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Copy file name to clipboardExpand all lines: joss/paper.bib
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number = {8},
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pages = {184},
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author = {Rahil Makadia and Sabina D. Raducan and Eugene G. Fahnestock and Siegfried Eggl},
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title = {Heliocentric Effects of the DART Mission on the (65803) Didymos Binary Asteroid System},
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title = {Heliocentric Effects of the DART Mission on the (65803) {Didymos} Binary Asteroid System},
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journal = {The Planetary Science Journal},
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abstract = {The Double Asteroid Redirect Test (DART) is NASA’s first kinetic impact–based asteroid deflection mission. The DART spacecraft will act as a projectile during a hypervelocity impact on Dimorphos, the secondary asteroid in the (65803) Didymos binary system, and alter its mutual orbital period. The initial momentum transfer between the DART spacecraft and Dimorphos is enhanced by the ejecta flung off the surface of Dimorphos. This exchange is characterized within the system by the momentum enhancement parameter, β, and on a heliocentric level by its counterpart, β ⊙. The relationship between β and the physical characteristics of Dimorphos is discussed here. A nominal set of Dimorphos physical parameters from the design reference asteroid and impact circumstances from the design reference mission are used to initialize the ejecta particles for dynamical propagation. The results of this propagation are translated into a gradual momentum transfer onto the Didymos system barycenter. A high-quality solar system propagator is then used to produce precise estimates of the post-DART encounters between Didymos and Earth by generating updated close approach maps. Results show that even for an unexpectedly high β ⊙, a collision between the Didymos system and Earth is practically excluded in the foreseeable future. A small but significant difference is found in modeling the overall momentum transfer when individual ejecta particles escape the Didymos system, as opposed to imparting the ejecta momentum as a single impulse at impact. This difference has implications for future asteroid deflection campaigns, especially when it is necessary to steer asteroids away from gravitational keyholes.}
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}
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@article{Makadia2024,
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author = {Rahil Makadia and Steven R. Chesley and Davide Farnocchia and Shantanu P. Naidu and Damya Souami and Paolo Tanga and Kleomenis Tsiganis and Masatoshi Hirabayashi and Siegfried Eggl},
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journal = {The Planetary Science Journal},
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title = {{Measurability of the Heliocentric Momentum Enhancement from a Kinetic Impact: The Double Asteroid Redirection Test (DART) Mission}},
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title = {Measurability of the Heliocentric Momentum Enhancement from a Kinetic Impact: The {Double Asteroid Redirection Test (DART)} Mission},
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year = {2024},
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month = feb,
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number = {2},
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@article{Makadia2025,
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author = {Rahil Makadia and Davide Farnocchia and Steven R. Chesley and Siegfried Eggl},
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journal = {The Planetary Science Journal},
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title = {{Gauss-Radau Small-body Simulator (GRSS): An Open-Source Library for Planetary Defense}},
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title = {{Gauss-Radau Small-body Simulator (GRSS)}: An Open-Source Library for Planetary Defense},
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year = {2025},
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volume = {6},
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doi = {10.3847/PSJ/adbc88},
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@article{Kizner1961,
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author = {William Kizner},
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title = "{A Method of Describing Miss Distances for Lunar and Interplanetary Trajectories}",
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title = {A Method of Describing Miss Distances for Lunar and Interplanetary Trajectories},
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journal = {Planetary and Space Science},
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year = 1961,
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month = jul,
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@inproceedings{Chodas1999,
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author = {Paul W. Chodas and Donald K. Yeomans},
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title = {Orbit Determination and Estimation of Impact Probability for Near Earth Objects},
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title = {Orbit Determination and Estimation of Impact Probability for Near {Earth} Objects},
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booktitle = {AAS Guidance and Control Conference, Breckenridge, Colorado, USA},
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year = {1999},
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url = {https://hdl.handle.net/2014/16816}
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@Article{Farnocchia2019,
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author = {Farnocchia, Davide and Eggl, Siegfried and Chodas, Paul W. and Giorgini, Jon D. and Chesley, Steven R.},
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journal = {Celestial Mechanics and Dynamical Astronomy},
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title = {Planetary encounter analysis on the B-plane: a comprehensive formulation},
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title = {Planetary encounter analysis on the {B}-plane: a comprehensive formulation},
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year = {2019},
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issn = {1572-9478},
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month = aug,
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@article{Schwamb2023,
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author = {Schwamb, Megan E. and Jones, R. Lynne and Yoachim, Peter and Volk, Kathryn and Dorsey, Rosemary C. and Opitom, Cyrielle and Greenstreet, Sarah and Lister, Tim and Snodgrass, Colin and Bolin, Bryce T. and Inno, Laura and Bannister, Michele T. and Eggl, Siegfried and Solontoi, Michael and Kelley, Michael S. P. and Jurić, Mario and Lin, Hsing Wen and Ragozzine, Darin and Bernardinelli, Pedro H. and Chesley, Steven R. and Daylan, Tansu and Ďurech, Josef and Fraser, Wesley C. and Granvik, Mikael and Knight, Matthew M. and Lisse, Carey M. and Malhotra, Renu and Oldroyd, William J. and Thirouin, Audrey and Ye, Quanzhi},
Modeling the motion of small solar system bodies is of utmost importance when looking at the problem in the context of planetary defense. Reliably computing the orbit of an asteroid or a comet from various observations, and then predicting its trajectory in the future is critical in assessing the associated Earth-impact hazard. The NASA Center for Near-Earth Object Studies at the Jet Propulsion Laboratory (JPL) has developed a suite of state-of-the-art tools over the course of decades for this specific purpose. However, these tools are not publicly available. With the expected increase in the number of Near-Earth Object observations as well as discoveries when new observatories such as the Vera C. Rubin Observatory come online [@Schwamb2023], there is a need for a publicly available library that can reliably perform both orbit determination and propagation for small bodies in the solar system. Such a publicly available library will enable community efforts in planetary defense research.
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Modeling the motion of small Solar System bodies is of utmost importance when looking at the problem in the context of planetary defense. Reliably computing the orbit of an asteroid or a comet from various observations, and then predicting its trajectory in the future is critical in assessing the associated Earth-impact hazard. The NASA Center for Near-Earth Object Studies at the Jet Propulsion Laboratory (JPL) has developed a suite of state-of-the-art tools over the course of decades for this specific purpose. However, these tools are not publicly available. With the expected increase in the number of Near-Earth Object observations as well as discoveries when new observatories such as the Vera C. Rubin Observatory come online [@Schwamb2023], there is a need for a publicly available library that can reliably perform both orbit determination and propagation for small bodies in the solar system. Such a publicly available library will enable community efforts in planetary defense research.
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# Summary
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In this paper, we present ``GRSS``, the Gauss-Radau Small-body Simulator, an open-source library for orbit determination and propagation of small bodies in the solar system. ``GRSS`` is an open-source software library with a C++11 foundation and a Python binding. The propagator is based on the ``IAS15`` algorithm, a 15<sup>th</sup> order integrator based on Gauss-Radau quadrature [@Rein2014]. Only the particles of interest are integrated within ``GRSS`` to reduce computational cost. The states for the planets and 16 largest main-belt asteroids are computed using memory-mapped JPL digital ephemeris kernels [@Park2021] as done in the ``ASSIST`` orbit propagator library [@Holman2023]. In addition to the propagator, the C++ portion of the library also has the ability to predict impacts and calculate close encounter circumstances using various formulations of the B-plane [@Kizner1961; @Opik1976; @Chodas1999; @Milani1999; @Farnocchia2019].
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In this paper, we present `GRSS`, the Gauss-Radau Small-body Simulator, an open-source library for orbit determination and propagation of small bodies in the solar system. `GRSS` is an open-source software library with a C++11 foundation and a Python binding. The propagator is based on the `IAS15` algorithm, a 15<sup>th</sup> order integrator based on Gauss-Radau quadrature [@Rein2014]. Only the particles of interest are integrated within `GRSS` to reduce computational cost. The states for the planets and 16 largest main-belt asteroids are computed using memory-mapped JPL digital ephemeris kernels [@Park2021] as done in the `ASSIST` orbit propagator library [@Holman2023]. In addition to the propagator, the C++ portion of the library also has the ability to predict impacts and calculate close encounter circumstances using various formulations of the B-plane [@Kizner1961; @Opik1976; @Chodas1999; @Milani1999; @Farnocchia2019].
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The C++ functionality is exposed to Python through a binding generated using [``pybind11``](https://github.com/pybind/pybind11). The Python layer of ``GRSS`` uses the propagator as the foundation to compute the orbits of small bodies from a given set of optical and/or radar astrometry from the [Minor Planet Center](https://minorplanetcenter.net), the [JPL Small Body Radar Astrometry database](https://ssd.jpl.nasa.gov/sb/radar.html), and the [Gaia Focused Product Release solar system observations database](https://www.cosmos.esa.int/web/gaia/fpr#SSOs). Additionally, the orbit determination modules also have the ability to fit especially demanding measurements such as stellar occultations. These capabilities of the ``GRSS`` library have already been used to study the the heliocentric changes in the orbit of the (65803) Didymos binary asteroid system as a result of the DART impact [@Makadia2022; @Makadia2024] and for analyzing the impact locations of two asteroids, 2024 BX<sub>1</sub> and 2024 RW<sub>1</sub> [@Makadia2025].
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The C++ functionality is exposed to Python through a binding generated using [`pybind11`](https://github.com/pybind/pybind11). The Python layer of `GRSS` uses the propagator as the foundation to compute the orbits of small bodies from a given set of optical and/or radar astrometry from the [Minor Planet Center](https://minorplanetcenter.net), the [JPL Small Body Radar Astrometry database](https://ssd.jpl.nasa.gov/sb/radar.html), and the [Gaia Focused Product Release solar system observations database](https://www.cosmos.esa.int/web/gaia/fpr#SSOs). Additionally, the orbit determination modules also have the ability to fit especially demanding measurements such as stellar occultations. These capabilities of the `GRSS` library have already been used to study the the heliocentric changes in the orbit of the (65803) Didymos binary asteroid system as a result of the DART impact [@Makadia2022; @Makadia2024] and for analyzing the impact locations of two asteroids, 2024 BX<sub>1</sub> and 2024 RW<sub>1</sub> [@Makadia2025].
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``GRSS`` will continue to be developed in the future, with anticipated applications including the ability to perform mission studies for future asteroid deflections. ``GRSS`` is publicly available to the community through the Python Package Index and the [source code](https://github.com/rahil-makadia/grss) is available on GitHub. Therefore, ``GRSS`` is a reliable and efficient tool that the community has access to for studying the dynamics of small bodies in the solar system.
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`GRSS` will continue to be developed in the future, with anticipated applications including the ability to perform mission studies for future asteroid deflections. `GRSS` is publicly available to the community through the Python Package Index and the [source code](https://github.com/rahil-makadia/grss) is available on GitHub. Therefore, `GRSS` is a reliable and efficient tool that the community has access to for studying the dynamics of small bodies in the solar system.
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# Acknowledgements
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R.M. acknowledges funding from a NASA Space Technology Graduate Research Opportunities award, NASA contract No. 80NSSC22K1173. The work of S.R.C. and D.F. was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (No. 80NM0018D0004). S.E. acknowledges support by the National Science Foundation through Award AST-2307570. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This work has made use of data from the European Space Agency mission Gaia, processed by the Gaia Data Processing and Analysis Consortium. This library has also extensively used data and services provided by the International Astronomical Union Minor Planet Center (MPC). Data from the MPC's database is made freely available to the public. Funding for this data and the MPC's operations comes from a NASA Planetary Defense Coordination Office grant (80NSSC22M0024), administered via a University of Maryland - Smithsonian Astrophysical Observatory subaward (106075-Z6415201). The MPC's computing equipment is funded in part by the above award, and in part by funding from the Tamkin Foundation.
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