Date of Award


Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Darren Hitt

Second Advisor

Chris Danforth


A significant component of recent space exploration has been unmanned mission to comets

and asteroids. The increase in interest for these bodies necessitates an increase in demand

for higher fidelity trajectory simulations in order to assure mission success. Most available

methods for simulating trajectories about asymmetric bodies assume they are of uniform

density. This thesis examines a hybrid method that merges a mass concentration ("mascon")

model and a spherical harmonic model using the "Brillouin sphere" as the interface. This

joint model will be used for simulating trajectories about variable density bodies and, in

particular, contact binary asteroids and comets.

The scope of this thesis is confined to the analysis and characterization of the spherical

harmonic modeling method in which three bodies of increasing asymmetrical severity are

used as test cases: Earth, asteroid 101955 Bennu, and asteroid 25143 Itokawa. Since the

zonal harmonics are well defined for Earth, it is used as the initial baseline for the method.

Trajectories in the equatorial plane and inclined to this plane are simulated to analyze the

dynamical behavior of the environment around each of the three bodies. There are multiple

degrees of freedom in the spherical harmonic modeling method which are characterized as

follows: (1) The radius of the Brillouin sphere is varied as a function of the altitude of

the simulated orbit, (2) The truncation degree of the series is chosen based upon the error

incurred in the acceleration field on the chosen Brillouin sphere, and (3) The gravitational

potential and acceleration field are calculated using the determined radial location of the

Brillouin sphere and the truncation degree.

An ideal Brillouin sphere radius and truncation degree are able to be determined as a

function of a given orbit where the error in the acceleration field is locally minimized. The

dual-density model for a contact binary is found to more accurately describe the dynamical

environment around Asteroid 25143 Itokawa compared to the single density model.



Number of Pages

79 p.