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NASA NTRS1976

On the characteristic exponents of the general three-body problem

A description is given of some properties of the characteristic exponents of the general three-body problem. The variational equations on which the analysis is based are obtained by linearizing the Lagrangian equations of motion in the neighborhood of a given known solution. Attention is given to the fundamental matrix of solutions, the characteristic equation, the three trivial solutions of the variational equations of the three-body problem, symmetric periodic orbits, and the half-period properties of symmetric periodic orbits.

Broucke, R.↗

NASA NTRS1977

Numerical simulation of spacecraft charging phenomena

A numerical simulation program is being constructed having the following features: (1) infinite circular cylindrical geometry with angle-dependence, (2) inclusion of incident particles, photoelectrons, secondary electrons, backscattered electrons, any gun emissions, and any internal current pathways including surface conductive layers, (3) quasistatic time-dependent iteration, in which sheath potential changes during particle transit times are ignored, (4) use of approximate, locally-dependent space charge density expressions in solving Poisson's equation for sheath potentials, with use of numerical orbit-following to determine surface currents, and (5) incident particle velocity distributions isotropic or beam-like, or some superposition of these. Rationales for each of these features are discussed.

Laframboise, J. G.↗

NASA NTRS1993

Light ion flow in the nightside ionosphere of Venus

The flow characteristics of the light ions H(+) and He(+) have been studied in the midnight region of the ionosphere of Venus. Measurements of ion composition, electron and ion temperatures and magnetic fields by instruments onboard the Pioneer Venus Orbiter have been used in rite electron and ion equations of conservation of mass and momentum to derive the vertical flow velocities of H(+) and He(+). When average height profiles of the measured quantities were used, H(+) was found to flow upward, accelerating to speeds of almost 1 km/s at the ion-exobase. In a similar fashion, He(+) was found to flow downward into the neutral atmosphere where it is readily quenched by charge transfer reactions. The polarization electric field played an important role in forcing H(+) upward, but did not contribute enough to the He(+) force balance to produce upward flow. At the ion-exobase, the outward electric polarization force on H(+) was shown to be five times the gravitational force. Using an analogy with the terrestrial ion-exosphere, H(+) was inferred to flow upward into the ionotail of Venus and accelerate to escape speeds. A planet averaged escape flux of 1.4 x 10 exp 7/sq cm/s was calculated, which is comparable to hydrogen loss rates estimated by other investigators.

Hartle, R. E.↗

NASA NTRS1993

The use of polar-orbiting satellite sounding data to estimate rural maximum and minimum temperatures

Atmospheric sounding products from NOAA's polar-orbiting satellites were used to derive and test predictive equations of rural shelter-level maximum and minimum temperatures. Sounding data from both winter and summer months were combined with surface data from over 5300 cooperative weather stations in the continental United States to develop multiple linear regression equations. Separate equations were developed for both maximum and minimum temperature, using the three types of sounding retrievals (clear, partly cloudy, and cloudy). Clear retrieval models outperformed others, and maximum temperatures were more accurately predicted than minimums. Average standard deviations of observed rural shelter temperatures within sounding search areas were of similar magnitude to root-mean-square errors from satellite estimates for most clear and partly cloudy cases, but were significantly less for cloudy retrieval cases. Model validation for surrogate polar and tropical climatic regions showed success in application of the four clear retrieval models (maximum and minimum temperature, for both winter and summer). This indicates the potential adaptability of these models to estimates of rural shelter temperature in areas outside of the United States.

Johnson, Gregory L.↗

NASA NTRS1993

Orbit and sampling requirements: TRMM experience

The Tropical Rainfall Measuring Mission (TRMM) concept originated in 1984. Its overall goal is to produce datasets that can be used in the improvement of general circulation models. A primary objective is a multi-year data stream of monthly averages of rain rate over 500 km boxes over the tropical oceans. Vertical distributions of the hydrometers, related to latent heat profiles, and the diurnal cycle of rainrates are secondary products believed to be accessible. The mission is sponsored jointly by the U.S. and Japan. TRMM is an approved mission with launch set for 1997. There are many retrieval and ground truth issues still being studied for TRMM, but here we concentrate on sampling since it is the single largest term in the error budget. The TRMM orbit plane is inclined by 35 degrees to the equator, which leads to a precession of the visits to a given grid box through the local hours of the day, requiring three to six weeks to complete the diurnal cycle, depending on latitude. For sampling studies we can consider the swath width to be about 700 km.

North, Gerald↗

NASA NTRS2000

Global Monitoring of Air Pollution Using Spaceborne Sensors

The MODIS sensor onboard EOS-Terra satellite provides not only daily global coverage but also high spectral (36 channels from 0.41 to 14 microns wavelength) and spatial (250m, 500m and 1km) resolution measurements. A similar MODIS instrument will be also configured into EOS-Aqua satellite to be launched soon. Using the complementary EOS-Terra and EOS-Aqua sun-synchronous orbits (10:30 AM and 1:30 PM equator-crossing time respectively), it enables us also to study the diurnal changes of the Earth system. It is unprecedented for the derivation of aerosol properties with such high spatial resolution and daily global converge. Aerosol optical depth and other aerosol properties, e.g., Angstrom coefficient over land and particle size over ocean, are derived as standard products at a spatial resolution of 10 x 10 sq km. The high resolution results are found surprisingly useful in detecting aerosols in both urban and rural regions as a result of urban/industrial pollution and biomass burning. For long-lived aerosols, the ability to monitoring the evolution of these aerosol events could help us to establish an system of air quality especially for highly populated areas. Aerosol scenarios with city pollution and biomass burning will be presented. Also presented are the method used in the derivation of aerosol optical properties and preliminary results will be presented, and issue as well as obstacles in validating aerosol optical depth with AERONET ground-based observations.

Chu, D. A.↗

NASA NTRS1973

Space shuttle GN and C equation document: Entry and transition guidance

The entry-guidance routine presented is designed to take the orbiter vehicle from entry interface through the critical heating phase of entry down to the start of the approach phase. The material includes: (1) a functional flow diagram, (2) input and output variables, (3) a description of equations, and (4) detailed flow diagrams.

Marcus, F. J.↗

NASA NTRS1975

Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration

Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, this technique is extended to mass points and mass disks in the gravity field. This requires the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.

Ananda, M.↗

NASA NTRS2017

Reachability Subspace Exploration Using Continuation Methods

Reachability manifold computation suffers from the curse of dimensionality and for large state spaces is computationally intractable. This paper examines the use of continuation methods to address this issue by formulating the reachability sub-space manifold calculation into a number of initial valued problems. As a result of computing the reachability manifold for a subspace of interest, an exponential improvement in computational cost occurs. This concept is applied to a position subspace reachability problem of a spacecraft in a Keplerian orbit under maximum thrust constraints. Future work includes a comparison of the proposed method with computing reachability manifolds using viscosity solutions of the Hamilton Jacobi Bellman partial differential equation.

orbital mechanics↗

NASA NTRS1977

Impedance characteristics of coaxial and planar magnetoplasma capacitors

A theory has been developed for the impedance of a homogeneous magnetoplasma enclosed between two specular reflecting coaxial electrodes, with a static magnetic field parallel to the electrode axes. The parallel-plate magnetoplasma capacitor is treated as a sub-case. Starting with the Vlasov equation, an integral equation is derived for the electric field. Solving this equation, and integrating to obtain the voltage, gives the capacitor impedance. This includes a capacitive component, and a resistive component expressing the Landau damping associated with the open orbits of electrons reflected at the electrodes. A direct numerical solution of the field integral equation has been carried out for a range of values of magnetic field, plasma density, and signal frequency. The values of impedance so obtained are compared with the predictions of macroscopic theory, and of an approximate microscopic theory in which open orbits are ignored and solutions are obtained using finite Fourier transform methods. The mathematical relations between these theories are demonstrated.

Harker, K. J.↗

NASA NTRS2010

Development of a Response Surface Thermal Model for Orion Mated to the International Space Station

A study was performed to determine if a Design of Experiments (DOE)/Response Surface Methodology could be applied to on-orbit thermal analysis and produce a set of Response Surface Equations (RSE) that accurately predict vehicle temperatures. The study used an integrated thermal model of the International Space Station and the Orion Outer mold line model. Five separate factors were identified for study: yaw, pitch, roll, beta angle, and the environmental parameters. Twenty external Orion temperatures were selected as the responses. A DOE case matrix of 110 runs was developed. The data from these cases were analyzed to produce an RSE for each of the temperature responses. The initial agreement between the engineering data and the RSE predictions was encouraging, although many RSEs had large uncertainties on their predictions. Fourteen verification cases were developed to test the predictive powers of the RSEs. The verification showed mixed results with some RSE predicting temperatures matching the engineering data within the uncertainty bands, while others had very large errors. While this study to not irrefutably prove that the DOE/RSM approach can be applied to on-orbit thermal analysis, it does demonstrate that technique has the potential to predict temperatures. Additional work is needed to better identify the cases needed to produce the RSEs

Miller, Stephen W.↗

NASA NTRS1976

Effects of atomic oxygen on graphite ablation

It is shown that a previously derived semiempirical equation for describing observed ablation rates of isotropic graphites cannot be applied to low-density flows containing dissociated oxygen. Experimentally determined reaction probabilities of isotropic graphites to molecular and atomic oxygen are used to calculate heat-transfer rates and stagnation-point ablation rates for typical conditions. Integrated mass losses are computed for a group of flight trajectories which start from geosynchronous orbit and enter earth's atmosphere in a skipping motion following near-elliptic decaying orbits. A comparison of the results with those obtained by the equation under question shows excellent agreement for steep trajectories, but large discrepancies for shallow trajectories. The differences are attributed to surface oxidation by atomic oxygen.

Park, C.↗

NASA NTRS1989

Deterministic errors in the Magellan orbit due to attitude control thruster activity

The pitch and yaw attitude control thrusters of the Magellan spacecraft generate uncoupled moments about the spacecraft center of mass, perturbing the spacecraft's orbit. A strategy to model these perturbing forces in the spacecraft equations of motion is presented. This strategy can model the thruster forces occurring in the nominal and contingency modes of attitude control operation. In the nominal mode, the thrusters fire only to balance the daily unloading of the momentum wheels. The contingency case will occur if a pitch or yaw axis momentum wheel fails, and the thrusters could fire up to 1200 times around the orbit to replace the failed wheel's momentum contribution. Deterministic errors are computed and shown to be under specified error requirements.

Engelhardt, Douglas B.↗

NASA NTRS1994

Orbital coplanarity in solar-type binary systems: Implications for planetary system formation and detection

The equatorial inclinations of solar-type stars within visual binary systems are computed by combining v sin i measurements with rotational period information, or with expected rotational velocities based upon the age of the star in question. These inclinations are then compared with the orbital inclinations of the systems to test the alignment between the equatorial and orbital planes, and how the tendency for or against coplanarity varies as a function of parameters such as spectral type, separation, eccentricity, etc. The results are extended to planetary systems in order to determine the appropriateness of basing planetary search strategies upon a parent star's equatorial inclination, and to address issues in planetary system formation and evolution, including the stability of planetary orbits within binary systems. During the course of this project new or improved v sin i measurements are made for over 30 solar-type stars within binary systems, and (for the purposes of the study) tentative orbits are computed for thirteen long-period systems. The results suggest that approximate coplanarity between the equatorial and orbital planes exists solar-type binary systems with separations less than 30-40 AU. The coplanarity tendency, as well as this 'critical separation,' is not significantly affected by most of the other parameters studied. The one significant exception occurs with hierarchical multiple systems, where noncoplanarity may exist at relatively small separations. If it is assumed that planetary distances in our solar system are typical, the results suggest there is no reason to expect planets to orbit in planes significantly different from that of the parent star's equator, in turn suggesting that planetary formation models and search strategies dependent upon this assumption are valid from this standpoint. The results also suggest that noncoplanarity between the components of a binary system is not a significant issue in addressing the stability of planetary orbits within the system.

Hale, Alan↗

NASA NTRS2007

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.

Ross, Shane D.↗

NASA NTRS1992

The effectiveness of multi-layer insulation as meteoroid and orbital debris shielding

This paper presents the results of a study of the penetration resistance of Type I Multi-Layer Insulation (MLI) to meteoroid and orbital debris particles. Hypervelocity impact tests on MLI were performed and the collected data was compared to data and empirical equations developed for aluminum. The study results indicate that MLI can be an effective shield from meteoroids and orbital debris for short duration missions and for non-critical elements. However, long missions which require high levels of protection cannot rely on MLI without a thorough investigation of the overall system reliability.

Robinson, J. H.↗

NASA NTRS1979

Long-term risk analysis associated with nuclear waste disposal in space

An assessment and verification of previous analytic results on the long term risk of earth reentry for hazardous payloads is presented. The two areas were studied: (1) stability of nominal, near-circular storage orbits in the regions between Venus and earth and between earth and Mars, and (2) probability of earth reentry for off-nominal planet-crossing orbits resulting from deployment system failures. In the first area, numerical integrations of the equations of motion are compared with stability predications based on secular perturbation theory. The agreement is good in terms of the heliocentric distances covered and the general behavior of the orbital history, although certain near-resonance situations can lead to difficulty. In the second area, a Monte Carlo simulation of orbital evolution is used and the results compared with Opik's analytic theory of planetary encounters and collision statistics, with data verified to within a close order-of-magnitude.

Friedlander, A. L.↗

NASA NTRS1973

Geodesic synchrotron radiation

This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits, a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions.

Breuer, R. A.↗