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.     

Formation of the saturnian system: A modern Laplacian theory

A theory for the formation of Saturn and its family of satellites, which is based on ideas of supersonic turbulent convection applied to the original Laplacian hypothesis, is presented. It is shown that if the primitive rotating cloud which gravitationally contracted to form Saturn possessed the same level of turbulent kinetic energy as the clouds which formed Jupiter and the Sun, given by % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaai% aaigdaaeaacaaIYaaaaOGaaiikaiabeg8aYnaaBaaajea4baGaamiD% aaWcbeaakiaadAhadaqhaaqcKfaGaeaadaWgaaqcKjaGaeaacaWG0b% aabeaaaSqaaiaaikdaaaGccaGGPaGaeyypa0ZaaSqaaSqaaiaaigda% aeaacaaIYaaaaOGaeqOSdiMaeqyWdiNaam4raiaad2eacaGGOaGaam% OCaiaacMcacaGGVaGaamOCaaaa!4D3D!\[\tfrac{1}{2}(\rho _t v_{_t }^2 ) = \tfrac{1}{2}\beta \rho GM(r)/r\] where =0.1065 ± 0.0015, then it would shed a concentric system of orbiting gas rings each of about the same mass: namely, 1.0 × 10^–3 M _S. The orbital radii R _n (n = 0, 1, 2, ...) of these gas rings form a geometric sequence similar to the observed distances of the regular satellites. It is proposed that the satellites condensed from the gas rings one at a time, commencing with Iapetus which originally occupied a circular orbit at radius 11.4 R _S. As the temperatures of the gas rings T _n increase with decreasing orbital size according as T _n 1/R _n , a uniform gradient should be evident amongst the satellite compositions: Mimas is expected to be the rockiest and Iapetus the least rocky satellite. The densities predicted by the model coincide with the Voyager-determined values. Iapetus contains some 8% by weight solid CH₄. Titan is believed to be a captured satellite. It was probably responsible for driving Iapetus to its present distant orbit. Accretional time-scales and the post-accretional evolution of the satellites are briefly discussed.     

On the mass distribution law of systems of protocluster fragments

Starting from the hypothesis of coalescence through inelastic collisions of small fastmoving interstellar gas clouds, an attempt has been made to study the evolutionary mass distribution of a system of fragments simulating a protocluster. The assumption of a mass spectrum with a continuous injection of newly formed entities into the primeval system, and the condition of gravitational reduction of the impact cross-section, have been considered. Comparisons of numerical experiments with the mass spectrum in some well-known young galactic clusters, confirm the mass distribution power-law already obtained by other authors. The empirical Schmidt's law concerning the rate of star formation is also confirmed. The hypothesis of the universal validity of the luminosity function, should not be a priori rejected.     

Ammonia photolysis and the greenhouse effect in the primordial atmosphere of the earth

Photochemical calculations indicate that in the prebiotic atmosphere of the Earth ammonia would have been irreversibly converted to N₂ in less than 40 years if the ammonia surface mixing ratio were ≤ 10^?4. However, if a continuous outgassing of ammonia were maintained, radiative equilibrium calculations indicate that a surface mixing ratio of ammonia of 10^?5 or greater would provide a sufficient greenhouse effect to keep the surface temperature above freezing. With a 10^?4 mixing ratio of ammonia, 60 to 70% of the present day solar luminosity would be adequate to maintain surface temperatures above freezing. A lower limit to the time constant for accumulation of an amount of nitrogen equivalent to the present day value is 10 my if the outgassing were such as to provide a continuous surface mixing ratio of ammonia ≥ 10^?5.     

Phosphine absorption in the 5-μm window of Jupiter

Since the original suggestion by Gillett et al. (1969) it has generally been assumed that the region of partial transparency near 5 μm in Jupiter's atmosphere (the 5-μm window) is bounded by the v₄ NH₃ at 6.1 μm and the v₃ CH₄ band at 3.3 μm. New measurements of Jupiter and of laboratory phosphine (PH₃) samples show that PH₃ is a significant contributor to the continuum opacity in the window and in fact defines its short-wavelength limit. This has important implications for the use of 5-mu;m observations as a means to probe the deep atmospheric structure of Jupiter. The abundance of PH₃ which results from a comparison of Jovian and laboratory spectra is about 3 to 5 cm-am. This is five to eight times less than that found by Larson et al. [Astrophys. J. (1977) 211, 972–979] in the same spectral region, but is in good agreement with the result of Tokunaga et al. [Astrophys. J. (1979) 232, 603–615] from 10-μm observations.     

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.     

Feasibility study of a multiple flyby mission of main belt asteroids

Specific information on the surface morphology, composition, mean density, and internal structure of asteroids, which is necessary to advance our understanding of asteroids, can be obtained only by a detailed investigation of individual bodies: this will require space missions to individual targets. Since an essential characteristic of the asteroids is their variety, several objects must be visited. The Ariane launcher developed presently in Europe makes a multiple flyby mission possible. The first results of our feasibility study are particularly encouraging: during one revolution, five to six preselected main belt asteroids may be approached to within 1000 km with relative velocities which lie between 3 and 14 km/sec using a total impulse correction on the order of 1 to 2 km/sec. The weight of the spacecraft, excluding the engine and the propellant, would be at least 250 kg. This allows a scientific payload of 50 to 60 kg, in which priority will be given to an imaging system and radar altimeter.     

Solution of the equation of transfer for Rayleigh's phase function by the principle of invariance

In this paper we shall construct the solution of the equation of transfer in a semi-infinite atmosphere with no incident radiation for Rayleigh's phase function by the method of the Principles of Invariance and using the law of diffuse reflection. The solution will then be applied to find the laws of darkening for Rayleigh's phase function.     

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.