Certain results gained from investigating the moon using radiophysics methods nekot- oryye rezul'taty issledovaniya luny radio- fizicheskimi metodami
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Seasonal variations in geopotential and effect on long period variations in orbital elements of satellites
Two systems of formulas are presented for the determination of the long period perturbations caused by the Sun and the Moon in the motion of an artificial satellite. The first system can be used to determine the lunar effect for all satellites. The second method is more convenient for finding the lunar effect for close satellites and the solar effect for all satellites. Knowledge of these effects is essential for determining the stability of the satellite orbit. The basic equations of both systems are arranged in a form which permits the use of numerical integration. The two theories are more accurate and more adaptable to the use of electronic machines than the analytical developments obtained previously.
Radiochemical neutron activation analyses for Ag, Au, Bi, Br, Cd, Cs, Ge, In, Ir, Ni, Os, Pd, Rb, Re, Sb, Te, Tl, U and Zn were carried out on 11 samples from the Apollo 11 and 12 sites (two samples of rock 12013, one granitic and one KREEPy; 4 KREEP fragments from 2-4 mm soil 12033,2; 4 anorthositic fragments from 1-3 mm soil 10085,104; 1 sample of 'Luny' rock-felsite-KREEP breccia 12013 10085,31 LR-1). Most Apollo 12 samples were found to have an Imbrium meteoritic component; others, typified by the Luny breccia, apparently contain a new meteoritic component of low Re content. Components of higher Ir/Au ratio (3L, 5L and 7) were found in Apollo 11 anorthositic samples; the fact that their enrichment in meteoritic siderophiles parallels that of Fe, Mg, REE and other KREEP elements is consistent with progressive contamination of an anorthositic crust. The Luny rock was tentatively classified Group 2, supporting the assignment of this group to Serenitatis.
Data on zero applied field measurements of remanent magnetization and magnetic relaxation in a BCS superconductor LuNi 2 B 2 C and several hard ferromagnets are presented and compared. Apparent similarities and differences, in particular in Thermoremanent Magnetization (TRM) - like, Isothermal Remanent Magnetization (IRM) - like, and remanent magnetization measurements with zigzag temperature sweep measurements are outlined. It is discussed how these results could be relevant for the magnetization measurements in diamond anvil cells.
A short period luni-solar theory was generalized for application to arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements were derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.
A zonal geopotential is presented to degree 21 from evaluation of mean elements for 21 satellites including 2 of low inclination. Each satellite is represented by an arc of at least one apsidal rotation. The lengths range from 200 to 800 days. Differential correction of the initial elements in all of the arcs, together with radiation pressure and atmospheric drag coefficients, was accomplished simultaneously with the correction for the zonal harmonics. The satellite orbits and their variations are generated by numerical integration of the Lagrange equations for mean elements. Disturbances due to precession and nutation of the earth's pole, atmospheric drag, radiation pressure and luni-solar gravity are added at from 1- to 8-day intervals in the integrated orbits. The results agree well with recent solutions from other authors using different methods and different satellite sets.
Apollo 14 crystalline rocks (14053 and 14310) and crystalline rock fragments (14001,7,1; 14001,7,3; 14073; 14167,8,1 and 14321,191,X-1) on which Rb/Sr, Ar-40/Ar-39, or cosmic ray exposure ages have been determined by our colleagues were studied with the electron microprobe and the petrographic microscope. Rock samples 14053 and 14310 are mineralogically and petrologically distinct from each other. On the basis of mineralogic and petrologic characteristics all of the fragments, except 14001,7,1, are correlative with rock 14310. Sample 14073 is an orthopyroxene basalt with chemical and mineralogic affinities to ?KREEP,' the ?magic' and ?cryptic' components. Fragment 14001,7,1 is very similar to Luny Rock I.
Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 (1965-89A) and GEOS-2 (1968-002A) yielded the values k2 = 0.22 (sigma = 0.02) and 0.31 (sigma = 0.01) respectively for the second degree Love number. For GEOS-1 a new, purely numerical method involving osculating elements was employed. For GEOS-2 it was necessary to analyze the variations of the mean elements because of the very long period (450d) of the dominant solar tidal perturbation. An additional analysis of the variation of the mean elements of GEOS-1 confirmed the value of k2 obtained from the osculating elements.
The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.
The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r prime; r prime being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.
The luni-solar tidal perturbations in the inclination of the GEOS-I and GEOS-II satellite orbits were analyzed for the solid Earth and ocean tide conditions. Precision reduced camera and TRANET Doppler observations spanning periods of over 600 days for each satellite were used to derive mean orbital elements. Perturbations due to the earth's gravity field, solar radiation pressure, and atmospheric drag were modelled, and the resulting inclination residuals were analyzed for tidal effects. The amplitudes of the observed total tidal effects were about 1.2 arc seconds (36 meters) in the inclination of GEOS-I and 4.5 arc seconds (135 meters) for GEOS-II. The solid earth tides were then modelled using earth tide measurements, earth rotation observations, and seismic data. The resulting inclination residuals were analyzed for ocean tide parameters. The derived parameters consist of one second degree coefficient and an accompanying phase angle in a spherical harmonic expansion of the ocean tidal potential for each tidal constituent. The results are presented.
Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 and GEOS-2 has yielded the values 0.22 and 0.31 respectively for the apparent second degree Love number. For GEOS-1 a new purely numerical method involving osculating elements was employed. For GEOS-2 it was necessary to analyze the variations of the mean elements because of the very long period (450 days) of the dominant solar tidal perturbation. The disparate values indicate that the simple second degree zonal harmonic model of the tidal potential is accommodating other effects in addition to those caused by the solid earth tides. A recent paper by Lambeck et al. (1973) indicates that ocean tide effects have significant perturbations on satellite orbits and cannot be neglected.
A first order, semianalytical theory for the long term motion of resonant satellites is presented. The theory is valid for all eccentricities and inclinations and for all commensurability ratios. The method allows the inclusion of all the zonal and tesseral harmonics as well as luni solar perturbations and radiation pressure. The method is applied to a synchronous satellite including only the J sub 2 and J sub 22 harmonics. Global, long term solutions for this problem, eccentricity, argument of perigee, and inclination are obtained.
The luni-solar effects cause a large amplitude, long-period perturbation of the orbital plane. Canonical differential equations associated with this motion contain a singular point, and are expanded about this point to third order. A solution is given that is valid for long times and is not restricted to small inclinations. Higher order terms are investigated. Expressions are given for the inclination (I) and node as a function of time. Comparisons with a numerically integrated solution show a disagreement in inclination of only .03 deg after 11 years.
The equations of motion of an artificial satellite are given in nonsingular variables. Any term in the geopotential is considered as well as luni-solar perturbations up to an arbitrary power of r/r', r' being the geocentric distance of the disturbing body. Resonances with tesseral harmonics and with the moon or sun are also considered. By neglecting the shadow effect, the disturbing function for solar radiation is also developed in nonsingular variables for the long periodic perturbations. Formulas are developed for implementation of the theory in actual computations.