Honors Theses

Date of Award

5-2025

Document Type

Undergraduate Thesis

Department

Mechanical Engineering

Faculty Mentor

Joseph D. Richardson

Advisor(s)

Carlos Montalvo, Dhananjay Tambe

Abstract

In October 2017, the asteroid 1I/’Oumuamua first passed into viewing range [1]. The asteroid is notable for being the first interstellar object to enter the solar system. 1I/’Oumuamua was also unusual in its geometry; it is thought to have an aspect ratio of 6:1 and a length of approximately 400 m [2] [3]. The asteroid was observed to experience a non-Keplerian acceleration estimated to be on the order of 1⇥10−6 m s2 . Several theories have been proposed for the cause of this acceleration, all of which are non-gravitational in nature: volatile outgassing, photon pressure, and solar winds [1][4]. However, none of these sources have been definitively proven to be able to provide accelerations large enough to explain the unexpected motion [1] [5]. This project aims to examine the possibility of gravitational efforts on the orbital mechanics of 1I/’Oumuamua due to its elongated shape. For elongated objects, the center of mass and center of gravity are not generally at the same point on the body [6]. This offset between the center of mass and center of gravity causes a torque about the center of mass which is absent in objects able to be approximated as a particle. This project aims to determine whether the additional torque enables the development of an additional acceleration sufficient to explain the unexpected non-Keplerian acceleration observed in 1I/’Oumuamua. Lagrange’s equations were used to develop equations of motion for 1I/’Oumuamua, and these equations were solved through the use of an RK4 algorithm and compared to the Keplerian analytical solution for a particle. Ultimately, it was determined that the additional acceleration experienced by 1I/’Oumuamua of length 400 m at a perihelion distance of 38,100,000 km was potentially on the order of magnitude of 2.5195 ⇥ 10−18 m s2 , a value far too small to explain the additional acceleration observed for 1I/’Oumuamua. Additionally, an asteroid of 400 m experienced a maximum offset from the Keplerian orbital radius of approximately 394 m, an insignificant amount for any asteroid risk assessment efforts. However, pronounced effects were observed for asteroids of 1,000 km or greater, indicating that the additional torque does affect the orbital behavior of elongated asteroids. Additional efforts to quantify this effect for other orbital scenarios and initial conditions will further clarify the additional accelerations and altered orbital paths experienced by elongated asteroids and enable this analysis to be implemented into asteroid risk assessment efforts.

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