Utilization of H-reversal Trajectory of Solar Sail for Asteroid Deflection

Near Earth Asteroids have a possibility of impacting with the Earth and always have a thread on the Earth. This paper proposes a way of changing the trajectory of the asteroid to avoid the impaction. Solar sail evolving in a H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact with the object asteroid along a H-reversal trajectory. The impact velocity depends on two important parameters: the minimum solar distance along the trajectory and lightness number. A larger lightness number and a smaller solar distance lead to a higher impact velocity. Finally, the deflection capability of a solar sail impacting with the asteroid along the H-reversal is discussed. The results show that a 10 kg solar sail with a lead-time of one year can move Apophis out of a 600-m keyhole area in 2029 to eliminate the possibility of its resonant return in 2036.

💡 Research Summary

The paper proposes a novel asteroid‑deflection concept that exploits a solar‑sail spacecraft flying a so‑called H‑reversal trajectory. The authors first review the hazard posed by Near‑Earth Asteroids (NEAs) and the two traditional mitigation families: low‑thrust methods (laser ablation, mass drivers, gravity tractors, etc.) and high‑thrust methods (kinetic impactors, nuclear explosions). They argue that low‑thrust techniques require long lead times, while high‑thrust approaches demand massive launch vehicles and costly nuclear hardware.

Solar sails, powered solely by solar radiation pressure (SRP), can provide continuous thrust without propellant. The dynamics are expressed through the lightness number β, which relates the sail’s acceleration to the Sun’s gravity, and the areal density σ (β = 1.53/σ, with σ in g m⁻²). For β > 0.5 a fixed cone angle α can generate an H‑reversal trajectory; otherwise the cone angle must be varied.

An H‑reversal trajectory is characterized by a progressive reduction of the spacecraft’s angular momentum using SRP until it reaches zero (point C). Beyond this point the angular momentum becomes negative, placing the sail on a retrograde hyperbolic orbit. The sail continues inward, reaches perihelion (point D), and then accelerates outward at very high speed. Because the SRP magnitude scales with 1/r², a smaller perihelion distance (r_min) yields a larger kinetic‑energy gain, and the impact angle with a target asteroid is always greater than 90°, i.e., a head‑on collision.

The authors formulate the deflection problem as an optimal‑control problem. The trajectory is divided into two legs: Earth‑to‑zero‑momentum and zero‑momentum‑to‑impact. Each leg is discretized into N₁ and N₂ equal‑time segments; within each segment the cone angle α and clock angle δ are held constant. The decision vector therefore contains 2(N₁+N₂)+2 variables: departure time t₀, arrival time t_f, and the α_i, δ_i for every segment. Constraints enforce the physical limits of the sail (α ∈