Mission Functionality for Deflecting Earth-Crossing Asteroids/Comets

Abstract

IntroductionAn infrequent but significant hazard to life and property due to impacting asteroids and comets exists. Earth-approaching asteroids and comets also represent a significant resource for commercial exploitation, space exploration, and scientific research. The impact problem and those planetary bodies that could be a threat have been discussed in great depth in a wide range of publications. A popular planetary defense method is the deflection of asteroids and comets on a collision orbit with the Earth by changing their orbital velocities. It is fundamental to estimate required changes in the orbital velocities of dangerous objects to avoid a collision.A detailed optimization problem is formulated to calculate optimal impulses for deflecting Earthcrossing asteroids/comets, using nonlinear programming. The constrained optimization problem is based on a three-dimensional patched conic method to include the Earth's gravitational effects and the asteroid/ comet's orbital inclination. The magnitudes and impulse angles of optimal impulse change in velocity (∆V) are accurately computed at various points on the asteroid/comet's orbit to provide a given target separation distance. Based on these change in velocity analyses, we can establish the approximate cost and build strategies to prevent possible catastrophe due to the objects.

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

“…Under this deterministic condition, the closest approach distance is known to change periodically with respect to the asteroid arrival date of the spacecraft, and the local maximum value of the approach distance is reduced as the asteroid arrival date is delayed. [3][4][5] The closest approach distance is evaluated assuming the range of Earth departure date This result is identical to the results of Park and coauthors. [3][4][5] The blank region in Fig.…”

“…[3][4][5] The closest approach distance is evaluated assuming the range of Earth departure date This result is identical to the results of Park and coauthors. [3][4][5] The blank region in Fig. 5 suggests the C3 constraint is not satisfied or the closest approach distance is less than 5000 km.…”

“…2) Park and coauthors [3][4][5] investigated the optimal magnitude and direction of velocity increment required to deflect asteroids, but the interplanetary trajectory of the spacecraft has not been discussed. Ivashkin 6) showed that a spacecraft with a mass of 8 tonnes at launch could deflect Toutatis, which has a radius of less than 270 m. He also presented some models for the spacecraft impact asteroid with several different values of required momentum for deflecting the asteroid.…”

Semi-Analytical Solution for the Optimal Low-Thrust Deflection of Near-Earth Objects

“…Compared with methods that analytically propagate the perturbed trajectory using Lagrange coefficients [9][10][11][12], the proposed approach does not require any solution of the time equation for every variation of the orbit of the asteroid and is therefore less computationally expensive. On the other hand, it is conceptually and computationally equivalent to those approaches [8] that analytically propagate only the variation of position and velocity of the asteroid by using the fundamental perturbation matrix [24].…”

“…An analysis on the minimum v and the optimal impulse angle was performed by Park and Ross [9], who used Lagrange coefficients to propagate the deviated orbit of the asteroid rather than only its displacement with respect to the nominal course. They also included the effects of the Earth gravity [10,11]. Song et al [12] investigated the deflection of asteroids and comets using a powerlimited laser beam.…”