Dynamics of electron fluxes in the slot between radiation belts in November–December 2014 according to data of the <Emphasis Type="Italic">Vernov</Emphasis> satellite

The variations in the spatial structure and time in electron fluxes with E = 235–300 keV in the slot region (2 < L < 3) between the radiation belts in the period of November 1, 2014 through December 8, 2014 during weak and moderate geomagnetic disturbances (Kp < 4, Dst >–60 nT) are analyzed based on the data of the RELEC complex on board the Vernov satellite (the height and inclination of the orbit are from 640 to 830 km and 98.4°, respectively). Irregular increases in the fluxes of such electrons and formation of a local maximum at L ~ 2.2–3.0 were observed. It has been shown that the intensity of this maximum is inversely proportional to the L value and grows with an increase in the geomagnetic activity level. New features discovered for the first time in the dynamics of radiation belt electrons manifest in the variations in the local structure and dynamics of fluxes of subrelativistic electrons in the slot region.     

Compensation of gravitational attraction disturbance to pure gravity orbit for Inner Formation Flying System

The Inner Formation Flying System (IFFS) consisting of an outer satellite and an inner satellite which is a solid sphere proof mass freely flying in the shield cavity can construct a pure gravity orbit to precisely measure the earth gravity field. The gravitational attraction on the inner satellite due to the outer satellite is a significant disturbance source to the pure gravity orbit and is required to be limited to 10⁻¹¹ m s⁻² order. However, the gravitational disturbance force was on 10⁻⁹ m s⁻² order actually and must be reduced by dedicated compensation mass blocks. The region of relative motion of the inner satellite about its nominal position is within 1 cm in dimension, which raises the complexity of the compensation blocks design. The iterative design strategy of the compensation blocks based on reducing the gravitational attraction at the nominal position of the inner satellite is presented, aiming to guarantee the gravitational force in the relative motion region within requirements after the compensation. The compensation blocks are designed according to the current status of IFFS, and the gravitational disturbance force in the region is reduced to 10⁻¹¹ ms⁻² order with minimized adding mass.     

Exposure estimates for repair satellites at geosynchronous orbit

Communications and weather satellites in geosynchronous (GEO, altitude: 35,793 km.) and geostationary orbits (GSO) are revolutionizing our ability to almost instantly communicate with each other, capture high resolution global imagery for weather forecasting and obtain a multitude of other geophysical data for environmental protection purposes. The rapid increase in the number of satellites at GEO is partly due to the exponential expansion of the internet, its commercial potential and the need to deliver a large amount of digital information in near real time. With the large number of satellites operating at GEO and particularly at GSO, there is a need to think of viable approaches to retrieve, rejuvenate and perhaps repair these satellites. The first step in this process is a detailed understanding of the ionizing radiation environment at GEO. Currently, the most widely used trapped particle radiation environment definition near Earth is based on the NASA’s static AP8/AE8 models which define the trapped proton and electron intensities. These models are based on a large number of satellite measurements carried out in the 1960s and 1970s. In this paper, the AP8/AE8 models as well as a heavy ion galactic cosmic ray (GCR) model are used to define the radiation environments for protons, electrons and heavy ions at low Earth orbit (LEO), medium Earth orbit (MEO) and GEO. LEO and MEO dosimetric calculations are included in the analysis since any launch platform capable of delivering a payload to GEO will accumulate exposure during its transit through LEO and MEO. The computational approach (particle transport) taken in this paper is to use the static LEO, MEO, GEO and geomagnetically attenuated GCR environments as input to the NASA Langley Research Center (LaRC) developed deterministic particle transport codes high charge and energy transport (HZETRN) and coupled electron photon transport (CEPTRN). This is done through exposure prediction within a spherical shell, a legacy Apollo era command service module (CSM) configuration, and a large modular structure represented by a specific configuration of the international Space Station (ISS-11A, circa 2005). Based on the results of the simulations, conclusions are drawn on the exposure levels accumulated by these geometries throughout a mission to GEO.     

Electron flux variations at altitudes of 600–800 km in the second half of 2014. preliminary results of an experiment using RELEC equipment onboard the satellite <Emphasis Type="Italic">VERNOV</Emphasis>

The results of measurements of fluxes and spectra carried out using the RELEC (relativistic electrons) equipment onboard the VERNOV satellite in the second half of 2014 are presented. The VERNOV satellite was launched on July 8, 2014 in a sun-synchronous orbit with an altitude from 640 to 830 km and an inclination of 98.4°. Scientific information from the satellite was first received on July 20, 2014. The comparative analysis of electron fluxes using data from RELEC and using experimental data on the electron detection by satellites Elektro-L (positioned at a geostationary orbit) and Meteor-M no. 2 (positioned at a circular polar orbit at an altitude of about 800 km as the VERNOV satellite) will make it possible to study the spatial distribution pattern of energetic electrons in near-Earth space in more detail.     

Families of periodic solutions in three-dimensional restricted three-body problem

Planar orbits of three-dimensional restricted circular three-body problem are considered as a special case of three-dimensional orbits, and the second-order monodromy matrices M (in coordinate z and velocity v _z ) are calculated for them. Semi-trace s of matrix M determines vertical stability of an orbit. If |s| ≤ 1, then transformation of the subspace (z, v _z ) in the neighborhood of solution for the period is reduced to deformation and a rotation through angle φ, cosφ = s. If the angle ? can be rationally expressed through 2π,φ = 2π·p/q, where p and q are integer, then a planar orbit generates the families of three-dimensional periodic solutions that have a period larger by a factor of q (second kind Poincareé periodic solutions). Directions of continuation in the subspace (z, v _z ) are determined by matrix M. If |s| < 1, we have two new families, while only one exists at resonances 1: 1 (s = 1) and 2: 1 (s = ?1). In the course of motion along the family of three-dimensional periodic solutions, a transition is possible from one family of planar solutions to another one, sometimes previously unknown family of planar solutions.     

Fine structure of the interplanetary shock front according to measurements of the ion flux of the solar wind with high time resolution

According to the data of the BMSW/SPEKTR-R instrument, which measured the density and velocity of solar wind plasma with a record time resolution, up to ~3 ×10^–2 s, the structure of the front of interplanetary shocks has been investigated. The results of these first investigations were compared with the results of studying the structure of the bow shocks obtained in previous years. A comparison has shown that the quasi-stationary (averaged over the rapid oscillations) distribution of plasma behind the interplanetary shock front was significantly more inhomogeneous than that behind the bow-shock front, i.e., in the magnetosheath. It has also been shown that, to determine the size of internal structures of the fronts of quasi-perpendicular (θ_BN > 45°) shocks, one could use the magnetic field magnitude, the proton density, and the proton flux of the solar wind on almost equal terms. A comparison of low Mach (М _А < 2), low beta (β₁ < 1) fronts of interplanetary and bow shocks has shown that the dispersion of oblique magnetosonic waves plays an essential role in their formation.     

Evolution of the out-of-plane amplitude for quasi-periodic trajectories in the Earth–Moon system

The out-of-plane amplitude along quasi-periodic trajectories in the Earth–Moon system is highly sensitive to perturbations in position and/or velocity as underscored recently by the ARTEMIS spacecraft. Controlling the evolution of the out-of-plane amplitude is non-trivial, but can be critical to satisfying mission requirements. The sensitivity of the out-of-plane amplitude evolution to perturbations due to lunar eccentricity, solar gravity, and solar radiation pressure is explored and a strategy for designing low-cost deterministic maneuvers to control the amplitude history is also examined. The method is sufficiently general and is applied to the L₁ quasi-periodic orbit that serves as a baseline for the ARTEMIS P2 trajectory.     

MDO approach for early design of aerobraking orbital transfer vehicles

This paper presents a new multidisciplinary design optimization (MDO) methodology for preliminary design of an aeroassisted orbital transfer vehicle (AOTV) performing a two-way transfer between a low-Earth “parking” orbit and a high-energy orbit. This work has been performed in the frame of Onera's CENTOR [N. Bérend, C. Jolly, F. Jouhaud, D. Lazaro, Y. Mauriot, C. Monjaret, J.M. Moschetta, M. Parlier, J.L. Pastre, Y. Servouze, J.L. Vérant, Project CENTOR: Preparing the design of future orbital transfer vehicles; IAC-07-D.2.3.07, in: 58th International Astronautical Congress, 24–28/09/2007, Hyderabad, India] project whose objective is to prepare tools and methodology for studying and designing future space transportation systems for new kinds of missions such as on-orbit servicing (OOS), payload ferrying, or in-situ observation of space-debris. Using simplified models and an appropriate low-dimension formulation for the optimization problem the method makes possible to obtain rapidly and easily a global view of the trade-off between the payload mass and the total mass. It also makes possible to discuss the feasibility of the vehicle with regard to different multidisciplinary constraints and technology hypotheses for the heat shield. This approach is illustrated by eight different AOTV design studies, considering two different missions (LEO–MEO and LEO–GEO), two different propulsion technologies (LOX-LH2 and LOX-CH4) and two different thermal protection system (TPS) characteristics. In each case, we discuss the feasibility and characteristics of the lightest vehicle carrying a prescribed 100 kg payload, and, conversely, a heavy vehicle with a prescribed 18 ton total mass, carrying the heaviest possible payload.     

Orbit prediction and shuttle rendezvous strategy for eureca

The European Retrievable Carrier (EURECA) is a platform to be launched, deployed and retrieved in low Earth orbit by the Space Shuttle.A newly developed analytical orbit prediction method is described which meets the severe requirements for EURECA's orbit propagation. It is based on an averaging procedure including the Earth's zonal harmonics J₂, J₃ and J₄ and a refined treatment of the air drag perturbation where EURECA's large solar panels are taken into account. Some orbit prediction results are included.In order to offer more flexibility for the Shuttle retrieval of EURECA, it is proposed to execute a part of the rendezvous manoeuvres by EURECA. A corresponding strategy is described.     

Interaction of mental and orthostatic stressors

We assessed hemodynamic responses induced by orthostatic and mental stressors, using passive head up tilt (HUT) and mental arithmetic (MA), respectively. The 15 healthy males underwent three protocols: (1) HUT alone, (2) MA in supine position and (3) MA+HUT, with sessions randomized and ≥2 weeks apart. In relation to baseline, HUT increased heart rate (HR) (+20.4±7.1 bpm; p<0.001), mean blood pressure (MBP) (+4.7±11.3 mmHg; p<0.05), diastolic blood pressure (DBP) (+6.1±11.6 mmHg; p<0.05) and total peripheral resistance (TPR) (+155±232 dyne*s/cm⁵; p<0.001) but decreased stroke volume (SV) (?33.1±13.4 ml; p<0.001) and cardiac output (CO) (?0.6±1.0 l/min; p<0.01). MA increased HR (+8.0±6.0 bpm; p<0.001), systolic blood pressure (SBP) (+9.0±7.7 mmHg; p<0.001), MBP (+10.0±6.5 mmHg; p<0.001), DBP (+9.5±7.2 mmHg; p<0.001) and CO (+0.6±0.8 l/min; p<0.01). MA+HUT increased HR (+28.8±8.4 bpm; p<0.001), SBP (+4.6±14.3 mmHg; p<0.05), MBP (+11.2±11.6 mmHg; p<0.001), DBP (+13.5±10.1 mmHg; p<0.001) and TPR (+160±199 dyne*s/cm⁵; p<0.001) but SV (?34.5±14.6 ml; p<0.001) decreased. Mental challenge during orthostatic challenge elicited greater increases in heart rate, despite similar reductions in stroke volume such as those during orthostatic stress alone. Overall, cardiac output decreases were less with combinations of mental and orthostatic challenges in comparison to orthostasis alone. This would suggest that carefully chosen mental stressors might affect orthostatic responses of people on standing up. Therefore, additional mental loading could be a useful countermeasure to alleviate the orthostatic responses of persons, particularly in those with histories of dizziness on standing up or on return to earth from the spaceflight environment of microgravity.     

Solar cycle variation of “killer” electrons at geosynchronous orbit and electron flux correlation with the solar wind parameters and ULF waves intensity

To construct models for hazard prediction from radiation belt particles to satellite electronics, one should know temporal behavior of the particle fluxes. We analyzed 11-year variation in relativistic electron flux (E>2 MeV) at geosynchronous orbit using measurements made by GOES satellites during the 23rd sunspot cycle. As it is believed that electron flux enhancements are connected with the high-speed solar wind streams and ULF or/and VLF activity in the magnetosphere, we studied also solar cycle changes in rank order cross-correlation of the outer radiation belt electron flux with the solar wind speed and both interplanetary and on-ground wave intensity. Data from magnetometers and plasma sensors onboard the spacecraft ACE and WIND, as well as magnetic measurements at two mid-latitude diametrically opposite INTERMAGNET observatories were used. Results obtained show that average value of relativistic electron flux at the decay and minimum phases of solar activity is one order higher than the flux during maximum sunspot activity. Of all solar wind parameters, only solar wind speed variation has significant correlation with changes in relativistic electron flux, taking the lead over the latter by 2 days. Variations in ULF amplitude advance changes in electron flux by 3 days. Results of the above study may be of interest for model makers developing forecast algorithms.     

轨道分子屏极高真空实验室设计技术研究

给出了一种新型的近地轨道极高真空分子屏实验室设计。作者计算了可变翼分子屏周围大气分子的入射及散射、分子屏材料放气在屏内的分子数流密度。通过调整分子屏的翼角,分子屏内的压力可以达到10-12Pa。计算结果指出:在近地轨道选择合适的分子屏参数,可以在极高真空环境下加工超纯材料。     

Low-energy Earth–Moon transfers involving manifolds through isomorphic mapping

Analysis and design of low-energy transfers to the Moon has been a subject of great interest for decades. Exterior and interior transfers, based on the transit through the regions where the collinear libration points are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is concerned with a geometrical approach for low-energy Earth-to-Moon mission analysis, based on isomorphic mapping. The isomorphic mapping of trajectories allows a visual, intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Two types of Earth-to-Moon missions are considered. The first mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit at L₁ (corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit at L₁, with final injection in a periodic orbit around the Moon. The second mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit at L₁ (corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit at L₁, with final injection in a capture (non-periodic) orbit around the Moon. In both cases three velocity impulses are needed to perform the transfer: the first at an unknown initial point along the low Earth orbit, the second at injection on the stable manifold, the third at injection in the final (periodic or capture) orbit. The final goal is in finding the optimization parameters, which are represented by the locations, directions, and magnitudes of the velocity impulses such that the overall delta-v of the transfer is minimized. This work proves how isomorphic mapping (in two distinct forms) can be profitably employed to optimize such transfers, by determining in a geometrical fashion the desired optimization parameters that minimize the delta-v budget required to perform the transfer.     

Manifold dynamics in the Earth–Moon system via isomorphic mapping with application to spacecraft end-of-life strategies

Recently, manifold dynamics has assumed an increasing relevance for analysis and design of low-energy missions, both in the Earth–Moon system and in alternative multibody environments. With regard to lunar missions, exterior and interior transfers, based on the transit through the regions where the collinear libration points L₁ and L₂ are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is focused on the definition and use of a special isomorphic mapping for low-energy mission analysis. A convenient set of cylindrical coordinates is employed to describe the spacecraft dynamics (i.e. position and velocity), in the context of the circular restricted three-body problem, used to model the spacecraft motion in the Earth–Moon system. This isomorphic mapping of trajectories allows the identification and intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Heteroclinic connections, i.e. the trajectories that belong to both the stable and the unstable manifolds of two distinct periodic orbits, can be easily detected by means of this representation. This paper illustrates the use of isomorphic mapping for finding (a) periodic orbits, (b) heteroclinic connections between trajectories emanating from two Lyapunov orbits, the first at L₁, and the second at L₂, and (c) heteroclinic connections between trajectories emanating from the Lyapunov orbit at L₁ and from a particular unstable lunar orbit. Heteroclinic trajectories are asymptotic trajectories that travels at zero-propellant cost. In practical situations, a modest delta-v budget is required to perform transfers along the manifolds. This circumstance implies the possibility of performing complex missions, by combining different types of trajectory arcs belonging to the manifolds. This work studies also the possible application of manifold dynamics to defining suitable, convenient end-of-life strategies for spacecraft orbiting the Earth. Seven distinct options are identified, and lead to placing the spacecraft into the final disposal orbit, which is either (a) a lunar capture orbit, (b) a lunar impact trajectory, (c) a stable lunar periodic orbit, or (d) an outer orbit, never approaching the Earth or the Moon. Two remarkable properties that relate the velocity variations with the spacecraft energy are employed for the purpose of identifying the optimal locations, magnitudes, and directions of the velocity impulses needed to perform the seven transfer trajectories. The overall performance of each end-of-life strategy is evaluated in terms of time of flight and propellant budget.     

MDO approach for early design of aerobraking orbital transfer vehicles

This paper presents a new multidisciplinary design optimization (MDO) methodology for preliminary design of an aeroassisted orbital transfer vehicle (AOTV) performing a two-way transfer between a low-Earth “parking” orbit and a high-energy orbit. This work has been performed in the frame of Onera's CENTOR [N. Bérend, C. Jolly, F. Jouhaud, D. Lazaro, Y. Mauriot, C. Monjaret, J.M. Moschetta, M. Parlier, J.L. Pastre, Y. Servouze, J.L. Vérant, Project CENTOR: Preparing the design of future orbital transfer vehicles; IAC-07-D.2.3.07, in: 58th International Astronautical Congress, 24–28/09/2007, Hyderabad, India] project whose objective is to prepare tools and methodology for studying and designing future space transportation systems for new kinds of missions such as on-orbit servicing (OOS), payload ferrying, or in-situ observation of space-debris. Using simplified models and an appropriate low-dimension formulation for the optimization problem the method makes possible to obtain rapidly and easily a global view of the trade-off between the payload mass and the total mass. It also makes possible to discuss the feasibility of the vehicle with regard to different multidisciplinary constraints and technology hypotheses for the heat shield. This approach is illustrated by eight different AOTV design studies, considering two different missions (LEO–MEO and LEO–GEO), two different propulsion technologies (LOX-LH2 and LOX-CH4) and two different thermal protection system (TPS) characteristics. In each case, we discuss the feasibility and characteristics of the lightest vehicle carrying a prescribed 100 kg payload, and, conversely, a heavy vehicle with a prescribed 18 ton total mass, carrying the heaviest possible payload.     

Results of the early orbit manoeuvres of the ampte-uks

The Active Magnetospheric Particle Tracer Explorers (AMPTE) program consists of three satellites which were launched on 16th August 1984. The scientific aim of the mission is to inject lithium and barium tracer ions inside and outside the Earth's magnetosphere and to detect and monitor these ions as they diffuse through the inner magnetosphere. The first of these three satellites, the U.S. Charge Composition Explorer (CCE) was launched into an elliptical orbit of apogee 8 R_e. The other two satellites are the West German Ion Release Module (IRM) and the U.K. Subsatellite (UKS), both of which were launched on the same vehicle into a highly elliptical orbit of apogee 18 R_e. At discreet intervals during the mission the IRM will release ions into the solar wind, and the movement of these ions will be monitored by the UKS. Depending on the particular scientific requirement, the UKS has to be positioned accurately at a given distance behind the IRM. Initially the UKS has to be located 100 km behind the IRM, and held there for ～9 months. It will then be moved a distance of ～1 R_e behind the IRM. In order to manoeuvre the UKS around its orbit, a cold gas jet system is incorporated on the satellite, allowing impulses to be applied both along and perpendicular to the orbit velocity vector. The orbit control system also has to cater for relative orbit changes due to air drag at perigee, as the IRM and the UKS have different $\text{area}\text{mass}$ ratios. This paper presents an account of the orbit control system implemented on the UKS, together with the mathematical approach adopted, and results from manoeuvres made in the first weeks of the mission.     

Effects of small-scale plasma disturbance on the IKB-1300 spacecraft potential

The potential of the Intercosmos-Bulgaria-1300 (IKB-1300) satellite launched to a circular orbit at an altitude ～900 km was measured with several instruments. Care was taken to equalize the potential along the satellite surface. The satellite was placed inside the conducting screen and the solar cells had a metal coating. The satellite potential slightly varied along the trajectory and in the typical case it was “?2”B that corresponds to 5 kTe/e. While the satellite crossed the auroral zone small-scale fluctuations of plasma and field parameters, known as shocks, were recorded. In this region a sharp decrease of the satellite negative potential is often observed. In this case the potential variations well correlate with the increasing flux of energetic electrons. The observed variations can be explained by secondary electron emission from the satellite surface.     

Effect of reflected ions on the formation of the structure of interplanetary quasi-perpendicular shocks for Mach numbers lower than the first critical mach number

Based on the data of the BMSW instrument installed on the of SPEKTR-R spacecraft, as well as according to the data of instruments of the WIND spacecraft, etc., using two examples, the paper has studied the role of ions reflected from the front and associated structural features of quasi-perpendicular interplanetary shocks (IS) with the Alfvén Mach number М _A lower than the first critical Mach number М _c1 . It has been shown that BSs with the finite parameter 0.1 < β₁ < 1 contain a small fraction of reflected protons, which play a significant role in forming the front structure (β₁ is the ratio of gas-to-magnetic pressure before the shock front). In particular, in the case of a perpendicular shock recorded on August 24, 2013 (the angle between the magnetic field direction and the normal to the front θ_Bn ≈ 85°), an IS with a small Mach number (М_A ≈ 1.4) and small β₁ ≈ 0.2 is shown that the interactions of reflected ions with inflowing solar wind may result in the collisionless heating of ions in front of and behind it. The case of the oblique (θ_Bn = 63°) IS on April 19, 2014 with a small Mach number (М ^A ≈ 1.2) and small β₁ ≈ 0.5 has been investigated. It has been found that, before the front, there is a sequence of trains of magnetosonic waves, the amplitude of which decreases to zero upon increasing their distance from the front. The mechanism of their formation is associated with the development of instability caused by the ions reflected from the front.     

Collisions of stars by oscillating orbits of the second kind

Ordinary estimations of the number of star collisions in our galaxy—by simple kinematic considerations—lead to a very small number of such collisions: about one or even less every millions of years. However star collisions can occur through the following indirect way which has a much higher probability. (a) Binary stars are very common in our galaxy, about 30–50% of the stars. (b) If two binary stars meet a triple system can be formed by an ordinary exchange type motion. (c) A triple system is generally decomposed into the “inner orbit” (i.e. the relative orbit of the two nearest stars) and the “outer orbit” (i.e. the relative orbit of the third star with respect to the center of mass of the two nearest stars). The major axes of these two orbits have generally small perturbations and it is the same for the eccentricity of the outer orbit. On the contrary, if the relative inclination of the two orbits is large, the perturbations of the eccentricity of the inner orbit are important and can even in some cases lead to an eccentricity equal to one, that is to a collision of the two stars of the inner orbit.Such orbits can be called “oscillating orbits of the second kind”, indeed the first oscillating orbits—conceived by Khilmi and described for the first time in an example by Sitnikov—have unbounded mutual distances r_ij, but the system always come back to small sizes, it has an infinite number of very large expansions followed by strong contractions and, in the three-body case, an upper bound of lim inf (r_1.2 + r_1.3 + r_2.3) can be given in terms of the three masses and the integrals of motion. For the oscillating orbits of the second kind the mutual distances r_ij are bounded, but the velocities are unbounded (i.e. lim inf r_ij = 0 for at least one r_ij) and the system goes to a collision if the bodies have non-zero radius even small. The analytical study of the oscillating orbits of the second kind is a part of the general analytical study of the three-body problem, a part which must be valid for large eccentricities and large inclinations. The use of Delaunay's variables and of a Von Zeipel transformation lead to a first order integrable approximation, valid for any eccentricities and any inclinations, and giving the following results: (a) The oscillating orbits of the second kind occur when the angular momentum of the outer orbit has a modulus sufficiently close to the modulus of the total angular momentum of the three-body system. Hence these orbits occur for inclinations in the vicinity of 90°. (b) The oscillating orbits represent a set of positive measure of phase space and the first order study allows to give a rough estimation of the probability of collisions—even for stars of infinitely small radius. This probability, for given initial major axes and eccentricities and for isotropic arbitrary initial orientations, is generally of the order of m₃$\text{R}\text{M}$ (m₃ being the mass of the outer star, M the total mass and R the ratio of the period of the inner orbit to that of outer orbit).One question remains to be solved: how many collisions of stars are due to that phenomenon? That question is difficult because the probability of formation of a triple system by a random meeting of two binaries is very uneasy to estimate. However it seems that, compared to the usual evaluations based on pure kinematic considerations without gravitational effects, the number of collisions must be multiplied by a factor between one thousand and one million.     

Deployment history and design considerations for space reactor power systems

The history of the deployment of nuclear reactors in Earth orbits is reviewed with emphases on lessons learned and the operation and safety experiences. The former Soviet Union's “BUK” power systems, with SiGe thermoelectric conversion and fast neutron energy spectrum reactors, powered a total of 31 Radar Ocean Reconnaissance Satellites (RORSATs) from 1970 to 1988 in 260 km orbit. Two of the former Soviet Union's TOPAZ reactors, with in-core thermionic conversion and epithermal neutron energy spectrum, powered two Cosmos missions launched in 1987 in ～800 km orbit. The US’ SNAP-10A system, with SiGe energy conversion and a thermal neutron energy spectrum reactor, was launched in 1965 in 1300 km orbit. The three reactor systems used liquid NaK-78 coolant, stainless steel structure and highly enriched uranium fuel (90–96 wt%) and operated at a reactor exit temperature of 833–973 K. The BUK reactors used U-Mo fuel rods, TOPAZ used UO₂ fuel rods and four ZrH moderator disks, and the SNAP-10A used moderated U-ZrH fuel rods. These low power space reactor systems were designed for short missions (～0.5 kW_e and ～1 year for SNAP-10A, <3.0 kW_e and <6 months for BUK, and ～5.5 kW_e and up to 1 year for TOPAZ). The deactivated BUK reactors at the end of mission, which varied in duration from a few hours to ～4.5 months, were boosted into ～800 km storage orbit with a decay life of more than 600 year. The ejection of the last 16 BUK reactor fuel cores caused significant contamination of Earth orbits with NaK droplets that varied in sizes from a few microns to 5 cm. Power systems to enhance or enable future interplanetary exploration, in-situ resources utilization on Mars and the Moon, and civilian missions in 1000–3000 km orbits would generate significantly more power of 10's to 100's kW_e for 5–10 years, or even longer. A number of design options to enhance the operation reliability and safety of these high power space reactor power systems are presented and discussed.