The term “homeland security”, seems to have become synonymous with terrorism in the minds of the general public. However, there are other threats to the security of the United States homeland that can be just as, if not more, devastating than terrorism. Included among these other threats is the potential of an asteroid collision with Earth. Historically, asteroid impact events have been responsible for the devastation of our planet and many of the mass extinction events encountered throughout the geologic record. Knowledge of physical parameters such as structure and rotational dynamics of the asteroid are critical parameters in developing interception and deflection techniques, as well as assessing the risk associated with these bodies and mitigation planning in the event of impact. This thesis encompasses the study of eight potentially hazardous asteroids identified in conjunction with NASA’s OSIRIS REX Mission and observed via the Target Asteroid Project, along with observations from the Robotically Controlled Telescope, and the Asteroid Light Curve Database of Photometry. Photometric data was extracted from all observations. Rotation periods of each target were confirmed using Lomb-Scargle time series analysis, with possible secondary periods indicated in the cases of Hathor (2.2169 hours), Bede (161.1501 hours), and Phaethon (4.5563 hours). Shape models for 2002 FG7, 2004 JN13, and Icarus were produced using light curve inversion techniques These are believed to be the first such models for these asteroids.

<div> Space operations from the dawn of the Space Age have resulted in a large, and growing, resident space object population. However, the availability of sensor resources is limited, which presents a challenge to Space Situational Awareness applications. When direct communication with an object is not possible, whether that is due to a lack of access for active satellites or due to the object being characterized as debris, the only independent information source for learning about the resident space object population comes from measurements. Optical measurements are often a cost-effective method for obtaining information about resident space objects.<br></div><div> This work uses observability analysis to investigate the relationship between desired resident space object characteristics and the information resulting from ground-based optical measurements. Observability is a concept developed in modern control theory for evaluating whether the information contained within measurements is sufficient to describe the dynamical progression of a system over time. In this work, observability is applied to Space Situational Awareness applications to determine what object characteristic information can be recovered from ground-based optical measurements and under which conditions these determinations are possible. In addition, the constraints and limitations of applying observability to Space Situational Awareness applications are assessed and quantified.<br></div>

Light curve inversion is a standard method to determine shapes, rotation periods and spin axis orientations of asteroids. This method can be extended to determine the size, albedo, thermal inertia and surface roughness parameters of an asteroid by including observations in thermal infrared. A solution of the Heat Conduction Equation (HCE) is necessary to model infrared flux from the asteroid. We analyse the accuracy requirements of the extended method for numerical solution of the HCE. We show that current implementation leads to errors in flux that are substantial. We recommend changes in the current implementation of the HCE solving approach to address the accuracy issues. We discuss uniqueness and stability of the solutions produced by the extended method as well as the accuracy of the determined parameters and their stability. Shapes of asteroids are produced and their physical attributes are determined based on light curve and infrared data.

<p dir="ltr">Tracking and characterizing the space debris population in Earth orbit is necessary to ensure that space can continue to be used safely. However, because space objects are affected by non-conservative forces like drag and solar radiation pressure, predicting the long-term evolution of their orbits is impossible without knowledge of their attitude profiles. Such knowledge may be unavailable for inactive satellites or objects of which the observer is not the owner or operator. In many cases, attitude cannot be measured directly because resolved images of space objects are unavailable due to the distance between the object and the observer, and the effects of atmospheric seeing. However, the total brightness of objects can still be measured. A set of brightness measurements over time is referred to as a "light curve.'' An object's observed brightness is influenced by its attitude and other factors such as its orbit, shape, and reflective properties. If some of these other factors are known, attitude information may be extracted from a light curve. Existing methods of solving this attitude inversion problem either require a good initial guess for an object's rotational states or do not provide a full state estimate. The work in this thesis avoids both problems and provides a full state estimate without requiring an initial state guess.</p><p><br></p><p dir="ltr">The attitude estimation process assumes that the observation geometry and the observed object's shape, reflection properties, and inertia tensor are known. In this thesis, an initial method of searching for attitudes that could correspond to each measurement using the viewing sphere is described. These possible attitudes or "pseudo-measurements'' are then used to initialize a probability hypothesis density filter that is theoretically capable of representing the multi-modal nature of the attitude estimate using a Gaussian mixture model. However, the probability hypothesis density filter is found to often diverge from the truth because it is necessary to merge and prune components of the Gaussian mixture model to avoid computational intractability. In its place, a particle swarm optimizer method for performing an attitude inversion has been developed. This method uses analytic attitude solutions to quickly propagate a large number of attitude time histories simultaneously. The particle swarm optimizer method is validated using simulated light curves for several objects. A preliminary attempt is made to estimate the attitude of an object using real light curve measurements.</p>