Bounded motion in a generalized two-body problem

In this paper we prove the existence of ring-type bounded motion in an isolated system consisting of a massive point particle and a homogeneous cube. We study the case of planar motion where the particle moves in a symmetry plane of the cube and we use a rotating frame of reference with its center at the mass center of the cube and its axes coinciding with the symmetry axes of the cube. We prove that, for negative values of the total energy and properly chosen values of the total angular momentum, the relative distance of the bodies has an upper and a lower bound-i.e., the regions of possible motion lie inside an annulus around the cube (motion inside a ring or an island).     

Convection flow over a uniform-flux vertical surface with variable viscosity

A regular perturbation analysis is presented for natural convection flow over an uniform flux vertical surface with temperature dependent viscosity. Numerical calculations are presented forP _r=6.7 which show that the first-order correction to the local temperature difference and to the local skin-fraction are negative whereas it is positive for the local Nusselt number. The effects of variable viscosity on the temperature, velocity profiles, the local temperature difference, the local Nusselt number and the local skin fraction are discussed.     

Lumped geopotential harmonics of order 14, from the orbit of 1967-11G

The satellite 1967-11G, which had an orbital inclination of 40°, passed through the 14th-order resonance with the Earth's gravitational field in 1974. The changes in its orbital inclination at resonance have been analysed to obtain values for four lumped 14th-order harmonics in the geopotential, with accuracies equivalent to about 5 cm in geoid height. Analysis of the eccentricity was also attempted, but did not yield useful results.As no previous satellite analysed at 14th-order resonance has had an inclination near 40°, the results have proved to be valuable in determining individual 14th-order harmonics in the geopotential.     

MANGALA VALLES, MARS: ASSESSMENT OF EARLY STAGES OF FLOODING AND DOWNSTREAM FLOOD EVOLUTION

The Mangala Valles system is an ∼ ∼900 km fluvially carved channel system located southwest of the Tharsis rise and is unique among the martian outflow channels in that it heads at a linear fracture within the crust as opposed to a collapsed region of chaos as is the case with the circum-Chryse channels. Mangala Valles is confined within a broad, north–south trending depression, and begins as a single valley measuring up to 350 km wide that extends northward from a Memnonia Fossae graben, across the southern highlands toward the northern lowlands. Approximately 600 km downstream, this single valley branches into multiple channels, which ultimately lose their expression at the dichotomy boundary. Previous investigations of Mangala Vallis suggested that many of the units mapped interior to the valley were depositional, related to flooding, and that a minimum of two distinct periods of flooding separated by tens to hundreds of millions of years were required to explain the observed geology. We use infrared and visible images from the THermal EMission Imaging System (THEMIS), and topographic data from the Mars Orbiting Laser Altimeter (MOLA), to investigate the nature of the units mapped within Mangala Vallis. We find that the geomorphology of the units, as well as their topographic and geographic distribution, are consistent with most of them originating from a single assemblage of volcanic flow deposits, once continuous with volcanic flows to the south of the Memnonia Fossae source graben. These flows resurfaced the broad, north–south trending depression into which Mangala Vallis formed prior to any fluvial activity. Later flooding scoured and eroded this volcanic assemblage north of the Mangala source graben, resulting in the present distribution of the units within Mangala Vallis. Additionally, our observations suggest that a single period of catastrophic flooding, rather than multiple periods separated by tens to hundreds of millions of years, is consistent with and can plausibly explain the interior geology of Mangala Vallis. Further, we present a new scenario for the source and delivery of water to the Mangala source graben that models flow of groundwater through a sub-cryosphere aquifer and up a fracture that cracks the cryosphere and taps this aquifer. The results of our model indicate that the source graben, locally enlarged to a trough near the head region of Mangala, would have required less than several days to fill up prior to any spill-over of water to the north. Through estimates of the volume of material missing from Mangala (13,000–20,000 km³), and calculation of mean discharge rates through the channel system (∼ ∼5 × 10⁶ m³ s⁻¹), we estimate that the total duration of fluvial activity through the Mangala Valles was 1–3 months.