Eur. Phys. J. Special Topics 229, 1463{1477 (2020) c EDP Sciences, Springer-Verlag GmbH Germany, THE EUROPEAN part of Springer Nature, 2020 PHYSICAL JOURNAL https://doi.org/10.1140/epjst/e2020-900183-y SPECIAL TOPICS Regular Article Dynamics of tethered asteroid systems to support planetary defense Flaviane C.F. Venditti1;a, Luis O. Marchi2, Arun K. Misra3, Diogo M. Sanchez2, and Antonio F.B.A. Prado2 1 NASA Solar System Exploration Research Virtual Institute (SSERVI) and Planetary Radar Department, Arecibo Observatory, University of Central Florida, Arecibo, PR, USA 2 Division of Space Mechanics and Control, National Institute for Space Research, Sao Jose dos Campos, SP, Brazil 3 Mechanical Engineering Department, McGill University, Montreal, QC, Canada Received 28 August 2019 / Received in final form 23 November 2019 Published online 29 May 2020 Abstract. Every year near-Earth object (NEO) surveys discover hun- dreds of new asteroids, including the potentially hazardous asteroids (PHA). The possibility of impact with the Earth is one of the main motivations to track and study these objects. This paper presents a tether assisted methodology to deflect a PHA by connecting a smaller asteroid, altering the center of mass of the system, and consequently, moving the PHA to a safer orbit. Some of the advantages of this method are that it does not result in fragmentation, which could lead to another problem, and also the flexibility to change the configuration of the system to optimize the deflection according to the warning time. The dynamics of the PHA-tether-asteroid system is analyzed, and the amount of orbit change is determined for several initial conditions. Only motion in the plane of the orbit of the PHA around the Sun is considered, thus the PHA chosen for the simulations has low orbit inclination. Analysis of the dynamics of the system shows that the method is feasible for planetary defense. 1 Introduction To date, more than 21 000 near-Earth asteroids (NEAs) have been discovered, includ- ing almost 2000 PHAs. Small bodies with perihelion of less than 1.3 AU and having orbits passing close to the orbit of the Earth are called near-Earth objects (NEOs), which can include asteroids and comets. Among NEAs there are the potentially haz- ardous asteroids (PHAs), which are objects larger than about 140 m and that can get closer than 0.05 AU, or approximately 20 times the distance from the Earth to the Moon. Potential impacts of NEOs are one of the biggest motivations to study and detect these objects. The threat of an asteroid on the collision path with the Earth has encouraged the development of several deflection techniques. Based on the warning a e-mail: [email protected] 1464 The European Physical Journal Special Topics time, the deflection method can be chosen from months to several years, or even decades. Some existing methods in the literature for this purpose are: fragmentation of the asteroid using nuclear explosives or collision with a massive asteroid [1]; using the impulse of a direct collision on the asteroid, called the kinetic impact method [2,3]; the use of solar energy with solar sails to cause a boost generated by the evaporation of the surface layers, slightly pushing the asteroid [4]; the use of the gravitational pull of a thereby stationary spacecraft or in a \tugging" mode near an asteroid to deflect it slowly, which is called the gravity tractor method [5,6]. In this work, the use of a tether assisted technique is considered. It consists of connecting two asteroids, a PHA and a smaller asteroid nearby, so that the motion of the secondary asteroid could change the initial trajectory of the larger one. The methodology aims to transfer a PHA to a new safer orbit through the displacement of the center of mass. Thus, no unwanted consequences related to fragmentation would happen after the deflection. The applications of this technique are especially important for planetary defense, but could also help in the scientific exploration of these objects. The study of small bodies has been growing fast in the past decade, and there are several missions to explore closely these objects, as well as planned for the future. One of the reasons to study asteroids and comets is that they may carry valuable information about the formation of the Solar System. Some of the past missions are: NEAR that landed on asteroid Eros [7]; Hayabusa, a mission developed by the Japanese Space Agency with the goal of collecting material from asteroid Itokawa and bring back samples [8]; Dawn orbiting Ceres and Vesta, which are the most massive asteroids in the solar system, respectively [9]; PROCYON and Hayabusa 2 [10], both launched in 2014, meeting their target asteroids in 2016 and 2018, respec- tively. There are also missions that were launched to orbit comets, such as Star- dust [11] in order to collect samples from the tail of comet P/Wild2, and Rosetta, which after performing a flyby on asteroids Steins and Lutetia, landed on comet 67P/Churyumov{Gerasimenko in late 2014 [12]. There are also ongoing and planned missions to small bodies. Launched in 2016, the OSIRIS-REx mission (Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer) encountered the potentially hazardous asteroid 1999 RQ36, or 101955 Bennu, by the end of 2018, and after mapping the surface of the asteroid it will collect a sample to bring back to Earth [13{16]. A mission named Lucy, scheduled to launch in 2021, will have the goal to explore six Trojan asteroids around the orbit of Jupiter [17]. The motivation arises due to the fact that Trojans are thought to be remnants of the primordial material that formed the outer planets, holding important information about the formation of the Solar System. Another mission planned for the future is Psyche, a solar electric propulsion spacecraft concept targeted to be launched in 2022 [18]. Psyche appears to be the exposed nickel-iron core of an early planet, which might help to understand planetary formation. It will be the first time that a metallic asteroid is visited. Another pioneer mission recently selected by NASA is Janus. The goal is to explore two binary asteroids to better understand how primitive bodies form and evolve into multiple asteroid systems. 2 Planetary defense { near-Earth asteroids The Solar System has a large number of irregularly shaped bodies. These objects are asteroids, comets, and even some satellites of planets. Most asteroids are located between the orbits of Mars and Jupiter, in the main belt asteroid, but NEAs orbit much closer, and sometimes may come uncomfortably near, even crossing the Earth's orbit, which are NEAs part of the Aten and Apollo groups. Celestial Mechanics in the XXIst Century 1465 The number of NEAs discovered by optical and infrared surveys grows each year, and most of the PHAs larger than 1 km are known. However, the list of asteroids larger than 140 m is still a work in progress. In addition, some asteroids that were not con- sidered a threat may have their orbits perturbed to a point where it could eventually become dangerous. An example is the thermal radiation driven Yarkovsky/YORP effect [19,20], or even by collision with other objects. Asteroids smaller than 140 m are more challenging to be detected by NEA surveys, but the damage in case it is on the collision course with the Earth is still considerable, like the Chelyabinsk meteor in Russia in 2013 [21]. Before sending a spacecraft to an asteroid, the environment around it must be carefully mapped. The first step is to obtain data of the asteroid by performing observation with ground-based or space telescopes. Characteristics such as shape, mass, rotation, and surface properties are some of the important information that should be known in advance, and can be obtained with ground radar observations at the Arecibo Observatory, in Puerto Rico, or the Goldstone Solar System Radar, in California [22]. Characterization is crucial especially for landing and sample return missions. Practically all missions to small bodies select targets that can be observed with radar prior to the mission. In the history of space missions there is no record of an asteroid mitigation test performed yet. The first proposed mission is the international collaboration AIDA (Asteroid Impact and Deflection Assessment) composed by NASA's DART, and the European Space Agency's Hera. DART stands for Double Asteroid Redirection Test, which will consist of testing the effects of kinetic impact. The goal is to crash a satellite on the secondary component of the binary system Didymos and analyze the consequences of the impact on the system [23]. One of the studies related to this mission is the effects of the ejecta resulted from the impact. 3 Methodology 3.1 Space tethers Tethers are long space cables with several different applications. Some of the first studies using the concept of space tethers started with the space elevator idea [24], and lunar elevator [25]. Also the use of tether satellite systems [26], tether nets for debris removal [27,28], and using tethers for power and propulsion [29], to name a few. Some projects that make use of tethers are: Tether Physics and Survivability (TiPS), from the US Naval Research Laboratory, with the goal to understand how the libration motion of endmasses affects the motion of the center of mass of the system; formation flying tethers, which are tether systems that can enable groups of satellites to fly in tight formation, for applications such as long baseline interferome- try, like SPHERES (NASA and MIT); electrodynamics tether, such as the Tethered Satellite System Reflight (TSS-1R), with the goal of interacting with the planet's magnetosphere to generate power or propulsion without consuming propellant.