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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.↗

NASA NTRS1974

Techniques for evaluating long periodic orbit variations

A method of analyzing long periodic variations of orbits from osculating elements is presented. A precision of 0.03 arc sec in inclination has been achieved with this technique for the GEOS 1 and 2 orbits. A combined numerical-analytical technique for computing mean elements is also described. This method has given mean elements with a precision of 0.1 arc sec in inclination and 10 cm in semimajor axis for the GEOS satellites. Application of these techniques to the determination of earth tidal parameters is also discussed.

Douglas, B. C.↗

NASA NTRS1975

Energetic solar proton vs terrestrially trapped proton fluxes

The relative importance of solar and trapped proton fluxes in the consideration of shielding requirements for geocentric space missions is analyzed. Using models of these particles, their fluences encountered by spacecraft in circular orbits are computed as functions of orbital altitude and inclination, mission duration, threshold energy (10 to 100 MeV), and risk factor (for solar protons only), and ratios of solar-to-trapped fluences are derived. It is shown that solar protons predominate for low-altitude polar and very high-altitude missions, while trapped protons predominate for missions at low and medium altitudes and low inclinations. It is recommended that if the ratio of solar-to-trapped protons falls between 0.1 and 10, both fluences should be considered in planning shielding systems.

King, J. H.↗

NASA NTRS1975

15th order resonance terms using the decaying orbit of TETR-3

Fifteenth-order commensurability of the orbit of TETR-3 (1971-83B) is studied. The study is designed to obtain good discrimination of 15th-order resonances through a better range of inclinations. The first low inclination orbit, 33 deg, is used for this purpose; it is very sensitive to the high degree terms which were rather poorly represented by previously analyzed orbits.

Wagner, C. A.↗

NASA NTRS1975

Jupiter orbiter lifetime - The hazard of Galilean satellite collision

An assessment of the long-term collision risk is made for an uncontrolled orbiting spacecraft that repeatedly enters the spatial region occupied by the satellites. Numerical data are obtained for 50-year orbit propagations which account approximately for the major perturbative effects of Jupiter oblateness, solar gravity and satellite gravity. A broad statistical viewpoint regarding the question of collision likelihood is adopted and is based on a total sample size of 480 initial orbits distributed among 4 orbit classes, 8 inclinations and 15 initial epochs. Numerical results compare favorably with an analytical prediction formula which shows that eccentric, low-inclination orbits have high collision probability.

Friedlander, A. L.↗

NASA NTRS1975

Evidence for non-radial fields in the sun's photosphere and a possible explanation of the polar magnetic signal

The appearance of H-alpha fibrils suggests the presence of magnetic fields inclined at noticeably nonradial angles in the sun's chromosphere. Evidence is presented to suggest that these angles continue into the photosphere. The presence even of small nonradial inclinations can significantly affect the appearance of regions observed by a longitudinal magnetograph. In particular, a simple bipolar loop can appear unbalanced when viewed near the limb. It is suggested that the observed polar signal may be nothing more than a geometric effect arising when a balanced but systematically aligned array of bipolar pairs is viewed at an angle.

Pope, T.↗

NASA NTRS1975

Southern Hemisphere meteor stream determinations

Meteor orbits have been deduced from radio observations of meteor trails carried out at Adelaide, Australia, using a combined multistation CW and pulse radar system operating at 27 MHz. The orbits of 1667 meteors have been determined down to a limiting radio magnitude of +8. The data have been systematically searched for stream meteors, and the significance of minor associations has been appraised. Altogether, 40.4% of the orbits were found to be associated with at least one other orbit, and 29.8% with two or more. Numerous minor streams with high inclination and low eccentricity have been found at deep southern declinations from December to March, with little activity in this quarter during June and October. In addition to confirming several previously established cometary associations, a comprehensive search has indicated that 34 of the meteor associations may be related to 17 comets. Associations between several long-period comets and low-eccentricity high-inclination streams appear to be indisputable, and they confirm the origin of at least some of the 'toroidal group' meteors.

Gartrell, G.↗

NASA NTRS1976

Earth albedo as determined from Skylab data

Earth albedo calculated from Skylab flight data when correlated with latitude falls within the range of values obtained from previous investigations. The Skylab data ranged between latitudes of plus or minus 50 degrees. Seasonal variations show higher values for the winter months and lower values for the summer months. Surface geometry and orbit altitude had little effect on the orbit averaged albedo which was a function of orbit inclination, solar declination, and beta angle. A range of values is presented as a function of orbit inclination.

Prenger, F. C., Jr.↗

NASA NTRS1975

Jupiter orbiter lifetime - The hazard of Galilean satellite collision

An assessment of the long-term collision risk is made for an uncontrolled orbiting spacecraft that repeatedly enters the spatial region occupied by the satellites. Numerical data are obtained for 50-year orbit propagations which account approximately for the major perturbative effects of Jupiter oblateness, solar gravity and satellite gravity. A broad statistical viewpoint regarding the question of collision likelihood is adopted and is based on a total sample size of 480 initial orbits distributed among 4 orbit classes, 8 inclinations and 15 initial epochs. Numerical results compare favorably with an analytical prediction formula which shows that eccentric low-inclination orbits have high collision probability.

Friedlander, A. L.↗

NASA NTRS1977

Implications of outer-zone radiations on operations in the geostationary region utilizing the AE4 environmental model

The radiation exposure in the region of geostationary orbits is examined in search for means of optimizing human performance. It is found that the use of slightly inclined circular orbits is one means by which exposure and spacesuit thickness requirements can be reduced. Another effective technique is to limit the extravehicular activity to those days when the short term fluctuations result in low exposure. Space-suit shielding approaching 1/2 sq cm or less may be possible by utilizing work stoppages and inclined orbits. If aluminum and other low-atomic-number materials are used to construct the habitat, then excessive wall thicknesses are required. If special bremsstrahlung shielding is used, then the habitat shield may be reduced to as low as 2 g/sq cm. Numerous tables and graphs are presented for future analysis of dose in the geostationary region.

Wilson, J. W.↗

NASA NTRS1976

Theory of a cylindrical probe in a collisionless magnetoplasma

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma in the case where the probe axis is inclined at an angle to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit where probe radius is much less than Debye length. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if the ratios of probe radius to Debye length and probe radius to mean gyroradius are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for inclination angles from 0 to 90 deg and for probe-radius mean-gyroradius ratios from 0.1 to infinity. For an angle of 0 deg, the end-effect current is calculated separately.

Laframboise, J. G.↗

NASA NTRS1977

Measurement of post-separated flowfields on airfoils

A small combination pitch-yaw probe designed to facilitate measurement of post-separated flow fields on airfoils is described, along with its calibration. A five-tube probe is found 'ideally suited' to separated-flow measurements because of the pitch and yaw angle information provided in addition to static and total pressures. Wall proximity effects (in a low-speed tunnel) are described. Procedures for measurements in flows with small inclinations in pitch and yaw, for large flow angles, and for scanning flows with large inclinations are indicated.

Seetharam, H. C.↗

NASA NTRS1977

Geopotential resonances on Vanguard orbits

Since their establishment in 1959 the orbits of Vanguard 3 (1959-7A) and the Vanguard 2 rocket (1959-2B) have been slowly contracting through at least five strong resonances of eleventh order. Tracking with Baker-Nunn cameras and the U.S. Navy space surveillance (radio interferometer) system over a 14-year period has revealed resonant fluctuations on them of up to 0.035 deg in inclination (peak to peak). Six geopotential terms (lumped coefficients) of eleventh order and three of twenty-second order have been measured by using orbit inclinations derived from this tracking record. The terms of eleventh order are significantly smaller than is predicted by Kaula's rule. (The lumped coefficients are sensitive to geopotential effects as high as thirty-seventh degree.) These observed terms are compatible with a recent 27-satellite geopotential solution (GEM 7) whose formal coefficent errors are increased by a factor of 3.3.

Wagner, C. A.↗