2:15 PM - 2:30 PM
[MZZ45-03] On trajectory optimization for kinetic impector to deflect Earth-threatening asteroids
Keywords:Near-Earth asteroid, Kinetic impactor, trajectory optimization
Introduction
More than 30,000 of near-Earth asteroids (NEAs) have been detected and identified. Some fractions of NEAs are perturbed into orbits that may cross Earth’s orbit. The probability of major impacts with severe effects on humanity is sufficiently low, but not zero. Earth has been hit by one of these objects during its history. Since the impact event of PHAs would certainly pose a critical threat to most of the population of Earth, several methods to deal with the asteroidal event have been proposed and studied in some detail. The kinetic impactor (KI) is a spacecraft that impact an Earth-threatening asteroid with large relative velocity to deflect it from the Earth collision route. The orbital period of the asteroid is slightly changed by the KI impact and the distance between the asteroid and Earth at the predicted Earth collision date is increased. In 2022, the double asteroid redirection test (DART), which is the first demonstration experiment of the KI, successfully impacted a target asteroid and changed its orbital period. In this study, the authors propose a trajectory design method for KI, that increases the effectiveness of the KI mission.
Impact-geometry map and trajectory design for KI missions
The achievable deflection distance which is the change in the asteroid’s Earth approach distance to Earth is proportional to the time between the KI impact and predicted Earth impact, and the impact-geometry (IG). The IG is the dot product of the asteroid’s heliocentric velocity vector and spacecraft velocity relative to the asteroid. To increase the achievable deflection distance, increasing the absolute value is important. As in the authors’ previous works, the largest absolute value of the IG is analytically obtained if the spacecraft's semi-major axis and eccentricity are defined. By plotting the value of the IG as a function of the semi-major axis and eccentricity with a color contour plot, the impact-geometry map (IGM) was formulated. Since the IGM provides the largest absolute value of the IG for a given KI orbit, we investigate the efficiency of an impact of KI, in advance. Moreover, by differentiating the IG value by the spacecraft's true anomaly, the thrust control law that maximizes the change in the IG value is also obtained. The effectiveness of the locally optimal thrust control law was numerically investigated and the monotonic increase in the IG value was achieved. Obtained locally optimal trajectories can be used as the initial trajectories for trajectory optimization.
Some test cases and results
The proposed trajectory design method for KI missions is numerically demonstrated for a fictional asteroid deflection scenario. A fictional asteroid that is created from actual PHA is assumed to be a target of the KI mission. The semi-major axis is 2.08 au, eccentricity is 0.622, the inclination is 0.669 deg, the node of perihelion is 241 deg, the ascending node is 273 deg, the mean anomaly is 171 deg, and the mass is 3.3 x 10^9 kg, respectively. The predicted Earth collision date is Dec. 25, 2050. The mass of KI is 1,000 kg. In addition, we assume that the thruster of the spacecraft can generate up to 40 mN. We attached an example of the optimal KI trajectory figure. As in the figure, the KI successfully impacts the target asteroid. The KI launched on Aug. 24, 2023, and impacts the asteroid after a flight time of 1272 d. The impact efficiency was 98.96%, and thus, it was an efficient trajectory. The achievable deflection distance is 20,873 km on the b-plane. The proposed trajectory design method was successfully worked and a KI mission that yields a sufficiently large deflection distance was obtained.
Conclusion
In this study, we proposed the trajectory design method for the KI mission that deflects an Earth-threatening asteroid with an impact of a spacecraft. By using the impact-geometry map, the effectiveness of the impact, and, the achievable deflection distance can be increased.
More than 30,000 of near-Earth asteroids (NEAs) have been detected and identified. Some fractions of NEAs are perturbed into orbits that may cross Earth’s orbit. The probability of major impacts with severe effects on humanity is sufficiently low, but not zero. Earth has been hit by one of these objects during its history. Since the impact event of PHAs would certainly pose a critical threat to most of the population of Earth, several methods to deal with the asteroidal event have been proposed and studied in some detail. The kinetic impactor (KI) is a spacecraft that impact an Earth-threatening asteroid with large relative velocity to deflect it from the Earth collision route. The orbital period of the asteroid is slightly changed by the KI impact and the distance between the asteroid and Earth at the predicted Earth collision date is increased. In 2022, the double asteroid redirection test (DART), which is the first demonstration experiment of the KI, successfully impacted a target asteroid and changed its orbital period. In this study, the authors propose a trajectory design method for KI, that increases the effectiveness of the KI mission.
Impact-geometry map and trajectory design for KI missions
The achievable deflection distance which is the change in the asteroid’s Earth approach distance to Earth is proportional to the time between the KI impact and predicted Earth impact, and the impact-geometry (IG). The IG is the dot product of the asteroid’s heliocentric velocity vector and spacecraft velocity relative to the asteroid. To increase the achievable deflection distance, increasing the absolute value is important. As in the authors’ previous works, the largest absolute value of the IG is analytically obtained if the spacecraft's semi-major axis and eccentricity are defined. By plotting the value of the IG as a function of the semi-major axis and eccentricity with a color contour plot, the impact-geometry map (IGM) was formulated. Since the IGM provides the largest absolute value of the IG for a given KI orbit, we investigate the efficiency of an impact of KI, in advance. Moreover, by differentiating the IG value by the spacecraft's true anomaly, the thrust control law that maximizes the change in the IG value is also obtained. The effectiveness of the locally optimal thrust control law was numerically investigated and the monotonic increase in the IG value was achieved. Obtained locally optimal trajectories can be used as the initial trajectories for trajectory optimization.
Some test cases and results
The proposed trajectory design method for KI missions is numerically demonstrated for a fictional asteroid deflection scenario. A fictional asteroid that is created from actual PHA is assumed to be a target of the KI mission. The semi-major axis is 2.08 au, eccentricity is 0.622, the inclination is 0.669 deg, the node of perihelion is 241 deg, the ascending node is 273 deg, the mean anomaly is 171 deg, and the mass is 3.3 x 10^9 kg, respectively. The predicted Earth collision date is Dec. 25, 2050. The mass of KI is 1,000 kg. In addition, we assume that the thruster of the spacecraft can generate up to 40 mN. We attached an example of the optimal KI trajectory figure. As in the figure, the KI successfully impacts the target asteroid. The KI launched on Aug. 24, 2023, and impacts the asteroid after a flight time of 1272 d. The impact efficiency was 98.96%, and thus, it was an efficient trajectory. The achievable deflection distance is 20,873 km on the b-plane. The proposed trajectory design method was successfully worked and a KI mission that yields a sufficiently large deflection distance was obtained.
Conclusion
In this study, we proposed the trajectory design method for the KI mission that deflects an Earth-threatening asteroid with an impact of a spacecraft. By using the impact-geometry map, the effectiveness of the impact, and, the achievable deflection distance can be increased.