Powered Swing-by Using Tether Cutting
- Paper number
IAC-16,D4,3,15,x33683
- Author
Mr. Tsubasa Yamasaki, Kyushu University, Japan
- Coauthor
Dr. Mai Bando, Kyushu University, Japan
- Coauthor
Dr. Shinji Hokamoto, Kyushu University, Japan
- Year
2016
- Abstract
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. \begin{equation} \theta''=\frac{1}{1+e\cos\alpha}\left\{2e(\theta'+1)\sin\alpha-\frac{3}{2}\sin2\theta\right\} \end{equation} where $e$ is an orbit eccentricity, $\alpha$ is a true anomaly, $\theta$ is an attitude angle and $l$ is tether length. The prime means the derivative with $\alpha$. The mother satellite and subsatellite can obtain not only the velocity change but the position change by the tether cutting; they are denoted as $\Delta\bf{v}$ and $\Delta\bf{r}$, and described in Eqs. (2) and (3), respectively. \begin{align} \Delta{\bf v}&=-l_1(\dot{\alpha}+\dot{\theta}) \begin{bmatrix} -\sin(\alpha+\theta)\\ \cos(\alpha+\theta) \end{bmatrix}\\ \Delta{\bf r}&=-l_1 \begin{bmatrix} \cos(\alpha+\theta)\\ \sin(\alpha+\theta) \end{bmatrix} \end{align} where $l_1$ is a distance between the center of gravity of the tethered-satellite and the mother satellite. Since $\alpha$ and $\theta$ are functions of time, $\Delta\bf{v}$ and $\Delta\bf{r}$ 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.
- Abstract document
- Manuscript document
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