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NASA NTRS1963

Lunar Flight Study Series: Volume 7. Earth-Moon Transit Studies Based on Ephemeris Data and Using Best Available Computer Program: Principles for Reducing Earth-Moon Trajectory Analysis to Fundamentals - 2

This report presents an empirical investigation of earth-to-moon trajectories. The primary objective is to uncover relationships that result in the reduction of mission analysis or trajectory analysis problems to fundamentals. It is considered imperative that the results be accurate to the extent that any relationships that are uncovered are not brought about by simplifying or unrealistic assumptions. Consequently, the model used is as accurate as is presently available for use and the computations are performed under strict error controls. Procedures are reasonable from the engineering viewpoint. Some very helpful principles are uncovered. These may be briefly stated as follows: 1) Trajectories of constant flight time to the moon (in the 66 hour to 90 hour range), and arriving within a few minutes of the same time pass over a common point on the moon regardless of the arrival altitude and inclination, This common point of passage for such a family of trajectories is arbitrarily referred to as a VERTEX point; 2) These VERTEX points lie within a bounded region on the lunar surface as arrival time varies throughout the years, for a given flight time or flight time spread; 3) Increasing flight time results primarily in a longitude shift of the VERTEX point for a given arrival time; 4) Launch azimuth should be treated as a strong parameter regarding its influence on the vertex. Launch azimuth variations up to +/- 20 degrees about 90 degrees can shift the vertex as much as 3 degrees in latitude even when one is free to pick launch time, coast time, and S-IVB burn time appropriately with launch azimuth; and 5) The locus of periselenum, as arrival inclination takes on all possible values, is nearly circular about the vertex point for a given arrival altitude. A publication is now in preparation that applies these principles to much advantage in the solution of various trajectory analysis problems.

LUNAR FLIGHT↗

NASA NTRS1970

Technique for improving hydrodynamic gyro bearings

Conical or spherical, spirally grooved grease bearings have an inclined surface which is machined inboard of the grooved surface. The indentation and inclined surface provide a reservoir for forced out lubricant, and when rotation begins, centrifugal force returns the lubricant to the grooved area.

Broussard, P., Jr.↗

NASA NTRS1971

New procedure for determining minimum time orbit transfers

Computer program includes time minimizing function required for propellant constrained minimum time impulsive transfer between coplanar circular orbits or unrestricted orbits. Basic formulation is extended to include inclined circular or inclined elliptic orbits.

Davis, D. A.↗

NASA NTRS1972

An analysis of the expected eccentricity perturbations for the second Radio Astronomy Explorer (RAE B)

Analytical prediction of expected eccentricity perturbations for the RAE 2 lunar orbit shows that the eccentricity will grow linearly in time. Parametric inclination studies and analysis of perturbation equations establish a critical retrograde inclination of 116.565 at which the positive perturbation slope vanishes for a circular orbit about 1100 m above the lunar surface with an eccentricity constraint of less than 0.005 during a period of about one year.

Murphy, J. P.↗

NASA NTRS1972

Some higher order analyses of earth and lunar orbiters

The accurate modelling of the translational behavior of a drag-free satellite in an almost circular near-earth orbit is investigated. All short and long period position fluctuations in the satellite's coordinates down to 1 m are determined. The general zonal and tesseral harmonic effects are considered as well as lunar and solar effects. A noncanonical approach is followed. A mean orbital plane is chosen so that no short period out-of-plane fluctuations greater than second order occur. Short period radial and cross-track fluctuations and in-track fluctuations are computed. Long period and secular rates of the mean elements which define the slowly varying plane of reference are determined to third order in the small quantities. The equations of motion are integrated analytically away from critical inclination and tesseral resonance. The resonant situation of a sun-synchronous orbit is discussed as a special case. The long-period behavior of a lunar orbiter is also considered, including the effects due to the inclination of the earth's apparent orbit about the moon and those described by Cassini laws on the equations of motion. Both resonant and nonresonant low orbits, and high orbits are discussed.

Dasenbrock, R. R.↗

NASA NTRS1972

On the use of the Hill variables in artificial satellite theory - Brouwer's theory.

By reformulating Brouwer's first-order satellite theory in terms of the Hill variables, it is demonstrated that these variables possess several advantages over the Delaunay variables. The final algorithm is simpler and more compact, there is no singularity at zero eccentricity, and the process of deriving the perturbations is considerably simplified. An algorithm for the computation of position and velocity is presented which is significantly simpler and faster in use than Brouwer's algorithm. Moreover, whereas the latter algorithm breaks down for circular and equatorial orbits, the present one holds for all eccentricities less than one and for all inclinations, with the exception of the critical inclination.

Aksnes, K.↗

NASA NTRS1972

Equinoctial orbit elements - Application to artificial satellite orbits.

The matrizant of the two-body problem is developed in terms of elements that are free from singularities for zero eccentricities and zero- and ninety-degree inclinations. Retrograde equinoctial elements eliminate the singularity for inclinations near 180 degrees, with only minor changes in the expressions for the matrizant. The 'single-averaged' variation-of-parameters equations for these elements are developed for third-body, oblateness, and drag effects. Higher order terms are included in the expansions for the third-body and oblateness potential. A computer program that uses these equations to predict orbital evolution is described. Numerical results are given for a near-circular orbit.

Cefola, P. J.↗

NASA NTRS1972

Control information in visual flight

The purpose of the inquiry is to determine how precisely a pilot can estimate the movements of his vehicle, and thus exercise control, during an unaided visual approach. The method is to relate changes in the forward view, due to movements along and across the approach path, to human visual thresholds and errors. The scope is restricted to effects of inclination, expansion, size, and rotation in runway features during approaches at small angles of elevation. Quantitative relations are given which provide a basis for ranking the several information mechanisms. Alignment by inclination of a ground line is found to be an accurate lateral mechanism, probably superior to the expansion mechanism. Vertical control mechanisms are complex, of questionable accuracy, and difficult to rank. The results throw some doubt on the usefulness of a runway symbol as a source of displayed information.

Naish, J. M.↗

NASA NTRS1972

Gravitational field modes GEM 3 and 4

A refinement in the satellite geopotential solution for a Goddard Earth Model (GEM 3) was obtained. The solution includes the addition of two low inclination satellites, SAS at 3 deg and PEOLE at 15 deg, and is based upon 27 close earth satellites containing some 400,000 observations of electronic, laser, and optical data. In addition, a new combination satellite/gravimetry solution (GEM 4) was derived. The new model includes 61 center of mass tracking station locations with data from GRARR, Laser, MOTS, Baker-Nunn, and NWL Tranet Doppler tracking sites. Improvement was obtained for the zonal coefficients of the new models and is shown by tests on the long period perturbations of the orbits. Individual zonal coefficients agree very closely among different models that contain low inclination satellites. Tests of models with surface gravity data show that the GEM 3 satellite model has significantly better agreement with the gravimetry data than the GEM 1 satellite model, and that it also has better agreement with the gravimetry data than the 1969 SAO Standard Earth 2 model.

Lerch, F. J.↗

NASA NTRS1973

Low-Speed Aerodynamic Characteristics of a Fuselage Model with Various Arrangements of Elongated Lift Jets

Data were obtained for a round jet located on the center of the bottom of a fuselage and for elongated slots separated spanwise by distances of 0.8 and 1.2 of the fuselage width. The effect of yawing the slots, inclining the jets laterally, and combining slot yaw with jet inclination was determined. Data were obtained in and out of ground effect through a range of effective velocity ratios and through a range of sideslip angles.

Vogler, R. D.↗

NASA NTRS1973

Polar motion and earth tides from Beacon Explorer C

Seventeen months of laser tracking of the Beacon Explorer C spacecraft by a Goddard Space Flight Center laser system were analyzed. The amplitude and phase of the solid-earth and ocean-tide perturbations of the orbit and the variation in latitude of the tracking station were determined. From an analysis of the orbital inclination obtained from 6 hour data spans the tidal perturbations of the orbit were found to have a magnitude equivalent to a second degree Love number, k sub 2, of 0.245 with a phase lag of about 3.2 degrees. These numbers are in complete agreement with values obtained previously from a much shorter data span, although k sub 2, is lower than the value derived from seismic data. This discrepancy is probably due to the influence of the oceans on the satellite result. After removing the tidal perturbations the residuals in inclination were of order 0.04 arcseconds. This implies that the variation in latitude of the station was being determined during the 17 months period with an rms deviation of about 1.4 meters with respect to the smoothed Bureau International de l'Heure values.

Kolenkiewicz, D. E.↗

NASA NTRS1974

Optimization of the acoustic absorption coefficients of certain functional absorbents

The sound absorption coefficients of some functional absorbents (mineral wool plates) are determined by the reverberation chamber method. The influence of the angle of inclination of the sound absorbing material with respect to the surface to be treated is analyzed as well as the influence of the covering index, defined as the ratio of the designed area of a plate and the area of the treated surface belonging to another plate. As compared with the conventional method of applying sound-absorbing plates, the analyzed structures have a higher technological and economical efficiency. The optimum structure corresponds to an angle of inclination of 15 deg and a covering index of 0.8.

Pocsa, V.↗

NASA NTRS1974

Lunar perturbations of artificial satellites of the earth

The disturbing function for the lunar perturbations of an artificial satellite are derived, using ecliptic elements for the moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the earth. The results can then be applied to numerical integration by using coordinates of the moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the moon's motion represented by a precessing and rotating elliptical orbit.

Giacaglia, G. E. O.↗

NASA NTRS1974

The local complex of O and B stars. I - Distribution of stars and interstellar dust

The O-B5 stars, supergiants, young clusters, and associations within 1 kpc of the sun populate two flat systems inclined to each other by 19 to 22 deg. The historical background, statistical significance, composition, spatial arrangement of the contents, and interstellar extinction in the two belts are discussed. A more or less random distribution in space and in age characterizes the O-B5 stars of the 'galactic belt', which is aligned nearly along the Milky Way. The 'Gould belt' is inclined to the Milky Way (north in Sco-Oph and south in Orion), and exhibits a projected distribution of O-B5 stars in its mean plane that resembles a 'dragonfly', with five major features defining it. A crude 'diameter' of the system is 750 to 1000 pc, and the sun's position is eccentric, lying toward Ophiuchus. The nuclear age of the system, while not unique, may be characterized as 30 m.y. from the spectral type of the broad main-sequence turnup near B2-5. Most of the O-B2 stars and youngest stellar groups near the sun belong to the Gould belt, but both belts have approximately equal space densities of B3-B5 stars and similar average values of interstellar extinction.-

Stothers, R.↗

NASA NTRS1974

Orbital flux integrations: Parameter values for effective computer time reductions

To improve computer utilization and to reduce the cost of orbital flux integrations, the effects of integration parameters 'duration' (T) and 'stepsize' (delta t) on integration results were investigated. Over given ranges of T and delta t, and within specified acceptable accuracy restraints, optimal values of these parameters were established for circular subsynchronous trajectories, in terms of the variables altitude (H) and inclination (i). It is shown that (1) above a certain statistically important value, duration is independent of both h and i; (2) stepsize has a relative altitude dependence; and (3) stepsize is not a function of inclination. The substantial savings in computer time are discussed along with the possibility of greater savings by relaxing accuracy restrictions while not exceeding the minimum model-associated uncertainty factors of the environments.

Stassinopoulos, E. G.↗

NASA NTRS1975

Fourteen years of resonance of Vanguard orbits

Tracking of Vanguard 3 and the Vanguard 2 rocket with Baker-Nunn cameras and the U.S. Navy's Space Surveillance (radio interferometer) system over a 14 year period revealed resonant fluctuations of up to 0.035 deg in inclination (peak to peak). Six geopotential terms (lumped coefficients) of 11th order and three of 22nd order were measured using orbit inclinations derived from this tracking record. The terms of 11th order are significantly smaller than Kaula's rule. (The lumped coefficients are sensitive to geopotential effects as high as 37th degree.) These observed terms are compatible with a recent 27-satellite geopotential solution whose formal coefficient errors are increased by a factor of 3.3.

Wagner, C. A.↗

NASA NTRS1975

Mission analysis for satellite measurements of stratospheric constituents by solar occultation

Orbital characteristics and launch vehicle requirements for a solar occultation experiment measuring atmospheric constituents, such as aerosols or ozone, during the Nimbus-G and Applications Explorer Missions are analyzed. The experiment to be flown is basically a sun photometer which measures the spectral attenuation of solar radiation by the earth's atmosphere during spacecraft sunrise and sunset, yielding two aerosol and/or ozone stratospheric profiles per orbit. The tangent latitudes and longitudes as well as frequency of these measurements are analyzed for various spacecraft orbits to define maximum geographical coverage capability. Results indicate that a 50 deg inclined orbit for Applications Explorer provides latitude coverage from approximately 70 deg north to 70 deg south every 2-1/2 weeks. A high-moon, sun-synchronous orbit with an inclination of 99 deg for Nimbus-G will provide for coverage of occultation measurements at high latitudes near the polar regions (i.e., 64 to 80 deg north and south). The solar pointing requirements of the experiment in terms of yaw and pitch angles are also defined.

Harrison, E. F.↗

NASA NTRS1975

Optimal orbit transfer for out-of-ecliptic mission using a solar electric spacecraft

This paper analyzes the performance capability of a Titan IIIE/Centaur/SEP (15 kw) for out-of-ecliptic missions. Two classes of orbital transfer modes are considered; circular-to-circular and circular-to-elliptic. The results presented compare the achievable heliographic inclination using these different transfer modes and also show the degradations in performance due to constrained launch azimuth and thruster life. It is observed that the latter transfer mode could deliver a spacecraft to a much higher inclination than the former, but the final orbit is very eccentric and could come very close to the sun. In view of the existence of many trajectories by which this mission can be performed, it is suggested that a trajectory other than IAU circular out-of-ecliptic type be used to explore more scientifically rewarding missions.

Yen, C.-W. L.↗