Spacecraft trajectory optimization is a near-infinite problem space with a wide variety of models and optimizers. As trajectory complexity increases, so too must the capabilities of modern optimizers. Common objective cost functions for these optimizers include the propellant utilized by the spacecraft and the time the spacecraft spends in flight. One effective method of minimizing these costs is the utilization of one or multiple gravity assists. Due to the phenomenon known as the Oberth effect, fuel burned at a high velocity results in a larger change in orbital energy than fuel burned at a low velocity. Since a spacecraft is flying fastest at the periapsis of its orbit, application of impulsive thrust at this closest approach is demonstrably capable of generating a greater change in orbital energy than at any other location in a trajectory. Harnessing this extra energy in order to lower relevant cost functions requires the modeling of these “powered flybys” or “powered gravity assists” (PGAs) within an interplanetary trajectory optimizer. This paper will discuss the use and modification of the Spacecraft Trajectory Optimization Suite, an optimizer built on evolutionary algorithms and the island model paradigm from the Parallel Global Multi-Objective Optimizer (PaGMO). This variant of STOpS enhances the STOpS library of tools with the capability of modeling and optimizing single and multiple powered gravity assist trajectories. Due to its functionality as a tool to optimize powered flybys, this variant of STOpS is named the Spacecraft Trajectory Optimization Suite - Flybys with Impulsive Thrust Engines (STOpS-FLITE). In three test scenarios, the PGA algorithm was able to converge to comparable or superior solutions to the unpowered gravity assist (uPGA) modeling used in previous STOpS versions, while providing extra options of trades between time of flight and propellant burned. Further, the PGA algorithm was able to find trajectories utilizing a PGA where uPGA trajectories were impossible due to limitations on time of flight and flyby altitude. Finally, STOpS-FLITE was able to converge to a uPGA trajectory when it was the most optimal solution, suggesting the algorithm does include and properly considers the uPGA case within its search space.

Once a satellite has completed its operational period, it must be removed responsibly in order to reduce the risk of impacting other missions. Geostationary Transfer Orbits (GTOs) offer unique challenges when considering disposal of spacecraft, as high eccentricity and orbital energy give rise to unique challenges for spacecraft designers. By leveraging small satellite research and integration techniques, a deployable drag sail module was analyzed that can shorten the expected orbit time of launch vehicle stages in GTO. A tool was developed to efficiently model spacecraft trajectories over long periods of time, which allowed for analysis of an object’s expected lifetime after its operational period had concluded. Material limitations on drag sail sizing and performance were also analyzed in order to conclude whether or not a system with the required orbital performance is feasible. It was determined that the sail materials and configuration is capable of surviving the expected GTO environment, and that a 49 m2 drag sail is capable of sufficiently shortening the amount of time that the space vehicles will remain in space.

There is an increased need for spacecraft to quickly and efficiently de-orbit themselves as the amount of debris in orbit around Earth grows. Defunct spacecraft pose a significant threat to the LEO environment due to their risk of fragmentation. If these spacecraft are de-orbited at the end of their useful life their risk to future spacecraft is greatly lessened. A proposed method of efficiently de-orbiting spacecraft is to use an inflatable thin-film envelope to increase the body's area to mass ratio and thusly shortening its orbital lifetime. The system and analysis presented in this project is sized for use on a CubeSat as they are an effective utility as a technology demonstration platform. Analysis has been performed to characterize the orbital dynamics of high area to mass ratio spacecraft as well as the leak rate of such an inflatable device in a vacuum environment. Results show that a 1U CubeSat can be de-orbited using a 1.7 meter diameter spherical device in just under one year while using 0.7 grams of inflating gas, this is compared to over 25 years without any method of post-mission disposal.

This thesis will present the effects of the orbital debris evolution in two key areas: the geosynchronous disposal orbit regime known as “graveyard” and the two geopotential wells found in 105◦ W and 75◦ E longitude bins. After developing a GEO specific orbit propagator for NASA Johnson Space Center’s Orbital Debris Of- fice, collisions were simulated throughout these regimes using a low velocity breakup model. This model considered the effects of perturbations particularly non-spherical Earth effects (specifically sectorial and zonal harmonics), lunar effects, third body effects and solar radiation pressure effects. The results show that CDPROP does well in simulating the presence of the Eastern and Western geopotential wells, as well as catching drifting GEO objects. It does not do as well in catching East-West trapped objects. Three collision test cases were then simulated in graveyard and the East and West geopotential wells.

A light curve is a plot of brightness versus time of an object. Light curves are dependent on orbit, attitude, surface area, size, and shape of the observed object. Using light curve data, several analysis methods have been developed to derive these parameters. These parameters can be used for tracking orbital debris, monitoring satellite health, and determining the mission of an unknown spacecraft. This paper discusses the development, verification, and utilization of a tool that simulates light curve data. This tool models ground-based observations, space-based observations, self-shadowing geometry, tumbling debris, and controlled spacecraft. The main output from the tool is the pass prediction plot and the light curve plot. The author intends to publish the tool and supporting documents for future researchers to utilize. This will save researchers time developing their own models and the tool can act as a baseline for comparisons between analysis methods. For clarity, this paper does not develop nor implement a light curve analysis method, but rather creates a tool to simulate light curve observations and data. Each section of the tool was verified independently to ensure that the simulated light curves were correct. The tool was verified with STK, matlab, and simulink. It predicts the start and end times of passes, eclipses, and ground-site night cycles within 1% of the total event duration, when compared to STK. The attitude propagator predicts the attitude of the target with offsets less than 0.06 degrees on average and a maximum offset less than 0.6 degrees when compared to provided attitude code.

The following thesis regards the use of small aperture telescopes for space domain awareness efforts. The rapidly populating space domain was motivation for the development of a new operation scheme to conduct space domain awareness feasibility studies using small telescopes. Two 14-inch Schmidt-Cassegrain Telescopes at the California Polytechnic State University and the Air Force Research Lab in Kirtland AFB, NM, in conjunction with a dedicated CCD camera and a commercial DSLR camera, were utilized to conduct optical observations on satellites in Earth orbit. Satellites were imaged during August 2019, and from January 2020 to March 2020, resulting in the collection of 77 valid images of 16 unique satellites. These images were used to obtain celestial spherical coordinates, which were used in Gauss and Double-R angles-only initial orbit determination methods. Initial orbit determination methods successfully produced valid results, reaffirming the feasibility of using small aperture telescopes for such methods. These orbit determinations were used to propagate orbit states forward in time to determine the feasibility of future imaging of the targets with the same apparatus. Propagation results demonstrated that initial orbit determinations rapidly decayed in accuracy over distant times and are most accurate for immediate satellite passes. In addition, an attempt to combine multiple initial orbit determinations using Lambert’s problem solutions was made. Combination of these multiple initial orbit determinations resulted in either no orbit state accuracy improvement compared to individual initial orbit determinations, or a decrease in accuracy compared to these methods. Ultimately, efforts demonstrated that small telescope usage is feasible for orbit determination operations, however there may be a need for hardware and operational revisions to improve the ability of the apparatus.

Attitude determination and estimation algorithms are developed and implemented in simulation for the Exocube satellite currently under development by PolySat at Cal Poly. A mission requirement of ±5˚ of attitude knowledge has been flowed down from the NASA Goddard developed payload, and this requirement is to be met with a basic sensor suite and the appropriate algorithms. The algorithms selected in this work are TRIAD and an Extended Kalman Filter, both of which are placed in a simulation structure along with models for orbit propagation, spacecraft kinematics and dynamics, and sensor and reference vector models. Errors inherent from sensors, orbit position knowledge, and reference vector generation are modeled as well. Simulations are then run for anticipated dynamic states of Exocube while varying parameters for the spacecraft, attitude algorithms, and level of error. The nominal case shows steady state convergence to within 1˚ of attitude knowledge, with sensor errors set to 3.5˚ and reference vector errors set to 2˚. The algorithms employed have their functionality confirmed with the use of STK, and the simulations have been structured to be used as tools to help evaluate attitude knowledge capabilities for the Exocube mission and future PolySat missions.

This graduate project compares legacy simplified general perturbation model (SGP4) code developed by NASA Johnson Space Center, Orbital Debris Program Office, to a recent public release of SGP4 code by David Vallado. The legacy code is a subroutine in a larger program named PREDICT, which is used to predict the location of orbital debris in GEO. Direct comparison of the codes showed that the new code yields better results for GEO objects, which are more accurate by orders of magnitude (error in meters rather than kilometers). The public release of SGP4 also provides effective results for LEO and MEO objects on a short time scale. The public release code was debugged and modified to provide instant functionality to the Orbital Debris Program Office. Code is provided in an appendix to this paper along with an accompanying CD. A User’s Guide is presented in Chapter 7.

<p dir="ltr">Characterizing unknown space objects is an important component of robust space situational awareness. Estimating the shape of an object allows analysts to perform more accurate orbit propagation, probability of collision, and inference analysis about the object’s origin. Due to the sheer distance from the camera combined with diffraction and atmospheric ef- fects, most resident space objects of interest are unresolved when observed from the ground with electro-optical sensors. State of the art techniques for object characterization often rely on light curves — the time history of the object’s observed brightness. The brightness of the object is a function of the object’s shape, material properties, attitude profile, as well as the observation geometry. The process of measuring real light curves is complex, involv- ing the physics of the object, the sensor, and the background environment. The process of recovering shape information from brightness measurements is known as the light curve shape inversion problem. This problem is ill-posed without further assumptions: modern direct shape inversion methods require that the attitude profile and material properties of the object is known, or at least can be hypothesized. This work describes improvements to light curve simulation that faithfully model the environmental and sensor effects present in true light curves, yielding synthetic measurements with more accurate noise characteris- tics. Having access to more accurate light curves is important for developing and validating light curve inversion methods. This work also presents new methods for direct shape inver- sion for convex and nonconvex objects with realistic measurement noise. In particular, this work finds that improvements to the convex shape inversion process produce more accurate, sparser geometry in less time. The proposed nonconvex shape inversion method is effective at resolving singular large concave feature.</p>

<p dir="ltr">This research considers orbit maintenance strategies for multi-body orbits in the context of the Earth-Moon Circular Restricted Three Body Problem (CR3BP). Dynamical requirements for successful long-term orbit maintenance strategies are highlighted.</p>