This paper presents the use of the kinetic impact technique to deflect asteroids that may present some risk of collision with Earth. Within the work to be developed here, we intend to evaluate in more detail the possibility to deflect the orbit of the asteroid 101955 Bennu by applying variations in its velocity ($$\Delta$$ Δ v) at different positions along its orbital period and measuring effects of close encounters with planet Earth. We will see that, in a relatively long period of time, the asteroid has several close encounters with the planet, thus suffering a natural gravitational perturbation. With the application of the impulses, the relative distances change, causing variations in the energy of the asteroid and a large variation in the relative distance between the asteroid and Earth over a long period after the impulse. We present results related to the magnitude of the impulse applied, which is important because its defines the mass and velocity of the impactor to be considered. Then, we mapped the positions of the impulses along a period of the orbit of the asteroid. We finish by explaining what happens to the orbit of the asteroid during the periods of gravitational perturbation, since the close encounters amount to “Swing Bys” that intensify the variations of the relative distances between the bodies after the impulse is applied.

The deflection of potentially dangerous asteroids has been treated with great intensity and has gained more and more attention in scientific research. Different techniques are developed over the years. Among these techniques, we found the kinetic impact deflection technique to be the most viable at the moment. In this work we address the kinetic impact deflection technique, but in a scenario where we have a short time to deflect an asteroid that will collide with Earth. For this, we also use a maneuver similar to a powered gravity-assisted maneuver with Earth in a previous passage to change the trajectory of the asteroid to avoid the collision. We apply this technique in three scenarios: (i) impulse before the close encounter, (ii) impulse during the close encounter, and (iii) impulse after the close encounter. We observe that some trajectories are symmetric with respect to the line Sun–Earth, and others are asymmetric. We show that, using this technique, it is possible to change the trajectory of the asteroid, even in a short period, to avoid the collision without using a large variation of velocity in the orbit of the asteroid.

<p lang="en-GB" align="justify"><strong>Abstract</strong></p> <p lang="en-US" align="justify"><span lang="en-US">The present work aims to study the use of a kinetic impact technique as a way to deflect asteroids that may present some risk of collision with the Earth at a given time. This is a very current topic of research and it is related to planetary defense. It has been receiving the attention of researchers worldwide. In the work to be developed here, intend to evaluate in more detail the possibility of deflecting the orbit of asteroid 101955 Bennu, taking into account specific aspects.</span></p> <ol> <li> <p lang="en-GB" align="justify"><strong>Introduction</strong></p> </li> </ol> <p lang="en-US" align="justify">Asteroids are the smallest bodies in the solar system, usually with diameters on the order of a few hundred’s, or even only tens of kilometers. The total mass of all asteroids in the solar system must be less than the mass of the Earth’s Moon. Despite this fact, they are objects of great importance. They must contain information about the formation of the solar system, since its chemical and physical compositions remain practically constant over time. These bodies also pose a danger to Earth, as many of these bodies are on a trajectory that passes close to Earth. There is also the possibility of mining on asteroids, in order to extract precious metals and other natural resources.</p> <p lang="en-US" align="justify"><span lang="en-US">Asteroids have a very irregular shape, which makes their study difficult. In addition, they have rotational movement, in general very complex, due to their irregular shape. Asteroids are classified into groups: NEA (Near-Earth Asteroid), Trojans, Kuiper Belt, etc. NEAs are the most dangerous from the point of view of collision with Earth, since their trajectories are close to Earth’s orbit. There is even a mission, AIDA (Asteroid Impact and Deflection Assessment), in which ESA aims to achieve a binary system (65803 Didymos). There is also the American Asteroid Redirect Mission (ARM), which plans to collected item over a long period of time to deflect the asteroid’s orbit. Within this context, the present work intends to focus on the application aimed at the deflection an asteroid on a hazardous course with Earth, utilizing the technique of kinetic impact. </span></p> <ol start="2"> <li> <p lang="en-GB" align="justify"><strong>Making variations in the velocity of the asteroid.</strong></p> </li> </ol> <p lang="en-US" align="justify">For this project we are using the numerical integrator package Mercury N-bodies, designed to simulate the orbit of bodies of different sizes around a central body. The different numerical integrators present in Mercury allow the user to obtain a good relationship between the computational cost and the resolution of the simulations. Mercury also allows the user to add forces from sources other than gravity, as well as to modify algorithms such as collisions that, by default, result in the perfect fusion of two bodies with mass conservations and linear momentum.</p> <p lang="en-US" align="justify"><span lang="en-US">For the input data for integration, the components of position and velocity of the bodies were used, taken from the JPL Horizons website, for the same date used in this work. The mass of (7,329 ± 0.009) × 10</span><sup><span lang="en-US">10</span></sup><span lang="en-US">kg and density of 1190 ± 13 kg.m</span><sup><span lang="en-US">-3</span></sup><span lang="en-US"> were considered for the asteroid Bennu (Kováčová et al.2020, Lauretta et al.2019a, Scheeres et al. 2019). We are not considering the composition and dimensions of the asteroid, as well as its rotation properties and minor disturbances that may occur due to its non-linear dynamics.</span></p> <p lang="en-US" align="justify"><span lang="en-US">For this work, we used velocity variations simulating an impact opposite to the direction of the asteroid's movement (Δv negative) and also in the same direction of movement of the asteroid (Δv positive). The variations used here were from 10 mm/s to 50 mm/s. We also divided the impact point into 16 parts of the asteroid's orbital period, approximately 27 days to achieve greater precision in the results and also to reach the perihelion and aphelion points.</span></p> <p lang="en-US" align="justify"><span lang="en-US">We are also monitoring the influence of all planets in the solar system, applying the technique of deflecting the asteroid considering all the planets of the solar system, a system of 4 bodies (Sun, Earth, Moon and asteroid) and a system of 5 bodies (Sun, Earth, Moon, Jupiter and asteroid), to determine Jupiter's influence on the results.</span></p> <p lang="en-GB" align="justify"><strong>Acknowledgements</strong></p> <p lang="en-US" align="justify">This work is funded by Fapesp (Proc. 2018/17864-1 ).</p> <p lang="en-GB" align="justify"><strong>References</strong></p> <p lang="en-US" align="justify">[1] J.E.Chambers (1999) “A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies”. Monthly Notices of the Royal Astronomical Society, vol 304, pp793-799..</p> <p lang="en-US" align="justify">[<span lang="en-US">2</span>]Holsapple, K.A., Housen, K.R. 2016. Momentum transfer in asteroid impacts. I. Theory and scaling. Icarus 221, 875-887.</p> <p lang="en-US" align="justify">[<span lang="en-US">3</span>] Brophy, J.R., AND Muirhead, B., Near-Earth Asteroid Retrieval Mission (ARM) Study. IEPC-2013-82, Presented at the 33rd International Electric Propulsion Conference, Washington, DC, October 6-10, 2013.</p> <p lang="en-US" align="justify">[<span lang="en-US">4</span>] Cheng, A. F. et al. Asteroid Impact Deflection Assessment mission: Kinetic impactor. AIDA TEAM. Avances in Space Research. Vol. 121, pages 27-35. 2016. http://dx.doi.org/10.1016/j.pss.2015.12.004.</p> <p lang="en-US" align="justify">[<span lang="en-US">5</span>] DART. Dart mission: Double Asteroid Redirection Test. http://dart.jhuapl.edu/Mission/index.php. Accessed in February, 2017.</p> <p lang="en-US" align="justify">[<span lang="en-US">6</span>] Falcone, G. et al. Attitude Control of the Asteroid Redirect Robotic Mission Spacecraft with a Captured Boulder. AIAA/AAS Astrodynamics Specialist Conference, AIAA SPACE Forum, (AIAA 2016-5645), 2016. HTTP://DX.DOI.ORG/10.2514/6.2016-5645.</p> <p lang="en-US" align="justify">[<span lang="en-US">7</span>] M. Kováčová, R. Nagy, et al. 101955 Bennu and 162173 Ryugu:dynamical modelling of ejected particles to the Earth. Planetary and Space Science. 2020. https://doi.org/10.1016/j.pss.2020.104897</p> <p lang="en-US" align="justify">[<span lang="en-US">8</span>] Jutzi, M., Michel, P. 2014. Hypervelocity impacts on asteroids and momentum transfer. I. Numerical simulations using porous targets. Icarus 229, 247-253.</p> <p lang="en-US" align="justify">[<span lang="en-US">9</span>] Kerslake, T.W. et al..”Structural Design Considerations for a 50 kW-Class Solar Array for NASAs Asteroid Redirect Mission”, 3rd AIAA Spacecraft Structures Conference, AIAA SciTech Forum, (AIAA 2016-1701). 2016. http://dx.doi.org/10.2514/6.2016-1701.</p> <p lang="en-US" align="justify">[<span lang="en-US">10</span>] Lauretta, D. S., DellaGiustina, D. N., Bennett, C. A. et al.: The unexpected surface of asteroid (101955) Bennu, Nature 568, 55-60, 2019a.</p> <p lang="en-US" align="justify">[<span lang="en-US">11</span>] Scheeres, D. J., McMahon, J. W., French, A. S. et al.: The dynamic geophysical environment of (101955) Bennu based on OSIRIS-REx measurements, Nature Astronomy 3, 352-361, 2019.</p> <p lang="en-US" align="justify"><br /><br /></p>

We will present the use of the kinetic impact technique as a way to deflect asteroids that may present some risk of collision with Earth at any given time. Within the work to be developed here, we intend to evaluate in more detail the possibility to deflect the orbit of the asteroid 101955 Bennu, applying variations in its velocity (∆v) at different positions within its orbital period and measuring close encounters with planet Earth. We will see that, in a relatively long period of time, the asteroid has several close encounters with the planet, thus suffering a natural gravitational perturbation. With the application of the impulses, the relative distances change, causing variations in the energy of the asteroid and a large variation in the relative distance between the asteroid and Earth over a long period after the impulse. We present results in relation to the intensity of the applied impulse, which is important due to the size of the impactor to be considered and, for that, we mapped the positions of the impulses along a period of the orbit of the asteroid (M.I.O.A.). We finish by explaining what happens to the orbit of the asteroid during the periods of gravitational perturbation, since it undergoes to several “Swing Bys’ that intensify the variations of the relative distances between the bodies after the impulses.