{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/132505"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/132505","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Design and modeling of kinetic impact missions for deflecting near-earth asteroids","abstract":"The solar system is full of small bodies such as asteroids and comets that are thought to be remnants of early planetary formation. As of June 2025, there are more than 1.4 million known small bodies in the solar system, more than 4,000 of which are classified as comets. These objects routinely cross the Earth's orbit at close distances. Some have even impacted our home planet in the past, causing significant damage. Therefore, studying them is critical – not just for understanding the history and evolution of the solar system, but for assessing potential existential threats to life on Earth. The field of planetary defense is dedicated to the study of asteroids and comets that might pose such natural hazards. It also focuses on the development of methods to mitigate these threats. Work done in this field involves discovering and characterizing potentially hazardous objects, predicting their future trajectories, and developing various methods to deflect or disrupt them if they are found to be on a collision course with Earth. The work presented in this dissertation focuses on the kinetic impact method for deflecting asteroids that could potentially hit the Earth. Kinetic impact deflection entails sending a spacecraft to crash into the threatening object at high speed, thereby altering its trajectory. Over time, this small change in the originally earthbound trajectory can accumulate into a significant change in the object's position, potentially preventing the impact. Within the time span of the work presented in this dissertation, NASA has launched and successfully completed the Double Asteroid Redirection Test (DART) mission. DART was the world's first demonstration of the kinetic impact deflection method at the (65803) Didymos binary asteroid system. The DART spacecraft collided with the asteroid Dimorphos in September 2022, successfully altering its orbit around its parent body, Didymos. In the context of the DART mission, I have developed new methodologies for modeling the momentum transfer from the deflection spacecraft to the target, which is crucial for predicting the outcome of kinetic impact. This includes methods for quantifying the measurability of the heliocentric momentum transfer, which characterizes the change in the target's orbit around the Sun. The framework developed here enables planetary defense programs to evaluate the effectiveness of a deflection, as this change is what ultimately determines whether the hazard from an asteroid has been successfully mitigated. Consequently, this dissertation also presents the first-ever measurement of the heliocentric orbit change for a celestial object in the solar system. This measurement for the DART mission is a significant milestone in planetary defense, as it provides concrete evidence of the effectiveness of kinetic impacts for deflecting asteroids. Additionally, a new method for designing future kinetic impact missions is also presented. This method relies on mapping keyholes onto the surface of a target asteroid. Gravitational keyholes are arbitrary regions in space that, if an asteroid passes through them, will guarantee a future impact with Earth. Keyhole mapping allows mission designers to plan deflection missions that can push asteroids away from the Earth while ensuring that they do not pass through a keyhole after the deflection. This can allow us to permanently push these objects away from Earth. Lastly, this dissertation also presents novel contributions to the broader field of dynamical systems theory by introducing a new method for computing the state transition matrix of a nonlinear dynamical system. Based on the concept of the unscented transform, this method allows for computation of the state transition matrix without the need of tedious analytic partial derivatives or arbitrary finite difference steps. Therefore, the results presented here provide new insights that extend the state of the art in planetary defense and will aid in the design and successful execution of future deflection missions. The demonstration of the kinetic impact method through the DART mission marked a pivotal moment in our ability to protect Earth from potential impacts. The methodologies developed in this dissertation will help ensure that we are better prepared for any future threats.","abstract_html":"The solar system is full of small bodies such as asteroids and comets that are thought to be remnants of early planetary formation. As of June 2025, there are more than 1.4 million known small bodies in the solar system, more than 4,000 of which are classified as comets. These objects routinely cross the Earth's orbit at close distances. Some have even impacted our home planet in the past, causing significant damage. Therefore, studying them is critical – not just for understanding the history and evolution of the solar system, but for assessing potential existential threats to life on Earth. The field of planetary defense is dedicated to the study of asteroids and comets that might pose such natural hazards. It also focuses on the development of methods to mitigate these threats. Work done in this field involves discovering and characterizing potentially hazardous objects, predicting their future trajectories, and developing various methods to deflect or disrupt them if they are found to be on a collision course with Earth. The work presented in this dissertation focuses on the kinetic impact method for deflecting asteroids that could potentially hit the Earth. Kinetic impact deflection entails sending a spacecraft to crash into the threatening object at high speed, thereby altering its trajectory. Over time, this small change in the originally earthbound trajectory can accumulate into a significant change in the object's position, potentially preventing the impact. Within the time span of the work presented in this dissertation, NASA has launched and successfully completed the Double Asteroid Redirection Test (DART) mission. DART was the world's first demonstration of the kinetic impact deflection method at the (65803) Didymos binary asteroid system. The DART spacecraft collided with the asteroid Dimorphos in September 2022, successfully altering its orbit around its parent body, Didymos. In the context of the DART mission, I have developed new methodologies for modeling the momentum transfer from the deflection spacecraft to the target, which is crucial for predicting the outcome of kinetic impact. This includes methods for quantifying the measurability of the heliocentric momentum transfer, which characterizes the change in the target's orbit around the Sun. The framework developed here enables planetary defense programs to evaluate the effectiveness of a deflection, as this change is what ultimately determines whether the hazard from an asteroid has been successfully mitigated. Consequently, this dissertation also presents the first-ever measurement of the heliocentric orbit change for a celestial object in the solar system. This measurement for the DART mission is a significant milestone in planetary defense, as it provides concrete evidence of the effectiveness of kinetic impacts for deflecting asteroids. Additionally, a new method for designing future kinetic impact missions is also presented. This method relies on mapping keyholes onto the surface of a target asteroid. Gravitational keyholes are arbitrary regions in space that, if an asteroid passes through them, will guarantee a future impact with Earth. Keyhole mapping allows mission designers to plan deflection missions that can push asteroids away from the Earth while ensuring that they do not pass through a keyhole after the deflection. This can allow us to permanently push these objects away from Earth. Lastly, this dissertation also presents novel contributions to the broader field of dynamical systems theory by introducing a new method for computing the state transition matrix of a nonlinear dynamical system. Based on the concept of the unscented transform, this method allows for computation of the state transition matrix without the need of tedious analytic partial derivatives or arbitrary finite difference steps. Therefore, the results presented here provide new insights that extend the state of the art in planetary defense and will aid in the design and successful execution of future deflection missions. The demonstration of the kinetic impact method through the DART mission marked a pivotal moment in our ability to protect Earth from potential impacts. The methodologies developed in this dissertation will help ensure that we are better prepared for any future threats.","abstract_has_math":false,"creators":["Makadia, Rahil"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Aerospace Engineering","degree_department":null,"school":null,"contributors":["Eggl, Siegfried","Chesley, Steven R","Farnocchia, Davide","Conway, Bruce A","Ilie, Raluca"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-12","date_published":"2025-12","updated_at":"2026-07-22T22:25:07Z","subjects":["Celestial Mechanics","Planetary Defense","Asteroid Deflection","Kinetic Impactor"],"languages":["en"],"rights":["Copyright 2025 Rahil Makadia. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/132505","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Eggl, Siegfried","Chesley, Steven R","Farnocchia, Davide","Conway, Bruce A","Ilie, Raluca"]},{"key":"dc:creator","label":"Author","values":["Makadia, Rahil"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-12","2025-11-19"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Aerospace Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Celestial Mechanics","Planetary Defense","Asteroid Deflection","Kinetic Impactor"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Rahil Makadia. All rights reserved."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/132505"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The solar system is full of small bodies such as asteroids and comets that are thought to be remnants of early planetary formation. As of June 2025, there are more than 1.4 million known small bodies in the solar system, more than 4,000 of which are classified as comets. These objects routinely cross the Earth's orbit at close distances. Some have even impacted our home planet in the past, causing significant damage. Therefore, studying them is critical – not just for understanding the history and evolution of the solar system, but for assessing potential existential threats to life on Earth. The field of planetary defense is dedicated to the study of asteroids and comets that might pose such natural hazards. It also focuses on the development of methods to mitigate these threats. Work done in this field involves discovering and characterizing potentially hazardous objects, predicting their future trajectories, and developing various methods to deflect or disrupt them if they are found to be on a collision course with Earth. The work presented in this dissertation focuses on the kinetic impact method for deflecting asteroids that could potentially hit the Earth. Kinetic impact deflection entails sending a spacecraft to crash into the threatening object at high speed, thereby altering its trajectory. Over time, this small change in the originally earthbound trajectory can accumulate into a significant change in the object's position, potentially preventing the impact. Within the time span of the work presented in this dissertation, NASA has launched and successfully completed the Double Asteroid Redirection Test (DART) mission. DART was the world's first demonstration of the kinetic impact deflection method at the (65803) Didymos binary asteroid system. The DART spacecraft collided with the asteroid Dimorphos in September 2022, successfully altering its orbit around its parent body, Didymos. In the context of the DART mission, I have developed new methodologies for modeling the momentum transfer from the deflection spacecraft to the target, which is crucial for predicting the outcome of kinetic impact. This includes methods for quantifying the measurability of the heliocentric momentum transfer, which characterizes the change in the target's orbit around the Sun. The framework developed here enables planetary defense programs to evaluate the effectiveness of a deflection, as this change is what ultimately determines whether the hazard from an asteroid has been successfully mitigated. Consequently, this dissertation also presents the first-ever measurement of the heliocentric orbit change for a celestial object in the solar system. This measurement for the DART mission is a significant milestone in planetary defense, as it provides concrete evidence of the effectiveness of kinetic impacts for deflecting asteroids. Additionally, a new method for designing future kinetic impact missions is also presented. This method relies on mapping keyholes onto the surface of a target asteroid. Gravitational keyholes are arbitrary regions in space that, if an asteroid passes through them, will guarantee a future impact with Earth. Keyhole mapping allows mission designers to plan deflection missions that can push asteroids away from the Earth while ensuring that they do not pass through a keyhole after the deflection. This can allow us to permanently push these objects away from Earth. Lastly, this dissertation also presents novel contributions to the broader field of dynamical systems theory by introducing a new method for computing the state transition matrix of a nonlinear dynamical system. Based on the concept of the unscented transform, this method allows for computation of the state transition matrix without the need of tedious analytic partial derivatives or arbitrary finite difference steps. Therefore, the results presented here provide new insights that extend the state of the art in planetary defense and will aid in the design and successful execution of future deflection missions. The demonstration of the kinetic impact method through the DART mission marked a pivotal moment in our ability to protect Earth from potential impacts. The methodologies developed in this dissertation will help ensure that we are better prepared for any future threats.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Rahil Makadia, accepted the attached license on 2025-11-18 at 17:39.","The student, Rahil Makadia, submitted this Dissertation for approval on 2025-11-18 at 17:51.","This Dissertation was approved for publication on 2025-11-19 at 09:16.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22888 on 2026-02-19 at 18:24:57"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Design and modeling of kinetic impact missions for deflecting near-earth asteroids"]}]}],"canonical_facts":{"dc:contributor":["Eggl, Siegfried","Chesley, Steven R","Farnocchia, Davide","Conway, Bruce A","Ilie, Raluca"],"dc:creator":["Makadia, Rahil"],"dc:date":["2025-12","2025-11-19"],"dc:description":["The solar system is full of small bodies such as asteroids and comets that are thought to be remnants of early planetary formation. As of June 2025, there are more than 1.4 million known small bodies in the solar system, more than 4,000 of which are classified as comets. These objects routinely cross the Earth's orbit at close distances. Some have even impacted our home planet in the past, causing significant damage. Therefore, studying them is critical – not just for understanding the history and evolution of the solar system, but for assessing potential existential threats to life on Earth. The field of planetary defense is dedicated to the study of asteroids and comets that might pose such natural hazards. It also focuses on the development of methods to mitigate these threats. Work done in this field involves discovering and characterizing potentially hazardous objects, predicting their future trajectories, and developing various methods to deflect or disrupt them if they are found to be on a collision course with Earth. The work presented in this dissertation focuses on the kinetic impact method for deflecting asteroids that could potentially hit the Earth. Kinetic impact deflection entails sending a spacecraft to crash into the threatening object at high speed, thereby altering its trajectory. Over time, this small change in the originally earthbound trajectory can accumulate into a significant change in the object's position, potentially preventing the impact. Within the time span of the work presented in this dissertation, NASA has launched and successfully completed the Double Asteroid Redirection Test (DART) mission. DART was the world's first demonstration of the kinetic impact deflection method at the (65803) Didymos binary asteroid system. The DART spacecraft collided with the asteroid Dimorphos in September 2022, successfully altering its orbit around its parent body, Didymos. In the context of the DART mission, I have developed new methodologies for modeling the momentum transfer from the deflection spacecraft to the target, which is crucial for predicting the outcome of kinetic impact. This includes methods for quantifying the measurability of the heliocentric momentum transfer, which characterizes the change in the target's orbit around the Sun. The framework developed here enables planetary defense programs to evaluate the effectiveness of a deflection, as this change is what ultimately determines whether the hazard from an asteroid has been successfully mitigated. Consequently, this dissertation also presents the first-ever measurement of the heliocentric orbit change for a celestial object in the solar system. This measurement for the DART mission is a significant milestone in planetary defense, as it provides concrete evidence of the effectiveness of kinetic impacts for deflecting asteroids. Additionally, a new method for designing future kinetic impact missions is also presented. This method relies on mapping keyholes onto the surface of a target asteroid. Gravitational keyholes are arbitrary regions in space that, if an asteroid passes through them, will guarantee a future impact with Earth. Keyhole mapping allows mission designers to plan deflection missions that can push asteroids away from the Earth while ensuring that they do not pass through a keyhole after the deflection. This can allow us to permanently push these objects away from Earth. Lastly, this dissertation also presents novel contributions to the broader field of dynamical systems theory by introducing a new method for computing the state transition matrix of a nonlinear dynamical system. Based on the concept of the unscented transform, this method allows for computation of the state transition matrix without the need of tedious analytic partial derivatives or arbitrary finite difference steps. Therefore, the results presented here provide new insights that extend the state of the art in planetary defense and will aid in the design and successful execution of future deflection missions. The demonstration of the kinetic impact method through the DART mission marked a pivotal moment in our ability to protect Earth from potential impacts. The methodologies developed in this dissertation will help ensure that we are better prepared for any future threats.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo terms","The student, Rahil Makadia, accepted the attached license on 2025-11-18 at 17:39.","The student, Rahil Makadia, submitted this Dissertation for approval on 2025-11-18 at 17:51.","This Dissertation was approved for publication on 2025-11-19 at 09:16.","DSpace SAF Submission Ingestion Package generated from Vireo submission #22888 on 2026-02-19 at 18:24:57"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/132505"],"dc:language":["en"],"dc:rights":["Copyright 2025 Rahil Makadia. All rights reserved."],"dc:subject":["Celestial Mechanics","Planetary Defense","Asteroid Deflection","Kinetic Impactor"],"dc:title":["Design and modeling of kinetic impact missions for deflecting near-earth asteroids"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Aerospace Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:07Z"}