*********************************
There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
*********************************
Michela Mancini
(Advisor: Dr. John A. Christian] will defend a master’s thesis entitled,
An analysis on the application of algebraic geometry in initial orbit
determination problems
On
Wednesday, November 16 at 10:30 a.m.
Weber 200
Abstract
Initial Orbit Determination (IOD) is a classical problem in astrodynamics. The space around Earth
is crowded by a great many objects whose orbits are unknown, and the number of space debris is
constantly increasing because of break-up events and collisions. Reconstructing the orbit of a body
from observations allows us to create catalogs that are used to avoid collisions and program
missions for debris removal. Also, comparing the observations of celestial bodies with predictions
of their positions made on the basis of our knowledge of the universe has been in the past, and is
still today, one of the most effective means to make improvements in our cosmological model.
In this work, a purely geometric solution to the angles-only IOD problem is analyzed and its
performance under various scenarios of observations is tested. The problem formulation is based on
a re- parameterization of the orbit as a disk quadric, and relating the observations to the
unknowns leads to a polynomial system that can be solved using tools from numerical algebraic
geometry. This method is time-free and does not require any type of initialization. This makes it
unaffected by the problems related to the use of time that usually must be accounted for to improve
the accuracy of the solution.
A similar approach may be used to analyze the performance of the solver when streaks are used,
together with lines of sight, as inputs to the problem. Streaks on digital images form, together
with the camera location, planes that are tangent to the orbit. This produces two different types
of constraint that can be imposed, and also in this case a polynomial system is obtained. The
accuracy and the robustness of the solver are decreased by the presence of streaks, but they remain
a valid input when diversity in the observed directions guarantees the departure from the singular
configuration of almost coplanar observations.
Committee
• Dr. John A. Christian – School of Aerospace Engineering (advisor)
• Dr. Brian C. Gunter– School of Aerospace Engineering
• Dr. Anton Leykin – School of Mathematics
