Impulsive Deflection Research Articles

Applying centrifugal propulsion to enable asteroid deflection

To date, asteroid trajectory modification techniques employ the “big bang” approach. An impulsive deflection is imparted by slamming one or more high-speed kinetic impactor spacecraft into the object or by detonation of a nuclear device in its proximity. This is a “hit it once and hope for the best” approach.Instead of relying on this restrictive method, centrifugal propulsion offers an alternative, where a centrifuge and power supply land on a threatening asteroid to collect and incrementally project portions of the asteroid, using momentum transfer of the recoil to gradually adjust the trajectory away from Earth.This process sequentially allows “ejection, measurement, and repetition” to gradually fine-tune the trajectory needed for course correction. This offers flexible operation parameters that can be varied for convenience and optimization, including the location of the landing site, weight of each ejected payload, launch speed, direction, cadence, timing of successive ejections, and the relationship to the asteroid's velocity vector and spin axis. Once landed on an asteroid, the centrifugal system requires no consumables. Operating entirely on electrical power, it can operate indefinitely without additional support.This approach addresses aspects of Goal 3 of the 2018 U S. government's “National Near-Earth Object (NEO) Preparedness Strategy and Action Plan”—“Develop Technologies for NEO Deflection and Disruption Missions.” The centrifuge approach adds a sustainable and repeatable slow-push tool to the planetary defense toolbox, mitigating the risk and uncertainty of single-impulse methods.An on-site centrifuge could deflect Chelyabinsk and Tunguska-sized asteroids to miss Earth within a few weeks’ operation. The asteroid Bennu could be deflected in a few years of continuous spinner operation, depending upon the parameters chosen, which would be sufficient to eliminate a potential collision with Earth in the late 22nd century.The innovation of a self-contained power and kinetic launch capability without consumables opens new vistas for cost-effective asteroid deflection and other commercial, scientific, government, and international space missions.

A simplified approach to uncertainty quantification for orbits in impulsive deflection scenarios

For the majority of near-Earth Asteroid (NEA) impact scenarios, optimal deflection strategies use a massive impactor or a nuclear explosive, either of which produce an impulsive change to the orbit of the object. However, uncertainties regarding the object composition and the efficiency of the deflection event lead to a non-negligible uncertainty in the deflection delta-velocity. Propagating this uncertainty through the resulting orbit will create a positional uncertainty envelope at the original impact epoch. We calculate a simplified analytic evolution for impulsively deflected NEAs and perform a full propagation of uncertainties that is nonlinear in the deflection delta-velocity vector. This provides an understanding of both the optimal deflection velocities needed for a given scenario, as well as the resulting positional uncertainty and corresponding residual impact probability. Confidence of a successful deflection attempt as a function of launch opportunities is also discussed for a specific case.

Consequences of Asteroid Fragmentation During Impact Hazard Mitigation

The consequences of the fragmentation of an Earth-threatening asteroid due to an attempted deflection are examined in this paper. The minimum required energy for a successful impulsive deflection of a threatening object is computed and compared to the energy required to break up a small size asteroid. The results show that the fragmentation of an asteroid that underwent an impulsive deflection, such as a kinetic impact or a nuclear explosion, is a very plausible event.Astatistical model is used to approximate the number and size of the fragments as well as the distribution of velocities at the instant after the deflection attempt takes place. This distribution of velocities is a function of the energy provided by the deflection attempt, whereas the number and size of the asteroidal fragments is a function of the size of the largest fragment. The model also takes into account the gravity forces that could lead to a reaggregation of the asteroid after fragmentation. The probability distribution of the pieces after the deflection is then propagated forward in time until the encounter with Earth. A probability damage factor (i.e., expected damage caused by a given size fragment multiplied by its impact probability) is then computed and analyzed for different plausible scenarios, characterized by different levels of deflection energies and lead times.

Optimal Interplanetary Trajectories for Impulsive Deflection of Potentially Hazardous Asteroids under Velocity Increment Uncertainties

This paper investigates the interplanetary trajectories associated with the impulsive deflection of a potentially hazardous asteroid (PHA) considering the uncertainty of the velocity increment that a spacecraft gives to the PHA at the collision. The velocity increment is assumed to have uncertainties of magnitude and direction due to estimation errors of asteroid shape and mass distributions. The uncertainty is modeled using a convex model assuming that magnitude and direction vary independently. The effect of uncertainty is assessed by evaluating the worst (i.e. minimum) value for the closest approach distance between the PHA and Earth. The worst value of the closest approach distance can be determined analytically without searching the whole convex hull. The optimal spacecraft trajectory is designed by maximizing the worst value of the closest approach distance in terms of the Earth departure date and the asteroid arrival date of the spacecraft under C3 (Earth departure energy) constraint. Using a numerical example with a fictitious asteroid, the importance of considering the velocity increment uncertainty is demonstrated by comparing the optimal trajectory with the deterministic optimal trajectory. The uncertainty of the velocity increment direction is shown to have a significant effect on the deflection of the PHA.

地球接近小惑星軌道変更ミッションにおける速度増分の変動を考慮した軌道設計

This paper discusses the conceptual trajectory design associated with the impulsive deflection of a potentially hazardous asteroid (PHA) with considering uncertainty of velocity increment that spacecraft gives to the PHA at the time of collision. The effect of the uncertainty is evaluated as the worst value of the closest approach distance between the PHA and the Earth by modeling the uncertainty as a convex model, where the uncertainties of magnitude and the direction of the velocity increments are independently varied. It is shown that the worst value is determined uniquely without searching in the convex hull. Then, the most efficient spacecraft trajectory is evaluated by maximizing the worst approach distance in terms of the Earth departure date and the asteroid arrival date of the spacecraft under C3 constraint that considers the mission feasibility. The importance of considering the uncertainty is demonstrated by comparing the optimum trajectories with and without the uncertainty. Additionally, it is shown that the uncertainty of the velocity increment direction has the significant effect on the deflection of the PHA.

Optimal trajectories for the impulsive deflection of near earth objects

With the current technological level it is possible to deflect an asteroid such as 99942 Apophis in case its orbit refinement reveals an unacceptable collision risk. Thanks to the solution of an ad hoc defined global optimisation problem we show that a pre-keyhole deflection is possible even with a simple spacecraft and with a very late launch in 2026. We also give a mathematical description of the trajectory optimisation problems that have to be faced in the case of a more generic asteroid deflection mission defining analytically the objective function, that is the displacement in the encounter b -plane of the asteroid uncertainty ellipsoid.

Impulsive Free-Surface Flow Due to Rapid Deflection of an Initially Horizontal Bottom. Part II. Spatial Dependency

An analytical third-order small-time expansion is developed for inviscid, incompressible free-surface flow generated by impulsive deflection of an initially horizontal bottom. The deflection is rapid, and the deflection function is assumed separable in space and time. Nonlinear effects are taken into account at the bottom as well as at the free surface. The theory is formulated in both two and three dimensions. The spatial solutions to each order are given in terms of Fourier integrals. These solutions are evaluated numerically for rising rectangular and cylindrical blocks. * * *

Impulsive Free-Surface Flow Due to Rapid Deflection of an Initially Horizontal Bottom. Part I. Formulation and Temporal Expansion

An analytical third-order small-time expansion is developed for the inviscid, incompressible free-surface flow generated by impulsive deflection of an initially horizontal bottom. The deflection starts with nonzero velocity. The deflection is rapid, which means that its duration is smaller than the gravitational time. The deflection function obeys the constraint of being separable in space and time, but is otherwise arbitrary. Nonlinear effects are taken into account at the bottom as well as at the free surface. Temporal functions are determined to third order. Three special cases are demonstrated.

Initial free-surface elevation due to impulsive deflection of a two-dimensional bottom with small slope and small curvature

The incompressible free-surface elevation due to 2D impulsive bottom deformations is investigated analytically. The bottom geometry is arbitrary, with small slope and curvature. The equipotential condition is applied at the initially horizontal surface. The surface and bottom conditions are linearized. The surface elevation produced by an arbitrary bottom deflection is found to leading orders in slope and curvature.