprising result of this work is that in order for a model to have velocity-dispersion profiles that decrease with radius out to 1.5 r(e) along both principal axes, it must be dominated by fairly thin-walled tube orbits at large radii. This is very different from the spherical case, where radial orbits dominate at large radii.
Atmospheric occultation half-light times and scale heights, together with updated ring-orbit model parameters, are presently used to ascertain the planetary limb shape and thereby derive the radius and oblateness of Uranus at the 1-microbar level from stellar occultation observations obtained on March 10, 1977, and March 23, 1983. Assuming that the planet is in hydrostatic equilibrium, the inferred rotation period is 17.7 + or - 0.6 hr in the -30 to +26 deg latitude range of these observations. These results are noted to be consistent with those based by Lindal et al. (1987) on Voyager 2 observations, where the period at 5 deg latitude is of the order of 18.0 + or - 0.3 hr.