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

IAC-16,D4,3,15,x33683.brief.pdf

Manuscript document

IAC-16,D4,3,15,x33683.pdf (🔒 authorized access only).

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