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At least 883 records · Page 49
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NASA NTRS1992

The orbital evolution of real asteroids near the 4:1 mean-motion resonance with Jupiter

Numerical integrations of the orbits of ten asteroids with osculating elements near the 4:1 mean-motion resonance with Jupiter have been performed over 200,000 years into the future. A variety of orbital evolutions was found, depending on the start values of the semi-major axis. The orbit of asteroid 1983 RJ4, which lies almost exactly at the resonance center, experiences large variations in eccentricity, evolving into an Earth-crosser on a time-scale of a few 10(exp 4) years. This makes this region a potential source for Apollo objects and meteoritic material, although the width of the resonance region in semi-major axis seems to be very narrow.

Dahlgren, Mats↗
NASA NTRS1992

The effect of secular resonances in the asteroid region between 2.1 and 2.4 AU

The asteroid region between 2.1 and 2.4 AU appears to be depopulated at inclinations i greater than 12 deg. This region is surrounded by the three main secular resonances nu(sub 5), nu(sub 6), and nu(sub 16) and is crossed by higher order secular resonances. Secular resonances appear to overlap in this region. Numerical integrations of the orbits of seventeen fictituous asteroids with initial inclinations 12 deg less than or equal to i less than or equal to 20 deg show the following: (1) this particular asteroid region is not depopulated in our computer experiment on timescales of 2.7 Myrs; (2) inclinations are pumped up by successive crossings through higher order secular resonances while eccentricities are not increased sufficiently to produce planet-crossers; (3) bodies located in the bordering nu(sub 6) resonance with semi-major axes a less than or equal to 2.4 AU become Earth-crossers on a time scale of 1 Myr; and (4) we confirm the result that modes due to higher order secular resonances must be eliminated when proper elements are computed.

Froeschle, Christiane↗
NASA NTRS1992

Asteroid-type orbit evolution near the 5:2 resonance

In this case of the 5:2 commensurability with the motion of Jupiter, an asteroid can reach the orbits of Mars, Earth, and Venus when eccentricity e is greater than 0.41, 0.65, and 0.74, respectively. For individual fictitious asteroids, Ipatov and Yoshikawa obtained a growth in e from 0.15 to 074-0.76. Rates of changes in orbital orientations are different for Mars, Earth, Venus, and the asteroid. Therefore, for corresponding values of e, the asteroid could encounter these planets and leave the gap at those encounters. In order to investigate this hypothesis of the 5:2 Kirkwood gap formation, Ipatov studied the regions of initial data for which the eccentricities of asteroids located near the 5:2 commensurability exceeded 0.41 during evolution. The orbit evolution for 500 fictitious asteroids was investigated by numerical integration of the complete (unaveraged) equations of motion for the three-body problem (Sun-Jupiter-asteroid). The equations of motion were integrated in the time intervals T is greater than or equal to 5(10)(exp 3)t(sub J) (t(sub J) is the heliocentric orbital period of Jupiter) in the planar model, T is greater than or equal to 10(exp 4)t(sub J) at initial inclination 5 deg is less than or equal to i(sub 0) is less than or equal to 20 deg and T = 10(exp 5)t(sub J) at i(sub 0) = 40 deg. The larger interval T was taken at i(sub 0) = 40 deg because in this case for the majority of runs maximum values of e and i were reached in the time delta(t) is greater than 2(10)(exp 4)t(sub J).

Ipatov, S. I.↗
NASA NTRS1992

Dynamical timescales in the Jupiter family

Numerically integrated fictitious comets starting in orbits perihelion tangent to Jupiter have been used to estimate the duration of a typical visit to the observable Jupiter family of comets. The results show values of 3 to 6 thousand years, narrowing the previously estimated interval of 10(exp 3) to 10(exp 4) years.

Lindgren, Mats↗
NASA NTRS1992

Cometary orbital evolution in the outer planetary region

Numerical integrations of fictitious objects are carried out in order to elucidate the dynamical behavior of potential short-period comets when they move in orbits at distances from the Sun comparable to those of Uranus and Neptune. As in the case of observed short-period comets, close encounters with the planets play a major role for the orbital evolution, and this is especially true for encounters with initial orbits nearly tangent to that of the planet. A comparison with integrations in which the planetary masses are larger by a factor 10 shows that, in the latter case, the orbital evolution is greatly accelerated, but the dynamical paths in phase space followed by the comets are altered.

Manara, Allesandro↗
NASA NTRS1992

Long-term orbital evolution of short-period comets found in Project Cosmo-DICE

Orbital evolutions of about 160 short-period (SP) comets are numerically integrated for 4400 years in the framework of a realistic dynamical model. By the round-trip error in closure test, a reliable time space of the integrated orbits is estimated for each comet. Majority of the SP comets with their Tisserand's constant(J) between 2.8 and 3.1 are found to evolve within the past 1000-2000 years from the orbits whose perihelia are near the Jovian orbit to the orbits with perihelia of 1-2 AU. This evolution is much more rapid than that expected from Monte Carlo simulations based on symmetric distribution of planetary perturbations, thus suggesting that asymmetry of perturbation distribution play an important role in cometary evolution. Several comets are shown to evolve from the near-Saturn orbits and then to be handed over under the control of Jupiter. We also find that a few comets were captured from long-period orbits (a = 75-125 AU) via only a few close encounters with Jupiter. It is confirmed that the captured SP comets of low-inclination with 2.7 less than J less than 3.1 show more or less strong chaotic behavior. On the other hand, comets with longer orbital period and/or of high inclination reveal slow or quasi-periodic orbital evolution.

Nakamura, Tsuko↗
NASA NTRS1992

1991 DA: An asteroid in a bizarre orbit

Asteroidal object 1991 DA has an orbit of high inclination, crossing the planets from Mars to Uranus. This is unique for an asteroid, but not unusual for a comet of the Halley-type: it therefore seems likely that 1991 DA is an extinct or dormant comet. Previous CCD imaging has shown no indication of a coma; spectroscopic observations of 1991 DA which lack any evidence of strong comet-like emissions are reported. Numerical integrations of the orbit of this object were performed which show that is has been remarkably stable for the past approximately 20,000 yr, but chaotic before that. This may allow a new estimate to be made of the physical lifetimes of comets.

Steel, Duncan↗
NASA NTRS1992

Formation of the Leonid meteor stream and storm

It is well known that some meteor showers display a very high level of activity at certain times, the most famous being the Leonid shower with very spectacular displays at roughly 33 year intervals. This period being also the period of the parent comet of the stream, Comet Tempel-Tuttle. An investigation of the geometry of the comet and the Earth at the time of each high activity occurrence by Yeomans suggests that most of the meteoroids are found outside the cometary orbit and lagging the comet. The formation process of such a stream by numerically integrating the orbits of dust particles ejected from the comet and moving under the influence of gravity and radiation pressure are simulated. The intersection of these dust particles with the Earth is also considered and it is concluded that about 12 percent of the ejected particles may be observed and that of those observable, 63 percent will be outside the cometary orbit and behind the comet.

Wu, Zidian↗
NASA NTRS1991

Use of non-spherical gravity harmonics for relative motion GN/C (category 2)

Detailed analysis of the Automatic Rendezvous and Capture problem indicate a need for three different regions of mathematical description for the GN&C algorithms: (1) multi-vehicle orbital mechanics to the rendezvous interface point, i.e., within 100 nm; (2) relative motion solutions (such as Clohessy-Wiltshire type) from the far-field to the near-field interface, i.e., within 1 nm and; (3) close proximity motion - the near-field motion where the relative differences in the gravitational and orbit inertial accelerations can be neglected from the equations of motion. Limit boundaries to these regions can be precisely defined by further analysis and will be functions of the tracking measurement accuracies and the computer resources available for the solution of the algorithms. This paper analyzes the relative motion in Regions 2 and 3 above and present the derivation and discussion of the general case of non-spherical gravitational perturbed relative motion. Mathematical deviations from the numerically integrated spherical gravity case and solutions from the Clohessy-Wiltshire equations are presented in the analysis. Based upon this preliminary analysis, it is recommended that further efforts be used to assess the relative position and velocity differences in Region 2 due to non-spherical gravity harmonics and that viable GN&C algorithms be developed to include these gravity perturbations (especially the effects of the first gravity harmonic, J2).

Henderson, David M.↗
NASA NTRS1992

An asymptotic theory of supersonic propeller noise

A theory for predicting the noise field of supersonic propellers with realistic blade geometries is presented. The theory, which utilizes a large-blade-count approximation, provides an efficient formula for predicting the radiation of sound from all three sources of propeller noise. Comparisons with a full numerical integration indicate that the levels predicted by this formula are quite accurate. Calculations also show that, for high speed propellers, the noise radiated by the Lighthill quadrupole source is rather substantial when compared with the noise radiated by the blade thickness and loading sources. Results from a preliminary application of the theory indicate that the peak noise level generated by a supersonic propeller initially increases with increasing tip helical Mach number, but is eventually reaches a plateau and does not increase further. The predicted trend shows qualitative agreement with the experimental observations.

Envia, Edmane↗
NASA NTRS1992

The structure of particle cloud premixed flames

The structure of premixed flames propagating in combustible systems containing uniformly distributed volatile fuel particles in an oxidizing gas mixture is analyzed. This analysis is motivated by experiments conducted at NASA Lewis Research Center on the structure of flames propagating in combustible mixtures of lycopodium particles and air. Several interesting modes of flame propagation were observed in these experiments depending on the number density and the initial size of the fuel particle. The experimental results show that steady flame propagation occurs even if the initial equivalence ratio of the combustible mixture based on the gaseous fuel available in the particles, phi sub u, is substantially larger than unity. A model is developed to explain these experimental observations. In the model, it is presumed that the fuel particles vaporize first to yield a gaseous fuel of known chemical composition which then reacts with oxygen in a one-step overall process. The activation energy of the chemical reaction is presumed to be large. The activation energy characterizing the kinetics of vaporization is also presumed to be large. The equations governing the structure of the flame were integrated numerically. It is shown that the interplay of vaporization kinetics and oxidation process can result in steady flame propagation in combustible mixtures where the value of phi sub u is substantially larger than unity. This prediction is in agreement with experimental observations.

Seshadri, K.↗
NASA NTRS1993

An analytical optimization of electric propulsion orbit transfer vehicles

Due to the electric propulsion's inherent propellant mass savings over chemical propulsion, electric propulsion orbit transfer vehicles (EPOTV's) are highly efficient mode of orbit transfer. When selecting an electric propulsion device (ion, MPD, or arcjet) and propellant for a particular mission, it is preferable to use quick, analytical system optimization methods instead of time intensive numerical integration methods. It is also of interest to determine each thruster's optimal operating characteristics for a specific mission. Analytical expressions are derived which determine the optimal specific impulse (Isp) for each type of electric thruster to maximize payload fraction for a desired thrusting time. These expressions take into account the variation of thruster efficiency with specific impulse. Verification of the method is made with representative electric propulsion values on a LEO-to-GEO mission. Application of the method to specific missions is discussed.

Oleson, Steven R.↗
NASA NTRS1992

Rapid time variations and radiative instabilities of astrophysical masers

The time-varying intensities are obtained for astrophysical masers that are radiatively unstable. Numerical integrations of the time-dependent, nonlinear equations of radiative transfer are performed with the usual approximation of a linear maser. At long times after changes in the physical conditions, the intensity of maser radiation reaches an asymptotic behavior and oscillates permanently in these idealized calculations with a period that is related to the length of the maser divided by the speed of light. The intensity varies by more than a factor of 10. These intensities depend upon the same four parameters as we originally found to determine the regime for radiative instabilities based on a stability analysis of the steady state. A detailed comparison is made between the predictions of the stability analysis and the time variations of the intensities. Calculations are performed for interacting pairs as well as isolated, individual masers.

Scappaticci, Gerardo A.↗
NASA NTRS1992

An asymptotic theory of supersonic propeller noise

A theory for predicting the noise field of a propeller with a realistic blade geometry is presented. The theory, which utilizes a large blade count approximation, provides an efficient formula for predicting the radiation of sound from all three sources of propeller noise. Comparisons with full numerical integration indicate that the noise levels predicted by this formula are quite accurate. Calculations based on this method also show that the radiation from the Lighthill quadrupole source is rather substantial when compared with thickness and loading noise for high speed propellers. A preliminary application of the theory to the problem of the sensitivity of the peak noise levels generated by a supersonic propeller to the variations in its tip helical Mach number has produced a trend that is in qualitative agreement with the experimental observations.

Envia, Edmane↗
NASA NTRS1993

Spatial simulation of boundary layer instability - Effects of surface roughness

The effects of an isolated, two-dimensional roughness element on the spatial development of instability waves in boundary layers are investigated by numerically integrating the two-dimensional, time-dependent, incompressible Navier-Stokes equations, using a finite difference/Chebyshev discretization. It is shown that (high) inviscid frequencies have higher growth rates than Tollmien-Schlichting frequencies, indicating that disturbances growing in the separation zone are controlled by the inviscid instability of the shear layer at the edge of the separation zone.

Danabasoglu, G.↗
NASA NTRS1992

Membrane triangles with corner drilling freedoms. II - The ANDES element

This is the second article in a three-part series on the construction of 3-node, 9-dof membrane elements with normal-to-its-plane rotational freedoms (the so-called drilling freedoms) using parametrized variational principles. In this part, one such element is derived within the context of the assumed natural deviatoric strain (ANDES) formulation. The higher-order strains are obtained by constructing three parallel-to-sides pure-bending modes from which natural strains are obtained at the corner points and interpolated over the element. To attain rank sufficiency, an additional higher-order 'torsional' mode, corresponding to equal hierarchical rotations at each corner with all other motions precluded, is incorporated. The resulting formulation has five free parameters. When these parameters are optimized against pure bending by energy balance methods, the resulting element is found to coalesce with the optimal EFF element derived in Part I. Numerical integration as a strain filtering device is found to play a key role in this achievement.

Felippa, Carlos A.↗
NASA NTRS1992

Long-term orbital and spin dynamics of Mars

This review of the long-term dynamical behavior of Mars covers secular variations of the orbit, oscillations of the obliquity, and polar wandering. Calculations of the large-scale obliquity oscillations of Mars are updated using the most recent orbit theory and contrasted with the earth. The motion for Mars is characterized by about 100,000-yr oscillations driven by differential spin axis and orbit plane precession rates during which the obliquity may change by as much as about 20 deg. The possible role of spin-orbit secular resonances to the spin axis histories of the earth and Mars is also considered. Numerical integrations of the equations of motion indicate that Mars may have passed through resonance as little as 5 Myr ago and that obliquities approaching about 45 deg could have been achieved during such an event.

Ward, William R.↗
NASA NTRS1993

Improved estimation of random vibration loads in launch vehicles

Random vibration induced load is an important component of the total design load environment for payload and launch vehicle components and their support structures. The current approach to random vibration load estimation is based, particularly at the preliminary design stage, on the use of Miles' equation which assumes a single degree-of-freedom (DOF) system and white noise excitation. This paper examines the implications of the use of multi-DOF system models and response calculation based on numerical integration using the actual excitation spectra for random vibration load estimation. The analytical study presented considers a two-DOF system and brings out the effects of modal mass, damping and frequency ratios on the random vibration load factor. The results indicate that load estimates based on the Miles' equation can be significantly different from the more accurate estimates based on multi-DOF models.

Mehta, R.↗