Brazilian researchers studied the feasibility of a space maneuver that could be used to change the course of satellites and even send spacecraft beyond the Solar System with less fuel (image: 99942 Apophis, used as a reference in the study, in a depiction showing how close the asteroid will be when it passes by the Earth in 2029, compared with the International Space Station (in purple) and other satellites (in blue)(© NASA/JPL-Caltech)

Published on 05/12/2021

André Julião  |  Agência FAPESP – A spacecraft docks to a 100 km cable anchored to an asteroid. Held fast by this space tether, the spacecraft rotates around the celestial body, gaining energy as it does so. Finally, it undocks from the tether and shoots off in a different direction. This type of tethered slingshot alters a trajectory by many kilometers and could even be used to send spacecraft out of the Solar System.

A paper on the theoretical feasibility of this maneuver was delivered to the Sixth International Conference on Tethers in Space, held at Carlos III University of Madrid (UC3M) in Spain on June 12-14, 2019. The lead author, Alessandra Ferraz Ferreira, won a Mario Grossi Award for the most innovative project by a young scientist presented at the conference.

Ferreira is a postdoctoral fellow at São Paulo State University’s Guaratinguetá School of Engineering (FEG-UNESP) in Brazil, with a scholarship from FAPESP and supervision by Rodolpho Vilhena de Moraes, Emeritus Professor at FEG-UNESP. Her research is part of the Thematic Project “On the relevance of small bodies in orbital dynamics”, for which the principal investigator is Othon Cabo Winter.

The award-winning paper establishes the parameters for a tethered slingshot maneuver in three-dimensional space and will be submitted for publication in a special issue of Acta Astronautica.

“One end of a cable is fastened to the surface of a body, such as an asteroid, and the other end has a docking device. A satellite or other object is launched toward the body and docks to the device on the free end of the tether. The speed at which it arrives forces the cable to rotate, producing a slingshot effect,” Ferreira said.

The model can be used to enable bodies with a smaller mass than that of planets and natural satellites to gain momentum. Other models can be used for larger bodies, such as swing-by maneuvers in which a thrust is applied to the spacecraft by the gravitational field, economizing fuel, a critical factor in space missions.

Ferreira’s work is designed to provide a theoretical basis for the feasible use of small bodies such as asteroids, which lack gravitational fields as powerful as those of planets, in slingshot maneuvers to save fuel.

Taking into account the initial conditions existing in space and the velocities achievable by spacecraft, Ferreira and colleagues concluded that the object must arrive at the docking device at 68.7 kilometers per second, equivalent to 247,320 kph, to dock, obtain the desired impulse and maximize energy gain. This would occur with an orbital inclination close to the plane.

The paper also analyzes other scenarios. If it approaches at, for example, 7.7 kps (27,720 kph), the body would gain a minimum amount of thrust. In the range of 15 kps (54,000 kph), it would be captured by the asteroid’s orbit and gravitate around it indefinitely.

“All these scenarios have to be foreseen. They are useful for other purposes, too, such as launching a satellite to orbit an asteroid,” Ferreira said.

The cable could also pull the spacecraft off course, away from its naturally elliptical trajectory. In this case, instead of orbiting indefinitely around the Sun after docking, it could switch to a hyperbole and leave the Solar System behind.

After receiving thrust from the cable, which in the scenario established in the study would be 100 km in length, the spacecraft would undock, gain energy and change course.

“The tether is a substitute for the effect gravity would have in the case of a larger body like a planet, and this also saves fuel,” Ferreira said.

Space elevator

Used in missions since Gemini 11, which was launched by NASA in 1967, space tethers are usually between 20 m and 1 km long. The rare exceptions include a 19.6 km tether used by NASA in 1996.

The concept dates from at least as far back as 1895, when Russian rocket scientist Konstantin Tsiolkovsky (1857-1935) described a space elevator consisting of a cable to lift cargo to a space station orbiting outside Earth’s atmosphere. However, space tethers on the scale proposed in that paper have never been used.

How such a cable would be made and of what material, how it would anchor to an asteroid and what the docking device would look like are all unanswered questions. The point of the Brazilian scientists’ study was to establish the parameters for a tethered slingshot maneuver, assuming these questions had already been answered.

“We used a generic asteroid system but based it on data from an existing system,” Ferreira said. “We calculated the satellite approach on the basis of the parameters for this system. In a real-world application, it would suffice to alter them to those of an actual system.”

The asteroid system used as a reference was 99942 Apophis, located 11,602,976 km from Earth.

An abstract of the paper “Three-dimensional tethered slingshot maneuver in the elliptic restricted problem” by Alessandra F. S. Ferreira, Rodolpho V. de Moraes, Antonio F. B. A. Prado and Othon Cabo Winter can be read on page 60 of the Book of Abstracts for the Sixth International Conference on Tethers in Space, available at: https://eventos.uc3m.es/_files/_event/_17669/_editorFiles/file/Book_of_Abstracts.pdf .

Source: https://agencia.fapesp.br/31370