Oblateness Parameter Research Articles

Solar Perturbations in Saturnian Satellite Motions and Iapetus-Titan Interactions

AbstractSolar perturbations in Saturnian satellite motions are computed with accuracy of 10-5 to try to analyze observed data of orbital elements for Titan. Perturbations due to Iapetus in Titan’s orbit are also developed by taking into account the motion of the orbital plane of Iapetus. Then the mass of Iapetus is determined by the motion of the orbital plane of Titan. Also oblateness parameters of Saturn and the mass of Rhea are determined by seven secular motions for six satellites. It is also found in the analysis that G. Struve’s values for the semi-major axes adopted in almanacs differ from the computed values by using the new data.

Mechanical properties of the neutron lattice in PSR 0833-45

The mechanical properties of a possible solid core in the pulsar PSR 0833-45 are examined in relation to the observed changes in period and their interpretation by Pines, Shaham and Ruderman (1972). Qualitative arguments based on known characteristics of solid He3 and assuming a manybody Hamiltonian with non-directional two-particle potentials indicate that the neutron lattice should have a high value of Poisson's ratio and allow dislocation glide at low applied stresses. A possible explanation of the sudden failure of the core and the upper limit for the creep rate may be found in the quantum mechanical tunnelling model of dislocation intersection introduced by Mott (1956). The present oblateness parameter is estimated to be ɛ≲4×10−5. It is predicted that the magnitude and frequency of period changes should decrease significantly in the remaining part of the century.

Use of the shock-layer approximation in the inverse hypersonic bluntbody problem.

The usefulness of the shock-layer approximation is studied as a method of attacking hypersonic gasdynamics of a blunt body. This paper is concerned mainly with the inverse problems of axisymmetric inviscid flow of a calorically perfect gas (in which the shock geometry is given). Methods that are consistent with approximations based on a high- shock- compression ratio (but modified for the contribution of the tangential pressure gradient and some other second-order terms) are proposed. Agreement in body shape and streamlines with other more exact (numerical) solutions is shown not only for specific heat ratios (as high as y = 2), but also for stagnation regions of very blunt configurations (for which the standard shock-layer theory completely fails). Analytic forms of the pressure field, body, and streamline geometries are developed for the conic-family shocks (of arbitrary degree of oblateness and eccentricity) in the stagnation regions. Nomenclature 6 = a length scale characterizing the subsonic region Bs = oblateness parameter for the conic section shock, Eq. (26) Hm, Ifco, Um = free-stream stagnation enthalpy, freestream Mach number, and free-stream velocity, respectively N, n = eMoc.2 and (Ar — 1)/2(N + 1), respectively p, p, u, v = pressure, density, velocity components parallel to x and y, respectively p, p, ii, v = p} p, u, and v nondimensionalized by Poof^co 2, Poo/e', Um and e'f/oo, respectively pj p, u, v = dimerisionless perturbation pressure, perturbation density, tangential velocity, and normal velocity, respectively, in the stagnation region, defined in Eq. (17) Q(rt r#)t R(r, r#) = functions defined in Eq. (8) r =

Formulae for an accurate intermediary orbit of an artificial satellite

view Abstract Citations (7) References (1) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Formulae for an accurate intermediary orbit of an artificial satellite Vinti, John P. Abstract Formulae are given for computing the drag-free orbit of an artificial satellite of an oblate planet moving in the field of a certain gravitational potential. This potential, expressed in oblate spheroidal coor- dinates and leading to separability of the Hamilton-Jacobi equation, fits the zeroth and second zonal harmonic exactly and, in the case of the earth, yields more than half the fourth zonal harmonic. The solution gives periodic terms through the second order in the oblateness parameter and secular terms exactly, for the given potential. It thus furnishes an intermediary orbit which should always remain very accurate. Publication: The Astronomical Journal Pub Date: November 1961 DOI: 10.1086/108452 Bibcode: 1961AJ.....66..514V full text sources ADS |

Vehicle Motion in the Equatorial Plane of a Planet: a Second Order Analysis in Ellipticity

This paper presents an approximate analytic solution of the drag-free equations of motion of a particle in the equatorial plane of an oblate spheroid subject only to the gravitational attraction of the spheroid. The solution, correct to second order in the planetary ellipticity e, is obtained using the Poincare-Lighthill-Kuo perturbation method. Additional results pertaining to the speed, flight-path angle, time, and the escape path are given as functions of angular displacement from an apse. Results are obtained as power series in the oblateness parameters J and D, and are valid for all eccentricities, i.e., no restriction is placed on \r)J. The results agree with similar results given by Tisserand and DeMoraes and offer excellent agreement with numerical data.

Satellite Motions About an Oblate Planet

The drag-free path of a vehicle in the vicinity of an oblate planet is discussed. Although the solution found is approximate in the sense that it is a truncated power series in the oblateness parameter / , there is no restriction on either the eccentricity or the inclination angle. Approximate analytic expressions are derived for the radial position, speed, angular momentum, deviation from the initial plane of motion, and rate of apsidal advance. In addition, the injection speed required for prescribed apses is derived. The differences between first-order results and inverse-square results are found from the analysis, and numerical results are given. A comparison of the analytical results with the results of integrating the equations of motion directly on a digital computer indicates excellent agreement over a wide range of inclination angles and eccentricities.

Planar Motions About an Oblate Planet

Two cases of plane motion (equatorial and polar) of a vehicle about an oblate planet are discussed. Further, the results of these drag free plane motion studies may be applied to the determination of radial position, speed, and angular momentum for a motion whose initial velocity vector is inclined at an arbitrary angle to the equatorial plane. Approximate analytic results are found by expanding the solution of the system of nonlinear differential equations of the path in powers of the oblateness parameter /. Although only the first power is retained in this solution, no restriction is placed on eccentricity. Thus, for example, the results for an eccentricity of 0.5 may be found from the analy­ sis. In fact, results for speeds in excess of escape speed (e.g., e = 1.1) may be found. Comparison with results obtained by numerically integrating the equations of motion indicates excellent agree­ ment with the analysis.

On the almost periodicity of satellite motion

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the almost periodicity of satellite motion Callender, E. David Abstract Using the Vinti model for an oblate earth it is possible to show that for small values of the oblateness parameters the motion of a near earth satellite is almost periodic. To prove this result, bounds on the varia- tion of the radial distance and the variation of the angle of inclination are obtained. Publication: The Astronomical Journal Pub Date: April 1961 DOI: 10.1086/108390 Bibcode: 1961AJ.....66..134C full text sources ADS |

Oblateness correction to impact points of ballistic rockets

A method is developed for finding the effect of the Earth's oblateness on the impact points of ballistic rockets. Suitable descriptive variables are chosen so that the oblateness perturbations can be obtained by quadrature, and explicit results are obtained correct to first order in an oblateness parameter; specifically, changes in range angle, a lateral displacement angle, and time of flight. The short range limiting forms of the corrections are obtained and interpreted, and an illustrative numerical example is given for a long range trajectory.