The proper connection number pc(G) of a connected graph G is defined as the minimum number of colors needed to color its edges, so that every pair of distinct vertices of G is connected by at least one path in G such that no two adjacent edges of the path are colored the same, and such a path is called a proper path. In this paper, we show that for every connected graph with diameter 2 and mini...

Material collected from an asteroid’s surface can be used to increase gravitational attraction between the asteroid and a Gravity Tractor (GT); the spacecraft therefore operates more effectively and is referred to as an Enhanced Gravity Tractor (EGT). The use of tethers and solar sails to further improve effectiveness and simplify operations is investigated. By employing a tether, the asteroida...

We describe a significant practical consequence of taking anthropic biases into account in deriving predictions for rare stochastic catastrophic events. The risks associated with catastrophes such as asteroidal/cometary impacts, supervolcanic episodes, and explosions of supernovae/gamma-ray bursts are based on their observed frequencies. As a result, the frequencies of catastrophes that destroy...

extensive set of trajectories in both resonances. Moreover, we have included the 4/3 resonance in our study. The frequency map analysis was applied to the fairly realistic models of the 2/1, 3/2, and 4/3 jovian resonances and the Figure 1 shows the basic characteristics of the first-order results were compared with the asteroidal distribution at these mean–motion resonances in the averaged, pla...

Hilary Downes, David W Mittlefehldt, Pierre Hudon, Christopher S. Romanek and Ian Franchi Lunar and Planetary Institute, Houston, Texas, USA ([email protected]); School of Earth Sciences, Birkbeck, University of London, London, UK; NASA/Johnson Space Centre, Houston, Texas, USA; Dept. of Earth and Planetary Sciences, McGill University, Montreal, Quebec, Canada; 5 Savannah River Ecology Labora...

Recent studies show that chaotic motion should be considered as the rule rather than the exception in the asteroid belt, if the perturbations of many planets are taken into account. Assuming that asteroids are constantly diffusing away from the main belt, we may model their transport, i.e. the evolution of a distribution of initial conditions in the action space of the respective dynamical syst...

Effects of solar wind and solar electromagnetic radiation on motion of asteroids are discussed. The results complete the statements presented in Vokrouhlický and Milani (2000). As for the effect of electromagnetic radiation, the complete equation of motion is presented to the first order in v/c – the shape of asteroid (spherical body is explicitly presented) and surface distribution of albedo s...