Stable longitudes for 12 hour eccentric orbit satellites
Accelerated longitude drift regimes of eccentric 12 hour orbits due to resonant geopotential
Wagner, C. A.↗
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A note on 'The main problem of satellite theory for small eccentricities, by A. Deprit and A. Rom, 1970.'
Criticism of Deprit and Rom's (1970) extension of Brouwer's (1959) first-order satellite theory to the third order in J sub 2. It is noted that Deprit and Rom's theory suffers from the drawback that the perturbations of all orders are expressed as infinite power series in the eccentricity e. It is demonstrated that Deprit and Rom's reported failure to extend Brouwer's theory to the second order in a closed form by means of Lie transforms is due to an oversight and is not caused by difficulties inherent in the problem or in the particular perturbation method used.
Aksnes, K.↗
Stable longitudes for 12-hr eccentric orbit satellites.
The accelerated longitude drift regimes of eccentric 12-hr orbits are considered, due to the resonant geopotential. These quasi-stationary orbits are under investigation at NASA for large payload earth surveillance spacecraft in the small applications technology satellite (SATS) program. Inclinations near 'critical' are especially attractive because of their possible long term stability, and these are examined in detail. 'Stable' equator crossing longitudes for these satellites are found as functions of the argument of perigee. As long as the argument of perigee is between plus or minus 100 deg, these stable longitudes lie within a narrow range. Maximum 'east-west' stationkeeping requirements for these satellites at nonequilibrium positions are in the range of 0.3 to 3 m/sec/yr.
Wagner, C. A.↗
Orbital eccentricity of Mercury and the origin of the moon.
The results of some recent work conducted by Anderson (1972) are considered. If Anderson is correct in his conclusion that the bulk composition of the moon resembles that of the Allende inclusions, then the natural place for the formation of the moon in the solar system is inside the orbit of Mercury, through planetary accumulation from the condensed material to be found there. This explains the anomalous large eccentricity of the orbit of Mercury.
Cameron, A. G. W.↗
A note on the relations between true and eccentric anomalies in the two-body problem.
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.
Broucke, R.↗
Launch window analysis of satellites in high eccentricity or large circular orbits
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.
Renard, M. L.↗
Eccentricity and inclination of Miranda's orbit
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.
Whitaker, E.↗
Effects of inclination and eccentricity on optimal trajectories between earth and Venus
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.
Gravier, J.-P.↗
Eccentricity and inclination of Miranda's orbit
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.
Whitaker, E.↗
Non-numeric computation for high eccentricity orbits
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.
Sridharan, R.↗
A general time element using Cartesian coordinates: Eccentric orbit integration
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.
Janin, G.↗
Revised age estimates of Brunhes palaeomagnetic events - Support for a link between geomagnetism and eccentricity
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.
Rampino, M. R.↗
Aerodynamic stiffness of an unbound eccentric whirling centrifugal impeller with an infinite number of blades
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.
Allaire, P. E.↗
An experimental investigation of the vaporous/gaseous cavity characteristics of an eccentric journal bearing
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.
Braun, M. J.↗
Eccentric ringlet in the Maxwell gap at 1.45 Saturn radii Multi-instrument Voyager observations
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.
Esposito, L. W.↗
Designing Eccentric Aperture Optical Systems
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.
Rogers, J. R.↗
Dynamic stiffness characteristics of high eccentricity ratio bearings and seals by perturbation testing
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.
Bently, D. E.↗
Eccentricity and misalignment effects on the performance of high-pressure annular seals
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.
Chen, W. C.↗