On eccentricity functions for eccentric orbits

Situations arise in celestial mechanics where orbital eccentricities are large and yet it is desirable to maintain the Darwin-Kaula Fourier decomposition of the perturbing function. Evaluation of the appropriate eccentricity functionsG _lpq (e) requires a double summation which, for practical purposes, must be truncated. In this note criteria have been established for truncation of the expansion for eccentricities 0.75.     

Guide and examples for users of the ‘SPACEKAP’ style file

Guide and examples for users of the SPACEKAP style fileBasic instructions     

TREK: A cosmic-ray experiment on the Russian space station MIR

The goals of the TREK experiment, now in place on the MIR Space Station, are to resolve and measure the composition of both odd-Z and even-Z cosmic-ray nuclei up to uranium, to measure the isotopic composition of Fe-group nuclei, and to search for transuranic nucleic and exotic particles such as strangelets. To collect tracks of ultraheavy cosmic rays, exterior panels holding an array of BP-1 phosphate glass 1.2m² in area and 16 plates thick are now mounted outside the Kvant-2 module on MIR. Heaters and relays regulate the temperature of the glass at 25°±5°C. The detectors will record 10³ cosmic-ray tracks withZ50 during 2.5 years. An interior panel consisting of an array 0.09 m² in area and 32 plates thick and mounted on the inside wall of the Soyuz spacecraft (attached to the Space Station) will collect tracks of about 13000 Fe and 500 Ni nuclei.     

On periodic flybys of the moon

This paper considers the plane circular restricted three-body problem for small . Symmetric periodic solutions of the second species (passing near the body of mass ) and their distance from the center of the body of mass are studied by constructing perturbations of arc-solutions (solutions with consecutive collisions) existing for =0. Orbits which also pass near the body of mass 1- are studied in detail. The results are applied to finding periodic orbits in the Earth-Moon system and in the Sun-Jupiter system.Russian version: Preprint No. 91 (1978) of Inst. Appl. Math.; present English translation was made by L. M. Perko and W. C. Schulz (February 1979).     

On the perturbation of the anomalistic period of a highly eccentric orbit satellite due to the zonal harmonics

In this note a simple formula is given for the perturbation of the anomalistic period of a highly eccentric orbit due to the zonal harmonics. This perturbation depends essentially only on the semi-major axisa, the eccentricitye (or pericentre radius r =a(1-e)) and the latitude of the pericentre.     

Diffusion-deposition patterns in Martian streaks

The spreading angle of a number of light and dark Martian streaks is determined from selected Mariner 9 images. The resulting frequency distributions of spreading half-angles have maxima at ～5° for light, and ～7° for dark streaks; however the dark streaks have a secondary maximum spreading angle at ～14°. The smaller values, which include most streaks, are interpreted as crater-wake spreading phenomena. The larger value, found in only a few dark streaks or “tails,” may result from atmospheric diffusion and subsequent deposition of material from isolated sources such as vents or blowouts. An atmospheric diffusion-deposition analysis is presented, assuming this streak origin, from which it is possible to deduce the eddy diffusivity, K, in Mars' boudary layer. Calculated K values are found to agree with various theoretical estimates. They lie in the range 10⁷ and 10⁹ cm² sec^?1 and exhibit the proper scale dependence. Thus it appears that, in addition to streak-derived wind direction patterns and speed information, it is possible in a few cases to derive information on Mars' boundary-layer turbulence from streak-spreading measurements.     

Reflectance spectra for sodium and potassium doped ammonia frosts: Implications for Io's surface

This paper reports measurements of the reflection spectra of sodium and potassium doped ammonia frosts as a function of alkali metal concentration which cover the wavelength range 0.35–2.5 μm. The purpose of the measurements was to determine whether or not the reflection spectra for such a solid was compatible with the spectral albedo of Io. The data show that with a sufficiently large alkali metal concentration, the reflection spectra of the doped ammonia frost do not display the characteristic ammonia features at 2.0 and 2.25 μm. The high reflectance of the more concentrated samples and the character of the observed reflection spectrum make it difficult to rule out sodium doped ammonia frost as a surface constituent on Io on the basis of existing data.     

Interhemispheric flow of thermal plasma in a closed magnetic flux tube at mid-latitudes under sunspot minimum conditions

The coupled H⁺ and O⁺ time-dependent continuity and momentum equations are solved within a region of the L = 3 magnetic flux tube lying between (and including) the F2-layers of conjugate hemispheres. The method of solution is an extended and modified version of the Murphy et al. (1976) method. The model is used to study the coupling between the F2-layers of conjugate hemispheres during magnetically quiet periods.The results of the calculations strongly indicate that the protonosphere acts as a reservoir, with variable H⁺ content, which prevents direct coupling between the F2-layers of conjugate hemispheres. However there is generally a significant interhemispheric flow of plasma. This flow is caused by conditions in the summer and winter topside ionospheres and it maintains continuity in the plasma concentration within the protonosphere. There are times when the direction of flow is from the winter hemisphere to the summer hemisphere. It is suggested that maintenance of the winter F2-layer at night is not assisted directly by the F2-layer of the conjugate summer hemisphere.It is shown that during the first few days of protonosphere replenishment after a magnetic storm there is an upflow of H⁺ in the topside ionosphere at all times in the summer hemisphere. There is also an upflow of H⁺ during the daytime in both hemispheres. A comparison with the results obtained when the interhemispheric H⁺ flux is held permanently at zero shows that both F2-layers are little affected by the interhemispheric H⁺ flux. Nevertheless both F2-layers are affected by the H⁺ tube content of the protonosphere. When the H⁺ flux at 1000 km in one hemisphere is much greater than the H⁺ flux at 1000 km in the conjugate hemisphere, there is a corresponding signature in the interhemispheric H⁺ flux.The results suggest that there is insufficient time between magnetic storms for complete replenishment of the protonosphere to occur.     

Introduction to the restricted Jupiter orbiter problem

We consider a restricted six-body problem, consisting of Jupiter, the four Galilean satellites, and an orbiter. The Galilean satellites' orbits are circular and coplanar; Io, Europa, and Ganymede are in exact resonance; their mean longitudes obey the Laplace relation. We seek periodic orbits which avoid close approaches to any satellite; such orbits are of interest for mission planning. They are approximated as equilibrium points of sets of variational equations associated with time-averaged disturbing functions. Stability of the solutions is also determined. The orbits of greatest interest are:Planar: twice Callisto's period, eccentricity0.6Planar: four times Callisto's period, eccentricity0.75Slightly inclined: twice Callisto's period, eccentricity arbitraryPlanar: 4/5 or 5/4 Europa's period.