Upper-atmosphere rotation rate,from analysis of the orbit of 1970-43B

The orbit of Cosmos 347 rocket (1970-43B) has been determined in the form of 23 sets of orbital elements at intervals during its 8-month life, with the aid of the RAE orbit improvement program PROP, using about 850 observations from 47 observing stations. The values of orbital inclination obtained, which had standard deviations between 0.7 and 10 sec of arc, were analysed to give a mean atmospheric rotation rate of 1.40 ± 0.05 rev/day at a mean height near 240 km, for dates between July and December 1970, and local times ranging from 1800 hr to midnight to 0900 hr. This value is higher than those obtained from other satellites at similar heights.     

Upper-atmosphere zonal winds determined from orbital analysis of Cosmos 482, 1972-23A

The orbit of Cosmos 482 has been determined at 55 epochs during the period August 1975–October 1977. Inclined at 52° to the Equator, of eccentricity exceeding 0.3 and perigee height near 210 km, this high drag and high eccentricity orbit is the most eccentric as yet analysed by PROP. The combination of the orbital characteristics, restricted global coverage of observational data, and the many observations of angular measurement at extreme range proved to be troublesome. Cleared of other perturbations, the inclination is analysed to determine the atmospheric rotation rate, λ rev day^?1, of the zonal winds at a height near 235 km. Results reveal a diurnal and seasonal dependence, including a summer value, averaged over local time, of λ = 0.9 and an evening value of λ = 1.4 in the winter months. The resultant wind velocities vary between 48 m s^?1 East to West and 193 m s^?1 West to East, with an average of 48 m s^?1 West to East.     

Upper-atmosphere zonal winds from satellite orbit analysis

In this paper we review and interpret the values of upper-atmosphere rotation rate (zonal winds) obtained by analysing satellite orbits determined from observations. The history of the method is briefly reviewed, the basic principles are explained, objections to the method are answered, and three examples are given. Existing analyses of the atmospheric rotation rate A are critically reviewed, and, after rejecting some and revising others, we are left with 85 values. These are divided according to local time and season, to give the variation of A with height in nine situations—namely morning, evening and average local time, for summer, winter and average season. These observational results indicate that the value of Λ (in rev/day), averaged over both local time and season, increases from 1.0 at 125 km to 1.22 at 325 km and then decreases to 1.0 at 430 km and 0.82 at 600 km. The value of Λ is higher in the evening (18–24 h), with a maximum value (near 1.4) corresponding to a West-to-East wind of 150 m s^?1 at heights near 300 km. The value of Λ is lower in the morning (06–12 h), with East-to-West winds of order 50 m s^?1 at heights of 200–400 km. There is also a consistent seasonal variation, the values of Λ being on average 0.15 higher in winter and 0.1 lower in summer than the average seasonal value. No significant variation with solar activity is found, but there is a slight tendency for a greater rotation rate at lower latitudes for heights above 300 km. Unexpectedly, the values for the 1960s are found to be significantly higher than those for the 1970s. Finally, these observational values are compared with the theoretical global model of Fuller-Rowell and Rees: there is complete agreement on the trends, though there are some differences in the mean values.     

Trigonometric series representations of the orbital inclination function

In this paper, new trigonometric series representations of the orbital inclination functionF _imp (i) in multiples of cosines or sines will be established for all possible values ofl, m, andp. For such representations, the literal analytical expressions and the recurrence formulae satisfied by their coefficients will be established. Moreover, an economic algorithm for the table formulation of these coefficients for the possible values ofl, m, andp is given. Finally, numerical examples of the representations forl=2(1)4;m=0(1)l;p=0(1)l are also included.     

Analysis of the orbital inclination of 1963-27A

The Agena B upper-stage rocket 1963-27A was launched into near-circular orbit, inclined at 82.3° to the Equator, on 29 June 1963. Its orbital elements were available at 52 epochs over the 16 month interval prior to its decay on 26 October 1969. During this period the satellite passed through 31:2 resonance and the variation in orbital inclination near this event was analysed to obtain two lumped geopotential harmonics of order 31. Since the resonance was a weak feature in the data, the resulting values are poorly defined.Either side of the resonance period, the inclination was used to estimate the mean atmospheric rotation rate Λ rev day^?1. The values obtained were Λ = 0.85 ± 0.18 at a height of 440 km for the period June 1968 to February 1969 and Λ = 1.13 ± 0.10 at 338 km for the period June to October 1969.     

Tables for the trigonometric series representations of the orbital inclination function

In this paper, tables for the trigonometric series representations of the orbital inclination functionF _lmp (i) in multiples of cosines or sines will be represented forl=2(1)10;m=0(1)l;p=0(1)l.Astrophysics and Space Science Review Article.     

Orbital inclination of Iapetus and the rotation of the Laplacian plane

This paper explores the possibility that the orbit of Iapetus, with its relatively large inclination but small eccentricity, was generated by a rapid dispersal of a gaseous circumplanetary disk, assumed to be the progenitor of the satellite system. The orientation of the local Laplacian plane is shown to be a sensitive function of the disk's structure. Modification of the disk on a time scale comparable to the precesion of the orbit's nodal line, [i.e., $\text{O}$(10²?10³ years)], can produce a large inclination from one that is initially zero, while leaving the eccentricity unchanged. This time is of the same order of magnitude as the viscous evolution time scale for a fully turbulent disk. Hence Iapetus need not be a captured satellite to account for its curious orbital signature.     

Solar rotation rate from stable sunspot tracings

Positions of sunspots between 1966 and 1976 as observed at Kandilli Observatory were used to determine the differential rotation of the Sun. A total of 202 sunspot groups which were E, F, G, H, and J-types were chosen, and a least-squares solution was calculated with their daily rotations. A gradient difference was found between the two hemispheres of the Sun.     

The determination and analysis of the orbit of NIMBUS 1 rocket, 1964-52B: Variations in orbital inclination

The influence of aerodynamic drag and the geopotential on the motion of the satellite 1964-52B is considered. A model of the atmosphere is adopted that allows for oblateness, and in which the density behaviour approximates to the observed diurnal variation. A differential equation governing the variation of the orbital inclination combining the effects of air drag with those of the Earth's gravitational field is given.The 310 observed values of inclination are modified by the removal of perturbations due to luni-solar attraction, solid Earth and ocean tides, solar radiation pressure, low-order long-periodic tesseral harmonic perturbations and changes due to precession. The method of removal of these effects is given in some detail.The variations in inclination due to drag are analysed to give four values of the average atmospheric rotation rate at heights of 296–476 km at latitude 0–54°. These values are as expected from previous analyses.The analysis of the change in inclination due to solar radiation pressure shows that this rapidly tumbling cylindrical satellite may be considered as equivalent to a spherical satellite of a given area-to-mass ratio.Analysis of the inclination near 15:1 resonance with the geopotential yields values of lumped geopotential harmonics of order 15 and 30, namely, $\text{10}{}^9\text{C}\text{?}{}^{0.1}{}_{15}\text{= ?31.2 ± 2.3 10}{}^9\text{S}\text{?}{}^{0.1}{}_{15}\text{= ?4.4 ± 3.2 10}{}^9\text{C}\text{?}{}^{0.2}{}_{30}\text{= 39.0 ± 10.7 10}{}^9\text{S}\text{?}{}^{0.2}{}_{30}\text{= 51.8 ± 10.0}$     

Analysis of the orbital inclination of Tansei 3 rocket 1977-12B

The orbit of Tansei 3rocket(1977-12B) has been determined at 47 epochs between 1 October 1977 and 19 March 1979 using over 1700 observations and the RAE orbit refinement program PROP6. The rate of change of the inclination was examined to evaluate values of the atmospheric rotation rate, Λ rev day^?1. Analysis yielded the value Λ = 1.1 ± 0.05 at height 315 ± 30 km, average conditions; or alternatively Λ = 1.1 ± 0.1 at height 347 ± 12 km, slight winter bias and Λ = 1.07 ± 0.1 at height 270 ± 18 km, average conditions, supplying further evidence of a decrease in rotation rates from the 1960s to the 1970s.Analysis of the inclination at 15th-order resonance yielded the lumped harmonic values

$\text{10}{}^9\text{C}{}^{\mathrm{0,1}}{}_{15}\text{= 13.4 ± 6.2, 10}{}^9\text{S}{}^{\mathrm{0,1}}{}_{15}\text{= 0.7 ± 13.3}$

for inclination 65.485°.     

Lunar cratering asymmetries with high lunar orbital obliquity and inclination of the Moon

Accurate estimation of cratering asymmetry on the Moon is crucial for understanding Moon evolution history. Early studies of cratering asymmetry have omitted the contributions of high lunar obliquity and inclination. Here, we include lunar obliquity and inclination as new controlling variables to derive the cratering rate spatial variation as a function of longitude and latitude. With examining the influence of lunar obliquity and inclination on the asteroids population encountered by the Moon, we then have derived general formulas of the cratering rate spatial variation based on the crater scaling law. Our formulas with addition of lunar obliquity and inclination can reproduce the lunar cratering rate asymmetry at the current Earth-Moon distance and predict the apex/ant-apex ratio and the pole/equator ratio of this lunar cratering rate to be 1.36 and 0.87, respectively. The apex/ant-apex ratio is decreasing as the obliquity and inclination increasing. Combining with the evolution of lunar obliquity and inclination, our model shows that the apex/ant-apex ratio does not monotonically decrease with Earth-Moon distance and hence the influences of obliquity and inclination are not negligible on evolution of apex/ant-apex ratio. This model is generalizable to other planets and moons, especially for different spin-orbit resonances.     

Optical spectroscopy and photometry of main-belt asteroids with a high orbital inclination

We carried out low-resolution optical spectroscopy of 51 main-belt asteroids, most of which have highly-inclined orbits. They are selected from D-type candidates in the SDSS-MOC 4 catalog.Using the University of Hawaii 2.2 m telescope and the Inter-University Centre for Astronomy and Astrophysics 2 m telescope in India, we determined the spectral types of 38 asteroids. Among them,eight asteroids were classified as D-type asteroids. Fractions of D-type asteroids are 3.0 ± 1.1% for low orbital inclination main-belt asteroids and 7.3 ± 2.0% for high orbital inclination main-belt asteroids.The results of our study indicate that some D-type asteroids were formed within the ecliptic region between the main belt and Jupiter, and were then perturbed by Jupiter.     

Dynamics of Trojan asteroids with large orbital inclination: A preliminary report

Some Trojans have a remarkably large inclination. This fact raises the question whether or not these asteroids are dynamically different from Trojans with an inclination, say smaller than 10°. In this paper the author investigates the dynamics of selected Trojans. Common properties and differences between highly inclined orbits and practically planar ones are discussed.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

Tidal parameters from the variation of inclination of GEOS-1 and GEOS-2

Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 (1965-89A,i=59°) and GEOS-2 (1968-002A,i=106°.) has yielded the valuesk ₂=0.22 (=0.02) and 0.31 (=0.01) respectively for the apparent second degree Love number. For GEOS-1 a new purely numerical method involvingosculating elements was employed. For GEOS-2 it was necessary to analyze the variations of themean elements because of the very long period (450 days) of the dominant solar tidal perturbation. An additional analysis of the variation of the mean elements of GEOS-1 confirmed the value ofk ₂ obtained from the osculating elements. The disparate values indicate that the simple 2nd degree zonal harmonic model of the tidal potential employed by ourselves and all other investigators is accommodating other effects in addition to those caused by the solid Earth tides. A recent paper by Lambecket al. (1973) indicates that ocean tide effects have significant perturbations on satellite orbits and cannot be neglected.     

The secular accelerations of the moon's orbital motion and the earth's rotation

The results and methods of determining the secular accelerations of the Moon's orbital motion and the Earth's rotation from astronomical observations are critically reviewed. In particular, the effect on these results is considered should Spencer Jones' value for the secular acceleration of the Moon be revised. General relationships are deduced between these accelerations, the rate of dissipation of energy in the Earth and the fractional change in the rate of rotation of the Earth. It is shown that the theory of tidal torques alone does not completely account forany of the wide range of results for the retardation of the Earth deduced from astronomical observations.Presented to the NATO Advanced Study Institute on Lunar Studies, Patras, Greece, September 1971.     

On diurnal variations of the solar rotation rate as derived from sunspot tracings

The heliographic positions of more than 100 sunspots were accurately measured several times a day from 1974 until 1979 by means of the computer-controlled tracing method described by Schröter and Wöhl (1975). A striking degree of constancy of the solar rotation rate (about 0.15% or 3 m s^–1) is found, when east-west proper motion components of each individual stable sunspot is considered. However, large differences of the rotation rate are observed (up to 7% or 130 m s^–1) when comparing different sunspots. We found no significant correlation of these fluctuations with characteristics of the sunspots (age, evolution, etc.).Mitteilungen aus dem Kiepenheuer-Institut Nr. 191.     

Secular evolution of the period and inclination of the magnetic to rotation axis and recycled pulsars

Statistical analysis has been carried out of the relations between period and the ageP–t _c, and the inclination of magnetic to rotation axis to the age –t _cof pulsars have been done.Up to characteristic agest _c=3×10⁷ years the period increases as expected for magneto-dipole radiation energy lossesP=P _m (1–exp(–t/ _B ))^1/n–1. Best-fitting parameters of this approximation are the time-scale of the magnetic moment decay _B =4×10⁶ years and breaking indexn=3.6. Fort _c>3×10⁷ years theP–t _cdependence is significantly different.The inclination of magnetic to rotation axis decreases versus age, showing a secular alignment of the axis. But this decrease continues also only up tot _c=3×10⁷ years. Thus bothP–t _cand –t _cdependencies indicate that most of the pulsars of agest _c>3×10⁷ years are not evolutionary continuations of more younger ones, but apparently represent another population of pulsars, which differ by their genetic history or physical processes. This population includes all known millisecond pulsars. We suggest, that this population is a so-called recycled pulsar. The list of candidates of recycled pulsars is presented.A new evaluation of the inclination of the magnetic to the rotation axis for 105 pulsars is presented.     

Additional measurements of the high-latitude sunspot rotation rate

We report measurements of the sunspot rotation rate at high sunspot latitutdes for the years 1966–1968. Ten spots at ¦latitude¦ 28 deg were found in our Mees Solar Observatory H patrol records for this period that are suitable for such a study. On the average we find a sidereal rotation rate of 13.70 ± 0.07 deg day^-1 at 31.05 ± 0.01 deg. This result is essentially the same as that obtained by Tang (1980) for the succeeding solar cycle, and significantly larger than Newton and Nunn's (1951) results for the 1934–1944 cycle. Taken together, the full set of measurements in this latitude regime yield a rotation rate in excellent agreement with the result =14^°.37₇–2^°.77 sin², derived by Newton and Nunn from recurrent spots predominatly at lower latitudes throughout the six cycles from 1878–1944.Summer Research Assistant.     

The equatorial rotation rate of the supergranulation cells

The equatorial rotation rate of the supergranulation cells has been observed to be 14.72±0.07°/day. Velocity patterns observed at different times are cross-correlated to derive the rotation rate. The observed rate is 3% faster than recent observations of the surface rotation rate by Doppler shifts. The difference between the cell rate and surface rate is consistent with a model of the supergranular convection in which angular momentum per unit mass is conserved in the radial flow (Foukal, 1977).Stationed at: Kitt Peak National Observatory. Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.