Safety Analysis for Near Rectilinear Orbit Close Approach Rendezvous in the Circular Restricted Three-Body Problem

On the road to a human exploration of Mars, several mission scenarios beyond Low Earth Orbit have been identified by the International Space Exploration Coordination Group (ISEGC) as significant landmarks. One fundamental step being considered includes the establishment of a new space station on a Near Rectilinear Orbit (NRO), at one of the libration points of the Earth-Moon system. In this context, the ability to rendezvous in cis-lunar space, necessary for the station deployment and its overall operability, will rely on the combined use of the NASA/ESA Orion Multi-Purpose Crew Vehicle and the Space Launch System (SLS), both currently under development. The Near Rectilinear Orbits (NROs) selected for this work have already been studied in literature but, to the author’s knowledge, never considered for a rendezvous analysis. In this paper, a design of Orion’s NRO close approach rendezvous strategy is developed using the Circular Restricted Three-Body Problem (CRTBP) as a baseline framework. First, different linear models used to describe cis-lunar relative motion, as the CRTBP linearized relative equations, the Clohessy-Wiltshire equations and the Straight Line equations are discussed and compared. Second, a direct two-impulse transfer is implemented as a tool to compare the results obtained from the linear models and the full non-linear relative model. It is shown that the error made with linear models is not generally satisfactory for high-precision maneuvers, especially in orbital regions where the lunar influence is highly predominant, such as the periselene. Third, different close approach strategies are implemented, taking into account Orion’s sensor suite, the existing requirements for a LEO rendezvous and the peculiar deep-space conditions. Fourth, a stochastic analysis is performed to validate and compare the results. Finally, a general close approach rendezvous strategy is built so that the safety of the procedure is ensured throughout the whole mission. The requirements deriving from this analysis are then discussed and compared with the ones currently employed for a rendezvous in Low Earth Orbit

Rendezvous Strategies in the Vicinity of Earth-Moon Lagrangian Points

In the context of Human Spaceflight exploration mission scenario, with the Lunar Orbital Platform- Gateway (LOP-G) orbiting about Earth-Moon Lagrangian Point (EML), Rendezvous and Docking (RVD) operational activities are mandatory and critical for the deployment and utilization of the LOP-G (station assembly, crew rotations, cargo delivery, lunar sample return). There is extensive experience with RVD in the two-body problem: in Low Earth Orbit (LEO) to various space stations, or around quasi-circular Low Lunar Orbits (LLO), the latter by Apollo by means of manual RVD. However, the RVD problem in non-Keplerian environments has rarely been addressed and no RVD has been performed to this date in the vicinity of Lagrangian points (LP) where Keplerian dynamics are no longer applicable. Dynamics in such regions are more complex, but multi-body dynamics also come with strong advantages that need to be further researched by the work proposed here. The aim of this paper is to present methods and results of investigations conducted to first set up strategies for far and close rendezvous between a target (the LOP-G, for example) and a chaser (cargo, crew vehicle, ascent and descent vehicle, station modules, etc.) depending on target and chaser orbit. Semi-analytical tools have been developed to compute and model families of orbits about the Lagrangian points in the Circular Restricted Three Body Problem (CR3BP) like NRHO, DRO, Lyapunov, Halo and Lissajous orbits. As far as close rendezvous is concerned, implementation of different linear and non-linear models used to describe cis-lunar relative motion will be discussed and compared, in particular for NRHO and DRO

Rendezvous strategies in the vicinity of Earth-Moon Lagrangian points

In the context of Human Spaceflight exploration mission scenario, with the Lunar Orbital Platform- Gateway (LOP-G) orbiting about Earth-Moon Lagrangian Point (EML), Rendezvous and Docking (RVD) operational activities are mandatory and critical for the deployment and utilization of the LOP-G (station assembly, crew rotations, cargo delivery, lunar sample return). There is extensive experience with RVD in the two-body problem: in Low Earth Orbit (LEO) to various space stations, or around quasi-circular Low Lunar Orbits (LLO), the latter by Apollo by means of manual RVD. However, the RVD problem in non-Keplerian environments has rarely been addressed and no RVD has been performed to this date in the vicinity of Lagrangian points (LP) where Keplerian dynamics are no longer applicable. Dynamics in such regions are more complex, but multi-body dynamics also come with strong advantages that need to be further researched by the work proposed here. The aim of this paper is to present methods and results of investigations conducted to first set up strategies for far and close rendezvous between a target (the LOP-G, for example) and a chaser (cargo, crew vehicle, ascent and descent vehicle, station modules, etc.) depending on target and chaser orbit. Semi-analytical tools have been developed to compute and model families of orbits about the Lagrangian points in the Circular Restricted Three Body Problem (CR3BP) like NRHO, DRO, Lyapunov, Halo and Lissajous orbits. As far as close rendezvous is concerned, implementation of different linear and non-linear models used to describe cis-lunar relative motion will be discussed and compared, in particular for NRHO and DRO

An empirical analysis of women’s working time, and an estimation of female labour supply in Italy

Empirical studies show that misspecification of the married (or cohabiting) women’s labour supply equation may produce inefficient wage-elasticity estimates. In order to reduce the variability of these estimates, we suggest a new approach based on instrumental variables given by the economic value of the domestic unpaid-work of women. Using Italian micro-data on time use (ISTAT Survey on Time Use), and applying both a parametric and a semiparametric procedure, we estimate robust wage-elasticity coefficients of married women’s labour supply. Our results suggest that women’s labour supply is negatively influenced by the indirect cost of their informal activity of childcare and domestic work

Protection and Management of the Annunziata River Mouth Area (Italy)

A better understanding and prediction of the dynamic processes that govern the coastal zone is the topic of the current paper; in particular, a deep investigation of the coastal processes that affect the shoreline dynamic and flood inundation risk is carried out at the Annunziata river mouth area (Italy). The Annunziata River is situated in the Northern part of Reggio Calabria city; it is, at the same time, a source of danger and an important environmental and hydrological resource for Reggio Calabria, since on the right side there is the city port and on the left side there is the public beach. The protection and management of coastal areas should be supported by a deep knowledge of the interaction between water motion and seabed topography, which affects the natural response of coastal systems to changes in external conditions and to human interferences. This work tries to analyze the coastal morphology through the use of some recent models based on spectral theory

Maximum likelihood estimation of an across-regime correlation parameter

In this article, we describe the mlcar command, which implements a maximum likelihood method to simultaneously estimate the regression coeffcients of a two-regime endogenous switching model and the coefficient measuring the correlation of outcomes between the two regimes. This coefficient, known as the \across-regime" correlation parameter, is generally unidentified in the traditional estimation procedures

Safety Analysis for Near Rectilinear Orbit Close Approach Rendezvous in the Circular Restricted Three-Body Problem

International audienceOn the road to a human exploration of Mars, several mission scenarios beyond Low Earth Orbit have been identified by the International Space Exploration Coordination Group (ISEGC) as significant landmarks. One fundamental step being considered includes the establishment of a new space station on a Near Rectilinear Orbit (NRO), at one of the libration points of the Earth-Moon system. In this context, the ability to rendezvous in cis-lunar space, necessary for the station deployment and its overall operability, will rely on the combined use of the NASA/ESA Orion Multi-Purpose Crew Vehicle and the Space Launch System (SLS), both currently under development. The Near Rectilinear Orbits (NROs) selected for this work have already been studied in literature but, to the author’s knowledge, never considered for a rendezvous analysis. In this paper, a design of Orion’s NRO close approach rendezvous strategy is developed using the Circular Restricted Three-Body Problem (CRTBP) as a baseline framework. First, different linear models used to describe cis-lunar relative motion, as the CRTBP linearized relative equations, the Clohessy-Wiltshire equations and the Straight Line equations are discussed and compared. Second, a direct two-impulse transfer is implemented as a tool to compare the results obtained from the linear models and the full non-linear relative model. It is shown that the error made with linear models is not generally satisfactory for high-precision maneuvers, especially in orbital regions where the lunar influence is highly predominant, such as the periselene. Third, different close approach strategies are implemented, taking into account Orion’s sensor suite, the existing requirements for a LEO rendezvous and the peculiar deep-space conditions. Fourth, a stochastic analysis is performed to validate and compare the results. Finally, a general close approach rendezvous strategy is built so that the safety of the procedure is ensured throughout the whole mission. The requirements deriving from this analysis are then discussed and compared with the ones currently employed for a rendezvous in Low Earth Orbit

Maximum likelihood estimation of an across-regime correlation parameter

In this article, we describe the mlcar command, which implements a maximum likelihood method to simultaneously estimate the regression coefficients of a two-regime endogenous switching model and the coefficient measuring the correlation of outcomes between the two regimes. This coefficient, known as the “across-regime” correlation parameter, is generally unidentified in the traditional estimation procedures

A scientific note on a new pest for European honeybees: first report of small hive beetle Aethina tumida, (Coleoptera: Nitidulidae) in Italy

International audienceThe small hive beetle (SHB), Aethina tumida Murray(Coleoptera Nitidulidae), is an important pest of honeybeesin many parts of the world. The beetle is native tosub-Saharan Africa and was unintentionally introducedinto USA (1996), Australia (2001) and in Canada(2002) (Ellis and Munn, 2005; Neumann and Ellis2008). In Europe the SHB was discovered in 2005 ina consignment of queens imported from Texas (USA)into Portugal and destroyed by the Portuguese NationalVeterinarian Services (Murilhas, 2005). Since then,Europe remained free from this pest