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In this work, we study the effects of solar radiation pressure (SRP) on the problem of changing the orbit of an asteroid to support planetary defense, scientific research, or exploitation of materials. This alternative considers a tethered reflective balloon (or a set of reflective balloons) attached to the asteroid, with a high area-to-mass ratio, to use the SRP to deflect a potentially hazardous asteroid (PHA) or to approximate the target asteroid to Earth. The tether is assumed to be inextensible and massless, and the motion is described only in the orbital plane of the asteroid around the Sun. The model is then used to study the effects that the tether length, the reflectivity coefficient, and the area-to-mass ratio have on the deviation of the trajectory of the asteroid.

The dynamics of a hanging cantilevered pipe aspirating fluid and simultaneously subjected to a partially confined external axial flow in the reverse direction has been investigated experimentally. A bench-top-size apparatus is used in this experiment consisting of a pressure vessel filled with water, a hanging cantilevered pipe and a shorter concentric outer rigid tube which is also vertically cantilevered. The flow configuration investigated in this paper is a simplified representation of the hydrocarbon storage mode of salt-mined caverns, which are large underground cavities used for storing hydrocarbons. An experimental investigation has been conducted to determine the effect of the size of the annular gap on the onset of instability for various external to internal flow velocity ratios, Uo/Ui, ranging from 0.015 to 0.80. It was found that, for the range of flow velocity ratios investigated, the pipe loses stability via first-mode flutter. For the lower ratios of flow velocity, namely Uo/Ui = 0.015–0.06, the bifurcation diagrams show an increase in the root-mean-square (rms) amplitudes at three different ascending rates as the internal flow velocity Ui increased. In contrast, for high flow velocity ratio bifurcation diagrams, i.e., for Uo/Ui = 0.40–0.80, there is an increase in rms amplitude at a certain rate, followed by a diminished rate of growth as the internal flow velocity is increased further. The results demonstrate that the onset of instability occurs at relatively lower flow velocities as the Uo/Ui ratio is increased. Moreover, enlarging the annular gap has a stabilizing effect on the aspirating pipe. In comparison with the narrower rigid tube, with a wider rigid tube the signal power of the second-mode frequency was significantly amplified.

The NASA DART and ESA Hera missions to binary asteroid 65803 Didymos have generated a lot of interest in the study of spacecraft dynamics in the vicinity of binary asteroids. The combination of the effect of the irregular shape and the rotation of the primary bodies makes them not only non-linear, but also non-autonomous systems. This study uses a technique to design reference trajectories in the context of a mission to a binary asteroid system using a fourth-order gravitational potential model for the two primary bodies. The rotation of the primary bodies, their elliptical mutual motion and the solar radiation pressure are also considered in the model, which makes this study unique. It then compares the control effort required when these reference trajectories are used with that required when reference trajectories are built with simpler models. The goal is to examine how the choice of the model used to compute reference trajectories influences the control effort required to keep the spacecraft close to them.

Use of a debris-tether-tug (DTT) system has been recognized as one of the most promising techniques for space debris removal. Attitude motion of the debris may give rise to severe disturbances to the debris removal system. In this case, a conventional DTT system with a single tether may no longer be capable of removing the debris in a stable manner. A hierarchical tether architecture is proposed to stabilize the debris with a main tether from the tug branched into multiple sub-tethers attached to the edges of the debris. The primary goal of this paper is to study the dynamics of a DTT system consisting of a tug, a rigid debris and the proposed tether architecture. First, a three-dimensional dynamics model is developed using Kane's method. A simplified model is studied analytically to determine the equilibrium configurations and their stability, and the frequencies of oscillation about the stable equilibrium points. Numerical simulations are then conducted to verify the analytical results with both rigid and elastic tethers. Additionally, the stabilization effect of the branched tether system is investigated considering various debris angular velocities.

Every year near-Earth object (NEO) surveys discover hundreds of new asteroids, including the potentially hazardous asteroids (PHA). The possibility of impact with the Earth is one of the main motivations to track and study these objects. This paper presents a tether assisted methodology to deflect a PHA by connecting a smaller asteroid, altering the center of mass of the system, and consequently, moving the PHA to a safer orbit. Some of the advantages of this method are that it does not result in fragmentation, which could lead to another problem, and also the flexibility to change the configuration of the system to optimize the deflection according to the warning time. The dynamics of the PHA-tether-asteroid system is analyzed, and the amount of orbit change is determined for several initial conditions. Only motion in the plane of the orbit of the PHA around the Sun is considered, thus the PHA chosen for the simulations has low orbit inclination. Analysis of the dynamics of the system shows that the method is feasible for planetary defense.

Missions to asteroids are now an important component of the space exploration program of major space agencies in the world, with the goal of better understanding the formation of the Solar system and learn about their dynamics to be able to react in case of a possible collision with the Earth. As binary asteroids compose approximately 16% of near Earth asteroids, they are getting more attention from researchers. One mission is currently being planned to binary asteroid system 65803 Didymos. This mission motivates research on the dynamics of a spacecraft near a binary asteroid. Since the primary bodies of these binary systems have small masses, perturbations like the Solar Radiation Pressure (SRP) or the shape of the primary bodies have a great influence on the dynamics of a spacecraft in their vicinity. Studies that already exist on the effect of the SRP on the dynamics of a spacecraft near binary asteroid systems have mostly used low-fidelity SRP acceleration models, such as the cannonball model or simple flat plate model with a purely reflecting spacecraft. This study shows how the choice of the model influences the strength of the SRP acceleration acting on the spacecraft and how it is possible to take advantage of the choice of the nominal attitude of the spacecraft to influence how the SRP affects the spacecraft dynamics when using a more complex SRP acceleration model. Various types of trajectories are studied, with different results and conclusions.

Asteroid missions are now an important component of space exploration, and binary asteroids compose approximately 16% of the near Earth asteroids (NEA) population. This fact, combined with the plan...

One of the most promising techniques to capture large debris on orbit consists in the use of tether-nets. With this concept currently at a medium technological readiness level only, numerical studies on tether-net removal missions are still needed. This paper presents a versatile simulator developed with the aim of gaining insight into the dynamics of tether-net capture of space debris. Its modular architecture supports multiple modeling choices and allows simulating diverse capture scenarios with different system designs. Simulation results are shown for the capture of a realistic launcher upper stage with the representation of the main components of the system, consisting in chaser, main tether, net, and two possible configurations of a closing mechanism. It is shown that only a closing mechanism with more than one attachment to each side of the net can guarantee containment of this type of debris after capture. It is also observed that a safer capture scenario is one in which the axis of rotation of the target is parallel to the direction of ejection of the net. Additional simulation results suggest that tether-nets could be used to capture not only large debris, but also small asteroids, and that this simulator could enable future studies.

This paper proposes the Coulomb tether double-pyramid satellite formation, which includes a cluster of charged satellites repelling each other by Debye-shielded Coulomb forces and two counterweights connecting to each satellite via elastic massless tethers. The center of mass of the formation is prescribed to move along the geostationary orbit. The equations of motion of the formation are obtained by using Lagrange's equation. Analytical individual satellite charges are derived for the spinning and non-spinning three-satellite configurations, respectively. When the number of satellites is more than three, approximate analytical charges are obtained. Numerical simulations indicate that the proposed formation may be successfully applied to the geostationary satellite collocation in the future.

This study analyzes numerically the nonlinear static and dynamic behaviours as well as the mass detection sensitivity of a geometrically imperfect cantilevered carbon nanotube (CNT) resonator. More specifically, a new nonlinear model is developed for the cantilevered CNT nanoresonator, taking into account the effects of the initial curvature and cross-sectional area imperfection; furthermore, the new nonlinear model accounts for nonlinear damping and small-scale effects, employing the Kelvin–Voigt damping model and the modified couple stress-based elasticity theory, respectively. The electrostatic interactions in the CNT nanoresonator are modelled through use of a new electrostatic load model, previously developed by the authors. The nonlinear equation of motion of the geometrically imperfect cantilevered CNT nanoresonator is obtained making use of Hamilton’s principle as well as the inextensibility condition. The electromechanical continuous model of the nanoresonator is reduced into a high-dimensional discretized model employing the Galerkin method. The discretized model, consisting of a set of coupled nonlinear ordinary differential equations, is solved numerically employing a continuation technique. The nonlinear behaviour of the nanoresonator is studied and the effect of different parameters on the static deflection and dynamic response is examined. Furthermore, the mass detection sensitivity of the nanoresonator is examined in detail and methods are proposed for enhancing the detection sensitivity.

Space elevators are expected to change significantly the method of deployment of Earth-orbiting satellites, offering a more efficient and elegant approach than chemical rockets. A space elevator consists of one or more ribbons (tethers) stretching from the surface of the Earth to a counterweight located beyond the geosynchronous altitude. Before a full space elevator is deployed, it is likely that a partial space elevator will be deployed. One of the key requirements for the design of a space elevator is the understanding of its mechanics. This article discusses the statics and dynamics of space elevators.

Space Manipulator Systems (SMSs) are complex systems made of a platform equipped with one or more deployable robotic arms and they will be playing a major role in future autonomous on-orbit missions. The latter may as well involve manipulation operations of the target object which needs to be moved from an initial configuration to a final one suitable for the specific task under consideration. In the present study, the mission being analyzed concerns the manipulation of a passive body by means of a flexible SMS after grasping operations have been performed. The dynamics model is derived in a three-dimensional context (non-linear formulation for the rigid-body motions and linear for the elastic dynamics). The SMS involved in the investigation has two actuated seven-degree of freedom arms. Furthermore, the modeling of the grasp constraint existing between the SMS end-effectors and the target object is a critical issue which is addressed in the present paper. A combination of Jacobian Transpose and Proportional-Derivative Control is synthesized to accomplish the desired mission goals. Numerical results proving the effectiveness of the proposed strategy are presented and discussed.

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

This research addresses the design and testing of a debris containment system for use in a tether-net approach to space debris removal. The tether-net active debris removal involves the ejection of a net from a spacecraft by applying impulses to masses on the net, subsequent expansion of the net, the envelopment and capture of the debris target, and the de-orbiting of the debris via a tether to the chaser spacecraft. To ensure a debris removal mission's success, it is important that the debris be successfully captured and then, secured within the net. To this end, we present a concept for a net closing mechanism, which we believe will permit consistently successful debris capture via a simple and unobtrusive design. This net closing system functions by extending the main tether connecting the chaser spacecraft and the net vertex to the perimeter and around the perimeter of the net, allowing the tether to actuate closure of the net in a manner similar to a cinch cord. A particular embodiment of the design in a laboratory test-bed is described: the test-bed itself is comprised of a scaled-down tether-net, a supporting frame and a mock-up debris. Experiments conducted with the facility demonstrate the practicality of the net closing system. A model of the net closure concept has been integrated into the previously developed dynamics simulator of the chaser/tether-net/debris system. Simulations under tether tensioning conditions demonstrate the effectiveness of the closure concept for debris containment, in the gravity-free environment of space, for a realistic debris target. The on-ground experimental test-bed is also used to showcase its utility for validating the dynamics simulation of the net deployment, and a full-scale automated setup would make possible a range of validation studies of other aspects of a tether-net debris capture mission.

DoS or Denial-of-service attacks are found in many forms and they're an explicit attempt to block the genuine access of user to the system via reducing availability of the system just similar to physical Dos attacks where for example intentionally the electrical power is removed. Sometimes the attacker may also play with a computing devices and make it inaccessible by altering the existem specification of the management information system. These physical intrusions are tackled by tough security measures and strategies. Although few software guards against some attacks, yet it flops to defend against DoS flooding attacks and it may further exploit unrestricted forwarding of internet packets. DDoS distributed denial of service attacks are another contiguous type of attack over the availability of Internet resources. The attackers are smart enough to penetrate into comparatively large number of computers exploiting weaknesses of different softwares so as to setup distributed attacks. These computers are unsuspecting in nature so they can be easily invoked for planning and attempting attack over more victim systems. Over the time the counter measures are developed attackers also improve the existing attack tools developing as well as imitating techniques for distributed denial-of-service attacks. So it is imperative develop complete expositions for defending against known attack variants of such kinds. However this procedure needs a complete understanding of techniques, prerequisites and scope used in diverse kinds of attacks. This paper tries to describe the scope of DDoS problem in possible comprehensive capacity. We have tried to propose new methods to categories different techniques used in DDoS attack, also categories attack networks and defining characteristics of different software tools that help to build up such attack networks. With this new approach we attempt to propose different classes’ methods the target this problem during, before, and after actual DDoS attacks. This work envisioned to stimulate research into efficient creative an effective ramparts, detection mechanism and methods for such attacks. This intern may help to create broad and ample solutions providing generalized approach towards countering known as well as derived DDoS attacks.

It is a new design concept to employ control moment gyroscopes (CMGs) as reactionless actuators for space robots. Such actuation has several noticeable advantages such as weak dynamical coupling and low power consumption over traditional joint motor actuation. This paper presents a robust control law for a CMG-actuated space robot in presence of system uncertainties and closed-chain constraints. The control objective is to make the manipulation variables to track the desired trajectories, and reduce the possibility of CMG saturation simultaneously. A reduced-order dynamical equation in terms of independent motion variables is derived using Kane's equations. Desired trajectories of the independent motion variables are derived by minimum-norm trajectory planning algorithm, and an adaptive sliding mode controller with improved adaptation laws is proposed to drive the independent motion variables tracking the desired trajectories. Uniformly ultimate boundedness of the closed loop system is proven using Lyapunov method. The redundancy of the full-order actual control torques is utilized to generate a null torque vector which reduces the possibility of CMG angular momentum saturation while producing no effect on the reduced-order control input. Simulation results demonstrate the effectiveness of the proposed algorithms and the advantage of weak dynamical coupling of the CMG-actuated system.

This study addresses a relative position coordinated control problem for spacecraft formation flying subject to directed communication topology. Two different kinds of communication delay cases, including time-varying delays and arbitrarily bounded delays are investigated. Using the backstepping control technique, two virtual velocity control inputs are firstly designed to achieve coordinated position tracking for the kinematic subsystem. Furthermore, a hyperbolic tangent function is introduced to guarantee the boundedness of the virtual controller. Then, a finite-time control algorithm is designed for the dynamic subsystem. It can guarantee that the virtual velocity can be followed by the real velocity after finite time. It is theoretically proved that the proposed control scheme can asymptotically stabilize the closed-loop system. Numerical simulations are further presented that not only highlight closed-loop performance benefiting from the proposed control scheme, but also illustrate its superiority in comparison with conventional formation control schemes.

This paper investigates the finite time coordinated formation control problem for spacecraft formation flying (SFF) under the assumption of directed communication topology. By using the neighborhood state measurements, a robust finite time coordinated formation controller is firstly designed based on the nonsingular terminal sliding mode surface. To address the special case that the desired trajectory of the formation is only accessible to a subset of spacecraft in the formation, an adaptive finite time coordinated formation controller is also proposed by designing a novel sliding mode surface. In both cases, the external disturbances are explicitly taken into account. Rigorous theoretical analysis proves that the proposed control schemes ensure that the closed-loop system can track the desired time-varying trajectory in finite time. Numerical simulations are presented that not only highlights the closed-loop performance benefits from the proposed control algorithms, but also illustrates the effectiveness in the presence of external disturbances when compared with the existing coordinated formation control schemes.

In this paper, a novel predictive smooth variable structure filter (PSVSF) is presented for attitude synchronization during satellite formation flying (SFF). The strategy is proposed based on variable structure control concept and applies to any nonlinear system with modeling errors. Because the modeling errors in the PSVSF are not restricted to Gaussian noise only, the technique can deal with various kinds of uncertainties, parameter variations, or noises. It also has low computational burden; therefore, it is more general than other nonlinear estimation methods. Sufficient conditions to analyze the stability and characteristics of the PSVSF are presented. Simulations are performed to demonstrate the accuracy, robustness, and stability of the proposed PSVSF for the attitude synchronization estimation of the SFF system.

A new nonlinear electrostatic load model for initially curved clamped–clamped carbon nanotube (CNT) resonators is developed in this study. In particular, first a 3D finite element analysis is performed in order to obtain the electrostatic force distribution on a clamped–clamped CNT resonator (with and without initial curvature). A nonlinear model for the electrostatic load is then developed based on the 3D finite element analysis results. Based on the newly developed electrostatic load model, the nonlinear equations of motion of the initially curved CNT resonator are derived employing Hamilton’s principle together with the modified couple stress theory. Moreover, the Kelvin–Voigt viscoelastic model is employed to model the energy dissipation. The new nonlinear model of the system, consisting of two strongly nonlinear coupled partial differential equations, is discretized into a set of nonlinear ordinary differential equations via Galerkin’s technique, and solved employing the pseudo-arclength continuation method. The numerical results are obtained for both static and dynamic cases, with special focus on the static pull-in behaviour and on the effects of the newly developed electrostatic load model, viscoelasticity, initial curvature, and length-scale parameter on the nonlinear resonant response.

A proposed method for containing the growth of space debris, which jeopardizes operation of spacecraft, is the active debris removal of massive derelict spacecraft and launcher upper stages by means of tether nets. The behavior of nets in space is not well known; therefore, numerical simulation is needed to gain understanding of deployment and capture dynamics. In this paper, a lumped-parameter approach for modeling the net and different models of contact dynamics are presented. A continuous compliant approach for the normal contact force and a modified damped bristle model for the friction force are chosen. The capability of the developed simulation tool to represent multiple dynamic conditions is demonstrated in this paper, and the results of a deployment dynamics simulation are presented; this reveals a snapping behavior of tension. Simulation of net-based capture of cylindrical debris in microgravity and vacuum conditions is performed with the presented tool. The effect of employing different contact ...

Dynamic analysis and trajectory tracking of a Tethered Space Robot (TSR) is investigated in this paper. A hybrid controller is used to perform the control task. It consists of two components, the first one deals with librational motion of the tether, while the second one takes care of the manipulator motion. A Nonlinear Model Predictive Control (NMPC) approach is used to control the tether libration; for this purpose, the libration is described by a single degree of freedom and the tether length rate is employed as the input to suppress the librational motion. A modified Computed Torque Method (CTM) is used to control the manipulator motion. The dynamic interaction between the manipulator motion and the librational motion is considered both in the system dynamics and control of the system. Using numerical simulations, performance of the proposed control system is evaluated for end-effector positioning as well as for trajectory tracking for two cases: a Low Earth Orbit (LEO) and the Geostationary Earth Orbit (GEO).

The present study develops a new size-dependent nonlinear model for the analysis of the behaviour of carbon nanotube-based resonators. In particular, based on modified couple stress theory, the fully nonlinear equations of motion of the carbon nanotube-based resonator are derived using Hamilton׳s principle, taking into account both the longitudinal and transverse displacements. Molecular dynamics simulation is then performed in order to verify the validity of the developed size-dependent continuum model at the nano scale. The nonlinear partial differential equations of motion of the system are discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. The pseudo-arclength continuation technique is employed to examine the nonlinear resonant behaviour of the carbon nanotube-based resonator. A new universal pull-in formula is also developed for predicting the occurrence of the static pull-in and validated using numerical simulations.

In present study, dynamic modeling and control of a tethered space robot system in trajectory tracking of its end effector is investigated. Considering variation of the tether length in the model, dynamics of the system is modeled using Lagrange’s method. Librational motion of the tether is controlled by adjusting the tether length similar to conventional manipulators,control of the robot is performed by its motors. It is clear that, in the trajectory tracking of the end effector, the tether length should be kept more or less constant, keeping them in a stable position. Limiting the tether length variation while using it as a tool for controlling the tether librational motion, is the main challenging part of the control system. To deal with this problem, a hybrid control system is proposed to control the system. A nonlinear model predictive control approach (NMPC) is utilized to control the tether librational motion and a modified computed torque method (CTM) is used to control the manipulator motion. Initially the NMPC controller is developed for a simple tethered satellite system. Then it is combined with the CTM controller.The proposed controller is employed to control motion of a space robot’s end effector on a predefined trajectory. Performance of the controller is then evaluated by numerical simulations.

Tether-nets are one of the more promising methods for the active removal of space debris. The aim of this paper is to study the dynamics of this type of systems in space, which is still not well-known and the simulation of which has multiple outstanding issues. In particular, the focus is on the deployment and capture phases of a net-based active debris removal mission, and on the effect of including the bending stiffness of the net threads on the dynamical characteristics of the net and on the computational efficiency. Lumped-parameter modeling of the net in Vortex Dynamics, without bending stiffness representation, is introduced first and validated then, against results obtained with an equivalent model in Matlab, using numerical simulations of the deployment phase. A model able to reproduce the bending stiffness of the net in Vortex Dynamics is proposed, and the outcome of a net deployment simulation is compared to the results of simulation without bending stiffness. A simulation of net-based capture of a derelict spacecraft is analyzed from the point of view of evaluating the effect of modeling the bending stiffness. From comparison of simulations with and without bending stiffness representation, it is found that bending stiffness has a significant influence both on the simulation results and on the computation time. When bending stiffness is included, the net is more resistant to the changes in its shape caused both by the motion of the corner masses (during deployment) and by the contact with the debris (during capture).

The tethered formation and the coulomb formation are two important concepts in constructing satellite formation architecture, and they have the advantage that the relative motion between satellites can be maintained quite accurately with minimal active control. In this study, a formation termed the “coulomb tether double-pyramid” is proposed to combine the best features of the tethered formation and the coulomb formation. Chief and deputy satellites are charged bodies and located in the Earth-facing plane normal to the geostationary orbit, with the chief at the center. Each deputy is connected with two anchor satellites via a massless, straight tether, such that the Earth-facing plane can be maintained by using gravity-gradient torques. First, the equations of motion are obtained via Lagrange equations. Then, the charges and tether extensions necessary to support a Hill-frame stationary formation are analytically determined. Finally, open-loop charge control strategies are designed to maintain the spinnin...

The problem of pendular oscillations of a tether attached to an irregularly shaped celestial body is studied in this paper. The dynamic analysis of the system is performed by examining the phase plane trajectories. The effect of the tether length as well as the higher order terms in the gravitational potential of the celestial body on the tether dynamics is investigated. It is demonstrated that consideration of the finite size of the celestial body can have significant effects on the tether dynamics, while the effect of the asphericity of the celestial body on the tether dynamics is negligible. This study is of practical relevance for asteroid deflection using tethers, as well as for the development of space elevators on small planets/moons.

Potentially hazardous near-Earth objects which can impose a significant threat on life on the planet have generated a lot of interest in the study of various asteroid deflection strategies. There are numerous asteroid deflection techniques suggested and discussed in the literature. This paper is focused on one of the non-destructive asteroid deflection strategies by attaching a long tether–ballast system to the asteroid. In the existing literature on this technique, very simplified models of the asteroid-tether–ballast system including a point mass model of the asteroid have been used. In this paper, the dynamical effect of using a finite size asteroid model on the asteroid deflection achieved is analyzed in detail. It has been shown that considering the finite size of the asteroid, instead of the point mass approximation, can have significant influence on the deflection predicted. Furthermore the effect of the tether-deployment stage, which is an essential part of any realistic asteroid deflection mission, on the predicted deflection is studied in this paper. Finally the effect of cutting the tether on the deflection achieved is analyzed and it has been shown that depending on the orbital properties of the asteroid as well as its size and rotational rate, cutting the tether at an appropriate time can increase the deflection achieved. Several numerical examples have been used in this paper to elaborate on the proposed technique and to quantitatively analyze the effect of different parameters on the asteroid deflection.