The restricted problem of n+ν bodies

The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses M_i, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mM_i not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (M_i), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.     

Radar observations of asteroid 1580 Betulia

Radar observations of the asteroid 1580 Betulia, made at a wavelength of 12.6 cm, show a mean radar cross section of 2.2 ± 0.8 km² and a total spectral bandwidth of 26.5 ± 1.5 Hz. Combining our bandwidth measurements with the optically determined rotation period sets a lower limit to the asteroid's radius of 2.9 ± 0.2 km.     

On the influence of mass loss and convective overshooting on the evolution of massive stars

Evolution of massive stars losing mass with the rateM H L/V C is computed (for =1,2,7). It is shown that observed mass loss rates correspond to 0.3 and, therefore, mass loss by stellar wind cannot play any significant role in the evolution of normal massive stars. However, for several types of massive stars (WR, OH/IR, X-ray sources) enhanced mass loss explains their peculiar features. Computations of evolutionary sequences of massive stars with convective overshooting taken into account (as a formal increase of the convective core) show that a significant broadening of the hydrogen-burning band in the H-R diagram may be obtained.     

Spectropolarimetry of the methane and ammonia bands of Jupiter between 6800 and 8200 Å

Spectropolarimetry of Jupiter at resolutions between 22 and 35 Å reveals a strong increase of linear polarization in the 7250-$\text{A}\text{?}$ CH₄ band. This is very probably due to the decreasing contribution toward the band center of the higher orders of scattering, which have a smaller net polarization than the first few orders. The linear polarization is also enhanced in the band at 7900 $\text{A}\text{?}$ comprising the 7920-$\text{A}\text{?}$ NH₃ and 7600- to 8200-$\text{A}\text{?}$ CH₄ bands. The normalized circular polarization shows a feature at 7250 $\text{A}\text{?}$ with a dispersion shape. This is most probably produced in a double-scattering process involving either a solid or liquid aerosol with an absorption at 7250 $\text{A}\text{?}$. Methane aerosols, the obvious candidates from a spectroscopic point of view, are, however, forbidden if current estimates of the Jovian atmospheric temperature are correct.     

Potential and inductive electric fields in the magnetosphere during auroras

During quiescent auroras the large-scale electric field is essentially irrotational. The volume formed by the plasma sheet and its extension into the auroral oval is connected to an external source by electric currents, which enter and leave the volume at different electric potentials and which supply sufficient energy to support the auroral activity. The location of the actual acceleration of particles depends on the internal distribution of electric fields and currents. One important feature is the energization of the carriers of the cross-tail current and another is the acceleration of electrons precipitated through relatively low-altitude magnetic-field-aligned potential drops.Substorm auroras depend on rapid and (especially initially) localized release of energy that can only be supplied by tapping stored magnetic energy. The energy is transmitted to the charged particle via electric inductive fields.The primary electric field due to changing electric currents is redistributed in a complicated way—but never extinguished—by polarization of charges. As a consequence, any tendency of the plasma to suppress magnetic-field-aligned components of the electric fields leads to a corresponding enhancement of the transverse component.     

Spectroscopic observations of winds on Venus: I. Technique and data reduction

We present out methods of measurement and reduction of high-dispersion photographic spectra of Venus. Our preliminary results are consistent with slow direct or no rotation at the level we sample, and disagree strongly with a 4-day retrograde rotation. A serious systematic error, which affects much published work, is due to blending of solar lines in the sky with those reflected from the planet. This always tends to produce a spurious retrograde “rotation.” Only data obtained in a dark sky, or daytime observations from which the sky lines have been accurately subtracted, can be relied upon. All such data give low wind speeds.     

High dispersion spectroscopic observations of Venus near superior conjunction IV. Results for the carbon dioxide bands in the IV-N photographic region

Phase curves for the CO₂ bands at 7883, 7820, and 8689 Å are presented. While the weaker bands at 7820 and 7883 Å show a definite “inverse phase effect,” the band at 8689 Å shows a more normal phase curve; it also exhibited much larger day-to-day variations in the CO₂ abundance near superior conjunction in 1971. Because the variation of the phase curves with band strength is comparable to temporal variations on Venus, simultaneous observations of strong and weak bands are still needed to determine the dependence on band strength accurately.     

Photometric properties of outer planetary satellites

We present optical broadband photometry for the satellites J6, J7, J8, S7, S9, U3, U4, N1, and polarimetry for J6, obtained between 1970 and 1979. The outer Jovian satellites resemble C-type asteroids; J6 has a rotational lightcurve with period ～9.5 hr. The satellites beyond Jupiter also show C-like colors with the exception of S7 Hyperion. S9 Phoebe has a rotational lightcurve with period near either 11.25 or 21.1 hr. For U4 and N1 there is evidence for a lightcurve synchronous with the orbital revolution. The seven brighter Saturnian satellites show a regular relation between the ultraviolet dropoff and distance to the planet, probably related with differences in the rock component on their surfaces.     

Does pluto have a substantial atmosphere?

The presence of CH₄ ice on Pluto implies that Pluto may have a substantial atmosphere consisting of heavy gases. Without such an atmosphere, sublimation of the CH₄ ice would be so rapid on a cosmogonic time scale that either such an atmosphere would soon develop through the exposure of gases trapped in the CH₄ ice or else the surface CH₄ ice would soon be all sublimated away as other, more stable, ices became exposed. If such stable ices were present from the beginning, the existence of CH₄ frosts would also imply that Pluto's present atmosphere contains a remnant of its primordial atmosphere.     

Galilean satellite eclipse studies: III. Jovian methane abundance

The methane abundance in the lower Jovian stratosphere is measured using Galilean satellite eclipse light curves. Spectrally selective observations in and between absorption bands are compared. An average mixing ratio at the locations measured is [CH₄]/[H₂] ～ 1.3 × 10^?3, larger than the value 0.9 × 10^?3 expected for a solar abundance of carbon. Some zenographic variation of the mixing ratio may occur. Observationally compatible values are 1.3–2.0 × 10^?3 in the STZ, 1.3– 2.6 × 10^?3 on the GRS/STrZ edge, and 0.7–1.3 × 10^?3 in the GRS.