Powered swing-by using tether cutting

The swing-by maneuver is known as a method to change the velocity of a spacecraft by using the gravity force of the celestial body. The powered swing-by has been proposed and researched to enhance the velocity change during the swing-by maneuver, e.g. Prado (1996). The research reports that applying an impulse maneuver at periapsis maximizes the additional effect to the swing-by. However, such impulsive force requires additional propellant. On the other hand, Williams et al. (2003) researched to use a tether cutting maneuver for a planetary capture technique. This current paper studies another way of the powered swing-by using tether cutting, which does not require additional propellant consumption. A Tethered-satellite is composed of a mother satellite, a subsatellite and a tether connecting two satellites. In a swing-by trajectory, a gravity gradient force varies according to the position of the tethered-satellite, and consequently its attitude motion is induced; the tethered-satellite starts to liberate and rotate. Cutting the tether during the tethered-satellites' rotation can add the rotational energy into the orbital energy. In this research, since the gravity gradient effect on orbital motion is small, the orbit can be considered a hyperbolic orbit. Assuming that the tether length is constant, Eq. (1) describes the equation of the attitude motion of a tethered-satellite within the SOI (sphere of influence) of the secondary body. θ = 1/1+ e cos α {2e (θ' + 1) sin α - 3/2 sin 2θ} where e is an orbit eccentricity, α is a true anomaly, θ is an attitude angle and l is tether length. The prime means the derivative with α. The mother satellite and subsatellite can obtain not only the velocity change but the position change by the tether cutting; they are denoted as Δv and Δr, and described in Eqs. (2) and (3), respectively. Δv = -l₁(α + θ) [-sin (α + θ) cos (α + θ)] Δr = -l₁ [cos (α + θ) sin (α + θ)] where l₁ is a distance between the center of gravity of the tethered-satellite and the mother satellite. Since α and θ are functions of time, Δv and Δr are also functions of time. This means that changing the tether cutting point can maximize the velocity change in this proposed powered swing-by maneuver. Furthermore, the optimum cutting point depends on the attitude and angular velocity when the tethered satellite enters the SOI. We propose a systematic design procedure to obtain the desired velocity change by optimizing the cutting point, the initial attitude and the initial angular velocity of the tethered satellites.