The occultation of κ geminorum by Eros

The predictions and observations of the occultation of κ Gem by Eros on January 24, 1975, are described. At least eight positive and several critical negative observations were made in western New England. The paucity of observations on the western side of the track makes the analysis somewhat ambiguous, but a circular cross section of diameter up to 23 km gives a good fit to most of the available data. Consideration of a crucial, unconfirmed negative observation indicates that an elliptical solution 17 by 7 km (with the long axis in the direction of motion of the “shadow” of Eros) may be preferable, but this does not represent the positive observations so satisfactorily. The ellipse was therefore distorted into a more irregular shape about 20 km long and 7 km wide, rounded on one long side and flattened on the other. Both this irregular shape and the ellipse yield geometric albedos near 0.5, which is considerably higher than has been derived for most other planets or satellites lacking an atmosphere. The albedo that corresponds to the circular solution (0.1) is less than the polarimetric albedo of 0.21 for Eros. It is suggested either that the circle should be warped into an ellipse of dimensions 21 by 13 km, or, if some weight is given to the critical negative observation and the westernmost positive observation, that the profile is a kind of dumbbell.     

A dynamical investigation of the conjecture that Mercury is an escaped satellite of Venus

The possibility that Mercury might once have been satellite of a Venus, suggested by a number of anomalies, is investigated by a series of numerical computer experiments. Tidal interaction between Mercury and Venus would result in the escape of Mercury into a solar orbit. Only two escape orbits are possible, one exterior and one interior to the Venus orbit. For the interior orbit, subsequent encounters are sufficiently distant to avoid recapture or large perturbations. The perihelion distance of Mercury tends to decrease, while the orientation of perihelion librates for the first few thousand revolutions. If dynamical evolution or nonconservative forces were large enough in the early solar system, the present semimajor axes could have resulted. The theoretical minimum quadrupole moment of the inclined rotating Sun would rotate the orbital planes out of coplanarity. Secular perturbations by the other planets would evolve the eccentricity and inclination of Mercury's orbit through a range of possible configurations, including the present orbit. Thus the conjecture that Mercury is an escaped satellite of Venus remains viable, and is rendered more attractive by our failure to disprove it dynamically.     

Fine structure in the sunspot spectrum-2 to 70 years

Application of a new data adaptive approach to power spectrum estimation has yielded evidence for a double solar cycle line in the Zurich sunspot time history. There is significant power from 8 to 15 yr in the spectrum with the primary line at 11.1 yr and three attendant multiplets that may be significant. The first four harmonics of the solar cycle are detected too. Quite marginal evidence for a peak at 65 yr in the spectrum is presented. These results closely correspond to those recently found in the geomagnetic spectrum.     

The post-eclipse brightening of Io

We review the photometric work on eclipse reappearances of Io. New observations of eclipse reappearances of Io confirm the post-eclipse brightness anomaly reported by Binder and Cruikshank (1964) but testify to its intermittent nature. A post-eclipse anomaly of approximately 0.07 mag was observed on two occasions in 1972, while observations of Europa and Ganymede showed no brightness anomaly greater than 0.01 mag. The atmospheric condensation model for the anomaly on Io is reviewed in terms of the quantity of frost required to produce the effect and the corresponding amount of gas liberated to the atmosphere upon sublimation. The observational data and the results from a stellar occultation are in general accord with the theoretical predictions of the stability of heavy gases on Io, while both observational and theoretical criteria are satisfied by a tenuous atmosphere of a heavy gas such as methane or ammonia having a surface pressure ～10^?7 bar.     

A dynamical model of the corona

The hydrodynamic equations for an ideal, inviscid, fully ionized hydrogen gas in a gravitational, but not magnetic, field are solved by an explicit Lax-Wendroff two-step technique using a one-dimensional slab symmetry. Radiation and thermal conductivity are included. The model spans 100000 km starting from the chromosphere-corona transition region. An initially isothermal gas is seen to evolve coronal properties in 4000 s, by which time it settles into dynamic equilibrium characterized by a 2000 km transition region, a temperature maximum of 1.6 × 10⁶ K at a height of 60000 km, and a solar wind mass flux of 10^-9 g cm^-2 s^-1.     

An analytical iterative algorithm for the prediction of special satellite orbit points with the Brouwer orbit theory

Employing a direct recursive algorithm in relation with analytical theories will yield a considerable saving in computer time, as opposed to simulating a point by point integration through repeated evaluations of the orbit theory. As a case in point, we shall compute the set of osculating orbiting elements corresponding to special events within the revolution of an artificial satellite.     

Quasi-periodic orbits about the translunar libration point

Analytical solutions for quasi-periodic orbits about the translunar libration point are obtained by using the method of Lindstedt-Poincaré and computerized algebraic manipulations. The solutions include the effects of nonlinearities, lunar orbital eccentricity, and the Sun's gravitational field. For a small-amplitude orbit, the orbital path as viewed from the Earth traces out a Lissajous figure. This is due to a small difference in the fundamental frequencies of the in-plane and out-of-plane oscillations. However, when the amplitude of the in-plane oscillation is greater than 32 379 km, there is a corresponding value of the out-of-plane amplitude that will produce a path where the fundamental frequencies are equal. This synchronized trajectory describes a halo orbit of the Moon.     

ROAD DRAINAGE AND EQUILIBRIUM IN SMALL STREAM BASINS*

Roads and road drainage accompany the development of the physical landscape for cultural purposes. The addition of a road network to a small stream basin creates a situation of geomorphic disequilibrium by adding to the length of surface drainage channels. Effects of road drainage on the geomorphic equilibrium of small stream basins are analyzed using Horton's Law of Stream Lengths. The effects of different types of road networks are analyzed using an hypothetical stream basin and eight hypothetical road networks, suggesting a method of predicting the location and extent of disequilibrium in a stream basin system as a result of road drainage.