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Two remarkably simple formulas are proposed for relating the eccentric and true anomalies in the two-body problem at no numerical trouble, no matter what the values of the angles are. The problem of the maximum difference between the two angles is also considered.
Numerical methods and computer programs for studying the stability and evolution of orbits of large eccentricity are presented. Methods for determining launch windows and target dates are developed. Mathematical models are prepared to analyze the characteristics of specific missions.
Careful re-measurement of all available plates showing Uranus V (Miranda), supplemented by some recently obtained images, shows that this satellite has both a pronounced orbital eccentricity and inclination (to the plane of the other satellites). Observations are sufficient in number and distribution to allow determinations of the precession rates of both pericenter and node, with implications for the dynamical oblateness of Uranus and the gravitational interaction of the satellites. An improved value for the revolution period is a byproduct of the investigation. The success of the study is due to the improved precision of the measures resulting from the adoption of a very simple, direct method of measurement.
The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.
Careful re-measurement of all available plates showing Uranus V (Miranda), supplemented by some recently obtained images, shows that this satellite has both a pronounced orbital eccentricity and inclination (to the plane of the other satellites). Observations are sufficient in number and distribution to allow determinations of the precession rates of both pericenter and node, with implications for the dynamical oblateness of Uranus and the gravitational interaction of the satellites. An improved value for the revolution period is a by-product of the investigation. The success of this study is due to the improved precision of the measures resulting from the adoption of a very simple, direct method of measurement.
Geocentric orbits of large eccentricity (e = 0.9 to 0.95) are significantly perturbed in cislunar space by the sun and moon. The time-history of the height of perigee, subsequent to launch, is particularly critical. The determination of 'launch windows' is mostly concerned with preventing the height of perigee from falling below its low initial value before the mission lifetime has elapsed. Between the extremes of high accuracy digital integration of the equations of motion and of using an approximate, but very fast, stability criteria method, this paper is concerned with the developement of a method of intermediate complexity using non-numeric computation. The computer is used as the theory generator to generalize Lidov's theory using six osculating elements. Symbolic integration is completely automatized and the output is a set of condensed formulae well suited for repeated applications in launch window analysis. Examples of applications are given.
A general time element, valid with any arbitrary independent variables, and used with Cartesian coordinates for the integration of the elliptic motion in orbits, is examined. The derivation of the time element from a set of canonical elements of the Delaunay type, developed in the extended phase space, is presented. The application of the method using an example of a transfer orbit for a geosynchronous mission is presented. The eccentric and elliptic anomaly are utilized as the independent variable. The reduction of the in track error resulting from using Cartesian coordinates with the time element is reported.
Revisions in the dates of reported geomagnetic excursions during the Brunhes Epoch are proposed in light of possible correlations between a section at Gioia Tauro, Italy, deep-sea cores, a core from Lake Biwa, Japan, and some lava flows. The anomalously long, double Blake Event reported at Gioia Tauro is here correlated with the Blake Event (approximately 110 kyr) and the Biwa 1 event (180 plus or minus 5 kyr); an hiatus may be present in the section between these two events. The alpha event at Gioia Tauro is correlated with the Biwa 2 event at about 295 kyr; the beta event with the 'Biwa 3' event at about 400 kyr; the gamma event with the Snake River event at 480 plus or minus 50; and the delta event, not recorded elsewhere, is estimated to have occurred at approximately 620 kyr. These proposed refinements in the age estimates of the excursions suggest an approximately 100 kyr cyclicity. If the events are real and the revised dating is correct, the timing of the geomagnetic events seems to coincide with times of peak eccentricity of the earth's orbit, suggesting a causal connection.
An unbounded eccentric centrifugal impeller with an infinite number of log spiral blades undergoing synchronous whirling in an incompressible fluid is considered. The forces acting on it due to coriolis forces, centripetal forces, changes in linear momentum, changes in pressure due to rotating and changes in pressure due to changes in linear momentum are evaluated.
This paper describes the experimental pressure and temperature results obtained when rotating a shaft in an eccentric lucite casing at velocities ranging from 209 to 628 rad/s (2000 to 6000 rpm). The results are presented in terms of three-dimensional plots and contour maps. Photographic evidence is presented to illustrate how the downstream and upstream regions of the cavity develop and evolve into the well-known finger patterns. A comparison between pressure and temperature profiles in air-saturated oil and carbon dioxide-saturated oil is presented; the origin and nature of the gases contained in the cavity are discussed. Three analytical models (Swift-Stieber, separation, Floberg) predicting the formation of the cavitation zone are presented and evaluated in light of the experimental results. A motion-picture supplement depicting these results is available upon request.
The results of Voyager experiments to characterize the eccentric ringlet at 1.45 Saturn radius are discussed. The Voyager I carried out microwave occultation trials with a dual-frequency transmitter, while Voyager 2 observed the occultation of delta Scorpii using an UV spectrometer and a photopolarimeter. The ringlet was associated with a basically empty region next to an edge of the C ring which decreased to a few hundred meters thickness. The width of the ringlet in the gap was estimated to vary from 38-88 km, and it maintains an elliptical shape. It precesses within the 265 km gap it occupies, and has a double-peaked core 15 km wide. The bulk of the ringlet is particles of less than 1 cm radius.
Computer program aids in design of eccentric aperture optical systems by predicting vector aberration that occurs in optical system having tilted or decentered optical elements. Computer program incorporates vector theory of aberrations.
The complex behavior of cylindrical bearings and seals that are statically loaded to eccentricities in excess of 0.7 are examined. The stiffness algorithms as a function of static load are developed from perturbation methodology by empirical modeling.
Annular pressure seals act as powerful hydrostatic bearings and influence the dynamic characteristics of rotating machinery. This work, using the existing concentric seal theories, provides a simple approximate method for calculation of both seal leakage and the dynamic coefficients for short seals with large eccentricity and/or misalignment of the shaft. Rotation and surface roughness effects are included for leakage and dynamic force calculation. The leakage calculations for both laminar and turbulent flow are compared with experimental results. The dynamic coefficients are compared with analytical results. Excellent agreement between the present work and published results have been observed up to the eccentricitiy ratio of 0.8.
The apsidal motion of the eccentric eclipsing binary DI Herculis (HD 175227) is determined from an analysis of the available observations and eclipse timings from 1959 to 1984. Least squares solutions to the primary and secondary minima extending over an 84-yr interval yielded a small advance of periastron omega dot of 0.65 deg/100 yr + or - 0.18/100 yr. The observed advance of the periastron is about one seventh of the theoretical value of 4.27 deg/100 yr that is expected from the combined relativistic and classical effects. The discrepancy is about -3.62 deg/100 yr, or a magnitude of about 20 sigma. Classical mechanisms which explain the discrepancy are discussed, together with the possibility that there may be problems with general relativity itself.
Analytical expressions are derived for the cutoff wavenumbers and the corresponding modes in annular-cross-section waveguides having inner conductors of small radius. Waveguides with circular and rectangular outer boundary are considered. In the case of the circular eccentric annular waveguide, comparison is made between the values of cutoff wavenumbers computed from the expressions derived in this paper and data obtained by a more rigorous numerical technique.
The effect on the orbital parameters of a classical nova of the ejection of mass during the nova explosion is considered. The most easily observable consequence is the generation of a small eccentricity in the orbit which leads to a luminosity modulation at a period just longer than the orbital period. Observation of such an effect would have implications not just for interpreting the dynamics of the explosion but also for measuring the secular effect of tidal interaction after the outburst.
The dynamic coefficients of seals are calculated for shaft movements around an eccentric position. The turbulent flow is described by the Navier-Stokes equations in connection with a turbulence model. The equations are solved by a finite-difference procedure.