Lagrangian Points and Jacobi Constants for a Class of Asteroids

<p>Asteroid Gravitational Potentials are difficult to model owing to their irregularity in shape. This thesis focuses on two approaches to model asteroid gravity fields, namely, multiple-body and spherical harmonics modeling. Computation of gravity potential serves as a first step to determine equilibrium points called Lagrangian points for a spacecraft orbiting as an asteroid. Further, Jacobi analysis is carried out to determine zero-velocity regions, i.e., inaccessible regions corresponding to the unstable Lagrangian points. Multiple sphere modeling was studied through analysis of so called Asteroid Restricted Three and Four Body Problems, providing insight into the method of modeling an asteroid as a cluster of multiple spheres in contact with each other and rotating with a constant angular velocity about the center of mass of the cluster. A spherical harmonics approximation was then investigated for a special case, an asteroid in the shape of an ellipsoid. This approach is common but yields highly complex equations of motivation due to multiple terms in the spherical harmonics expansion. Finally the equivalence of the above two methods was validated by considering a configuration of a cluster of spheres that can approximate an ellipsoid.</p>

Name thesis:degree_name

Master of Science in Aerospace Engineering

Level thesis:degree_level

Thesis - Open Access

Discipline thesis:degree_discipline

Aerospace Engineering

Year

2015

Author dc:creator

• Rashid, Tasneem

• Langrangian points
• Jacobi constants
• asteroids
• Aerospace Engineering

Repository record dc:identifier

https://commons.erau.edu/edt/236

OAI identifier oai:identifier

oai:commons.erau.edu:edt-1235