Presentation Title

Stability of the L4 and L5 Lagrange Points: An Explanation of Jupiter's Trojan Asteroids

Abstract

Jupiter’s “Trojan” asteroids orbit the L4 and L5 Lagrange Points of the Sun-Jupiter system and are speculated to be remnants of the collisions which formed planets in our solar system. In this study, we formally verify the stability of the Lagrange Points using a theorem-proving assistant called the “Lean Theorem Prover”. We also model their basin of attraction to develop a tool to determine the possible regions of asteroid origin. Ultimately we hope this research will contribute to our understanding of the solar system’s history and origin.

Primary Faculty Mentor Name

Francois Dorais

Secondary Mentor NetID

wlouisos, tlakoba, jrosebush

Secondary Mentor Name

William Louisos, Taras Lakoba, Joan Rosebush

Status

Undergraduate

Student College

College of Engineering and Mathematical Sciences

Program/Major

Mathematical Sciences

Primary Research Category

Engineering & Physical Sciences

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Stability of the L4 and L5 Lagrange Points: An Explanation of Jupiter's Trojan Asteroids

Jupiter’s “Trojan” asteroids orbit the L4 and L5 Lagrange Points of the Sun-Jupiter system and are speculated to be remnants of the collisions which formed planets in our solar system. In this study, we formally verify the stability of the Lagrange Points using a theorem-proving assistant called the “Lean Theorem Prover”. We also model their basin of attraction to develop a tool to determine the possible regions of asteroid origin. Ultimately we hope this research will contribute to our understanding of the solar system’s history and origin.