Estimating the Risk of Satellite Collisions in Densely Populated Orbit Shells

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence

Probabilities of Atomic Departures from the Slit System

The theoretical description of experimental data on transport in open systems has been of interest for more than a hundred years. Boltzmann proposed a new view of the transfer of matter. Now it is possible to describe the transfer processes from a microscopic point of view. The solution of the Boltzmann equation and the equations derived from it is a complex problem related to the mathematical problems of solving such equations. On the other hand, the complexity of the solution is related to the geometry of the system in which the transfer process takes place. Fundamental physical calculations are made for systems: flat, slotted, cylindrical, rectangular, etc. In the free molecular mode of gas flow, collisions of molecules occur mainly with the walls of systems. In this connection, there was a direction related to the calculation of the probabilities of atomic transport in the system. In this paper, we propose an approach for determining the probabilities of atomic outcomes from slit systems depending on the relative height of the walls of H systems. Exact formulas are obtained for calculating the probabilities of atomic departures from systems without colliding with walls, the distribution of atomic collisions over the height of the system wall, the probabilities of atoms entering the condensed phase after a single collision with the system walls, and the probabilities of atomic departures from systems after a single collision with walls. The accuracy of the obtained formulas was compared with the data obtained from computer experiments using the Monte Carlo method.

A Chemical Dynamics Study of the Reaction of the Methylidyne Radical (CH, X2Π) with Dimethylacetylene (CH3CCCH3, X1A1g)

The gas-phase reaction of the methylidyne (CH; X2Π) radical with dimethylacetylene (CH3CCCH3; X1A1g) was studied at a collision energy of 20.6 kJ mol-1 under single collision conditions with experimental results...

Directed Gas-Phase Preparation of the Elusive Phosphinosilylidyne (SiPH2, X2A’’) and Cis/Trans Phosphinidenesilyl (HSiPH; X2A’) Radicals Under Single-Collision Conditions

The reaction of the D1-silylidyne radical (SiD; X2Π) with phosphine (PH3; X1A1) was conducted in a crossed molecular beams machine under single collision conditions. Merging of the experimental results with...

A chemical dynamics study on the gas-phase formation of triplet and singlet C5H2carbenes

Since the postulation of carbenes by Buchner (1903) and Staudinger (1912) as electron-deficient transient species carrying a divalent carbon atom, carbenes have emerged as key reactive intermediates in organic synthesis and in molecular mass growth processes leading eventually to carbonaceous nanostructures in the interstellar medium and in combustion systems. Contemplating the short lifetimes of these transient molecules and their tendency for dimerization, free carbenes represent one of the foremost obscured classes of organic reactive intermediates. Here, we afford an exceptional glance into the fundamentally unknown gas-phase chemistry of preparing two prototype carbenes with distinct multiplicities—triplet pentadiynylidene (HCCCCCH) and singlet ethynylcyclopropenylidene (c-C5H2) carbene—via the elementary reaction of the simplest organic radical—methylidyne (CH)—with diacetylene (HCCCCH) under single-collision conditions. Our combination of crossed molecular beam data with electronic structure calculations and quasi-classical trajectory simulations reveals fundamental reaction mechanisms and facilitates an intimate understanding of bond-breaking processes and isomerization processes of highly reactive hydrocarbon intermediates. The agreement between experimental chemical dynamics studies under single-collision conditions and the outcome of trajectory simulations discloses that molecular beam studies merged with dynamics simulations have advanced to such a level that polyatomic reactions with relevance to extreme astrochemical and combustion chemistry conditions can be elucidated at the molecular level and expanded to higher-order homolog carbenes such as butadiynylcyclopropenylidene and triplet heptatriynylidene, thus offering a versatile strategy to explore the exotic chemistry of novel higher-order carbenes in the gas phase.