{"662830":{"#nid":"662830","#data":{"type":"event","title":"MS Defense by Michela Mancini","body":[{"value":"\u003Cp\u003EMichela Mancini\u003Cbr \/\u003E\r\n(Advisor: Dr. John A. Christian] will defend a master\u0026rsquo;s thesis entitled,\u003Cbr \/\u003E\r\nAn analysis on the application of algebraic geometry in initial orbit\u003Cbr \/\u003E\r\ndetermination problems\u003Cbr \/\u003E\r\nOn\u003Cbr \/\u003E\r\nWednesday, November 16 at 10:30 a.m.\u003Cbr \/\u003E\r\nWeber 200\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cbr \/\u003E\r\nAbstract\u003Cbr \/\u003E\r\nInitial Orbit Determination (IOD) is a classical problem in astrodynamics. The space around Earth\u0026nbsp;\u003Cbr \/\u003E\r\nis crowded by a great many objects whose orbits are unknown, and the number of space debris is\u0026nbsp;\u003Cbr \/\u003E\r\nconstantly increasing because of break-up events and collisions. Reconstructing the orbit of a body\u0026nbsp;\u003Cbr \/\u003E\r\nfrom observations allows us to create catalogs that are used to avoid collisions and program\u0026nbsp;\u003Cbr \/\u003E\r\nmissions for debris removal. Also, comparing the observations of celestial bodies with predictions\u0026nbsp;\u003Cbr \/\u003E\r\nof their positions made on the basis of our knowledge of the universe has been in the past, and is\u0026nbsp;\u003Cbr \/\u003E\r\nstill today, one of the most effective means to make improvements in our cosmological model.\u003Cbr \/\u003E\r\nIn this work, a purely geometric solution to the angles-only IOD problem is analyzed and its\u0026nbsp;\u003Cbr \/\u003E\r\nperformance under various scenarios of observations is tested. The problem formulation is based on\u0026nbsp;\u003Cbr \/\u003E\r\na re- parameterization of the orbit as a disk quadric, and relating the observations to the\u0026nbsp;\u003Cbr \/\u003E\r\nunknowns leads to a polynomial system that can be solved using tools from numerical algebraic\u0026nbsp;\u003Cbr \/\u003E\r\ngeometry. This method is time-free and does not require any type of initialization. This makes it\u0026nbsp;\u003Cbr \/\u003E\r\nunaffected by the problems related to the use of time that usually must be accounted for to improve\u0026nbsp;\u003Cbr \/\u003E\r\nthe accuracy of the solution.\u003Cbr \/\u003E\r\nA similar approach may be used to analyze the performance of the solver when streaks are used,\u0026nbsp;\u003Cbr \/\u003E\r\ntogether with lines of sight, as inputs to the problem. Streaks on digital images form, together\u0026nbsp;\u003Cbr \/\u003E\r\nwith the camera location, planes that are tangent to the orbit. This produces two different types\u0026nbsp;\u003Cbr \/\u003E\r\nof constraint that can be imposed, and also in this case a polynomial system is obtained. The\u0026nbsp;\u003Cbr \/\u003E\r\naccuracy and the robustness of the solver are decreased by the presence of streaks, but they remain\u0026nbsp;\u003Cbr \/\u003E\r\na valid input when diversity in the observed directions guarantees the departure from the singular\u0026nbsp;\u003Cbr \/\u003E\r\nconfiguration of almost coplanar observations.\u003Cbr \/\u003E\r\nCommittee\u003Cbr \/\u003E\r\n\u0026bull; \u0026nbsp;Dr. John A. Christian \u0026ndash; School of Aerospace Engineering (advisor)\u003Cbr \/\u003E\r\n\u0026bull; \u0026nbsp;Dr. Brian C. Gunter\u0026ndash; School of Aerospace Engineering\u003Cbr \/\u003E\r\n\u0026bull; \u0026nbsp;Dr. Anton Leykin \u0026ndash; School of Mathematics\u003Cbr \/\u003E\r\n\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"An analysis on the application of algebraic geometry in initial orbit determination problems"}],"uid":"27707","created_gmt":"2022-11-03 17:48:34","changed_gmt":"2022-11-03 17:48:34","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2022-11-16T10:30:00-05:00","event_time_end":"2022-11-16T12:30:00-05:00","event_time_end_last":"2022-11-16T12:30:00-05:00","gmt_time_start":"2022-11-16 15:30:00","gmt_time_end":"2022-11-16 17:30:00","gmt_time_end_last":"2022-11-16 17:30:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"111531","name":"ms defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}