Easily retrievable objects among the NEO population

Asteroids and comets are of strategic importance for science in an effort to understand the formation, evolution and composition of the Solar System. Near-Earth Objects (NEOs) are of particular interest because of their accessibility from Earth, but also because of their speculated wealth of material resources. The exploitation of these resources has long been discussed as a means to lower the cost of future space endeavours. In this paper, we consider the currently known NEO population and define a family of so-called Easily Retrievable Objects (EROs), objects that can be transported from accessible heliocentric orbits into the Earth’s neighbourhood at affordable costs. The asteroid retrieval transfers are sought from the continuum of low energy transfers enabled by the dynamics of invariant manifolds; specifically, the retrieval transfers target planar, vertical Lyapunov and halo orbit families associated with the collinear equilibrium points of the Sun-Earth Circular Restricted Three Body problem. The judicious use of these dynamical features provides the best opportunity to find extremely low energy Earth transfers for asteroid material. A catalogue of asteroid retrieval candidates is then presented. Despite the highly incomplete census of very small asteroids, the ERO catalogue can already be populated with 12 different objects retrievable with less than 500 m/s of Δv. Moreover, the approach proposed represents a robust search and ranking methodology for future retrieval candidates that can be automatically applied to the growing survey of NEOs

Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be considered as an extension of previous research work on the dynamics of orbits around simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates with backgrounds in celestial mechanics. In the synodic reference frame, the model of a rotating cube is established, the equilibria are calculated, and their linear stabilities are determined. Periodic orbits around the equilibria are computed using the traditional differential correction method, and their stabilities are determined by the eigenvalues of the monodromy matrix. The existence of homoclinic and heteroclinic orbits connecting periodic orbits around the equilibria is examined and proved numerically in order to understand the global orbit structure of the system. This study contributes to the investigation of irregular shaped celestial bodies that can be divided into a set of cubes.Comment: 29 pages, 16 figures, accepted for publication in Astrophysics & Space Scienc

Periodic orbits in the gravity field of a fixed homogeneous cube

In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different types of symmetry planes of the fixed cube, periodic orbits are obtained using the method of the Poincar\'e surface of section. While in general positions, periodic orbits are found by the homotopy method. The results show that periodic orbits exist extensively in symmetry planes of the fixed cube, and also exist near asymmetry planes that contain the regular Hex cross section. The stability of these periodic orbits is determined on the basis of the eigenvalues of the monodromy matrix. This paper proves that the homotopy method is effective to find periodic orbits in the gravity field of the cube, which provides a new thought of searching for periodic orbits around non-spherical celestial bodies. The investigation of orbits around the cube could be considered as the first step of the complicated cases, and helps to understand the dynamics of orbits around bodies with complicated shapes. The work is an extension of the previous research work about the dynamics of orbits around some simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates.Comment: 23 pages, 10 figures, accepted for publication in Astrophysics & Space Scienc

The hierarchical stability of the seven known large size ratio triple asteroids using the empirical stability parameters

In this study, the hierarchical stability of the seven known large size ratio triple asteroids is investigated. The effect of the solar gravity and primary’s J(2) are considered. The force function is expanded in terms of mass ratios based on the Hill’s approximation and the large size ratio property. The empirical stability parameters are used to examine the hierarchical stability of the triple asteroids. It is found that the all the known large size ratio triple asteroid systems are hierarchically stable. This study provides useful information for future evolutions of the triple asteroids

Extension of Earth-Moon libration point orbits with solar sail propulsion

This paper presents families of libration point orbits in the Earth-Moon system that originate from complementing the classical circular restricted three-body problem with a solar sail. Through the use of a differential correction scheme in combination with a continuation on the solar sail induced acceleration, families of Lyapunov, halo, vertical Lyapunov, Earth-centred, and distant retrograde orbits are created. As the solar sail circular restricted three-body problem is non-autonomous, a constraint defined within the differential correction scheme ensures that all orbits are periodic with the Sun’s motion around the Earth-Moon system. The continuation method then starts from a classical libration point orbit with a suitable period and increases the solar sail acceleration magnitude to obtain families of orbits that are parametrised by this acceleration. Furthermore, different solar sail steering laws are considered (both in-plane and out-of-plane, and either fixed in the synodic frame or fixed with respect to the direction of sunlight), adding to the wealth of families of solar sail enabled libration point orbits presented. Finally, the linear stability properties of the generated orbits are investigated to assess the need for active orbital control. It is shown that the solar sail induced acceleration can have a positive effect on the stability of some orbit families, especially those at the L2 point, but that it most often (further) destabilises the orbit. Active control will therefore be needed to ensure long-term survivability of these orbits

The danger of mapping risk from multiple natural hazards

In recent decades, society has been greatly affected by natural disasters (e.g. floods, droughts, earthquakes), losses and effects caused by these disasters have been increasing. Conventionally, risk assessment focuses on individual hazards, but the importance of addressing multiple hazards is now recognised. Two approaches exist to assess risk from multiple-hazards; the risk index (addressing hazards, and the exposure and vulnerability of people or property at risk) and the mathematical statistics method (which integrates observations of past losses attributed to each hazard type). These approaches have not previously been compared. Our application of both to China clearly illustrates their inconsistency. For example, from 31 Chinese provinces assessed for multi-hazard risk, Gansu and Sichuan provinces are at low risk of life loss with the risk index approach, but high risk using the mathematical statistics approach. Similarly, Tibet is identified as being at almost the highest risk of economic loss using the risk index, but lowest risk under the mathematical statistics approach. Such inconsistency should be recognised if risk is to be managed effectively, whilst the practice of multi-hazard risk assessment needs to incorporate the relative advantages of both approaches

A quantitative model for estimating risk from multiple interacting natural hazards: an application to northeast Zhejiang, China

Multi-hazard risk assessment is a major concern in risk analysis, but most approaches do not consider all hazard interactions when calculating possible losses. We address this problem by developing an improved quantitative model - Model for multi-hazard Risk assessment with a consideration of Hazard Interaction (MmhRisk-HI). This model calculates the possible loss caused by multiple hazards, with an explicit consideration of interaction between those hazards. There are two main components to the model. In the first, based on the hazard-forming environment, relationships among hazards are classified into four types for calculation of the exceedance probability of multiple hazards occurrence. In the second, a Bayesian network is used to calculate possible loss caused by multiple hazards with different exceedance probabilities. A multi-hazard risk map can then be drawn addressing the probability of multi-hazard occurrence and corresponding loss. This model was applied in northeast Zhejiang, China and validated by comparison against an observed multi-hazard sequence. The validation results show that the model can more effectively represent the real world, and that the modelled outputs, possible loss caused by multiple hazards, are reliable. The outputs can additionally help to identify areas at greatest risk, and allows a determination of the factors that contribute to that risk, and hence the model can provide useful further information for planners and decision-makers concerned with risk mitigation