Control of the inter-satellite distances within a cluster of colocated satellites located in the same GEO window is examined with regards to the close approaches between pairs of satellites. Firstly, the orbital evolution and station keeping control of a single GEO satellite is examined and a new IBM PC based software program capable of performing both these functions autonomously from initial values of the orbital position and date is detailed and validated. Cluster design ideas are then examined in detail and the propagation software is used to generate data for a cluster of four satellites. Two test cases are examined to quantify the frequency of close approaches between individual satellite pairs, each test case using a different orbital element separation strategy but the same station keeping control scheme. The results of the study are then compared with previous research and discussions are presented on the advantages of each method. Finally, a cluster geometry correction manoeuvre, based on Hill's equations of relative motion, is presented which requires only those thrusters used by typical station keeping. This manoeuvre is integrated into the computer software and the two test cases noted previously are again propagated and the close approach results analysed to demonstrate the reduction in the number of close approaches below 5 km.

Thesis submitted in fulfilment of the requirements for the degree Master of Technology: ELECTRICAL ENGINEERING in the Faculty of Engineering at the Cape Peninsula University of Technology 2014 / The thesis reports on the evaluation and comparison of various signal processing algorithms for estimating the direction of arrival (DOA) of a high frequency (HF) beacon signal from a CubeSat in Low Earth Orbit (LEO). The DOA of the HF beacon signal is expressed in terms of the two angles, azimuth ( α ) and elevation ( ). The azimuth and elevation angles of the received HF signal are calculated from the phase differences between signals observed at three elements of an L-shaped crossed-loop antenna array. The algorithms which were evaluated are the Zero Crossing (ZC), Cross Correlation (CC), Fast Fourier Transform (FFT) and Cross Power Spectral Density (CPSD) algorithms. A theoretical analysis was done to demonstrate that the phase differences at the radio frequency (RF) of the beacon are propagated to the baseband signals. The algorithms were thus tested using simulated baseband signals as would be derived from the RF signals intercepted by the three elements of an L-shaped crossed-loop antenna array. Gaussian noise with a given signal-to-noise ratio (SNR) was added to the simulated baseband signals. The algorithms were implemented in MATLAB. The criteria for the selection of the best algorithm were accuracy and speed. The standard deviation (SD) of the azimuth and elevation errors was used to measure the performance accuracy of each algorithm, while the computational time for a given number of samples and runs was used to express the speed of each algorithm. First the ZC, CC, FFT and CPSD algorithms were evaluated for various SNR values, and compared with respect to SD of the azimuth and elevation errors. The analysis of the simulations demonstrate that the FFT and CPSD algorithms outperform the ZC and CC algorithms by estimating the DOA with a small SD of errors even at the low SNR of 0 dB, where the noise amplitude is the same as the signal amplitude. The ZC algorithm estimates the DOA with a large SD of error at low SNR due to multiple ZC points occurring during the same cycle. The ZC algorithm breaks down when the SNR decreases below 35 dB. The accuracy of the ZC algorithm depends on the method by which the ZC points are detected. The CC algorithm breaks down when the SNR decreases below 10 dB. The CPSD and FFT algorithms break down when the SNR decreases below – 20 dB. However, at a high SNR of 40 dB and above, all the algorithms estimate the DOA with a SD of error smaller than 1˚ for the azimuth and elevation. Next, the ZC, CC, FFT and CPSD algorithms were compared with respect to computation time. The FFT was found to be the fastest algorithm. Although the CPSD and the FFT algorithms reach the same accuracy in the estimation of the DOA, the FFT was selected as the optimum algorithm due to its better computation time. Recommendations are made regarding the implementation of the proposed algorithms for real signals from the HF direction finding (DF) array. At the time of submission of this thesis, such signals were not yet available.

Using the Mars Atmosphere and Volatile Evolution Neutral Gas and Ion Mass Spectrometer data, we investigate the possible impact of crustal magnetic fields on the thermal structure of the Martian upper atmosphere. Our analysis reveals a clear enhancement in temperature over regions with strong crustal magnetic fields during two deep dip campaigns covering the periods of April 17-22 and September 2-8, both in 2015. Several controlling factors, such as solar EUV irradiance, relative atomic O abundance, and non-migrating tides, do not help to explain the observed temperature enhancement, and a magnetically driven scenario is favored. We evaluate the roles of several heating mechanisms that are likely modulated by the presence of crustal magnetic fields, including Joule heating, ion chemical heating, as well as electron impact heating via either precipitating solar wind electrons or locally produced photoelectrons. The respective heating rates of these mechanisms are substantially lower than the solar EUV heating rate, implying that none of them is able to interpret the observations.

A novel strategy for automatic satellite constellation design with satellite diversity is proposed. The automatic satellite constellation design means some parameters of satellite constellation design can be determined simultaneously. The total number of satellites, the altitude of satellite, the angle between planes, the angle shift between satellites and the inclination angle are considered for automatic satellite constellation design. Satellite constellation design is modelled using a multiobjective genetic algorithm. This method is applied to LEO, MEO and hybrid constellations. The advantage of this algorithm is automatic satellite constellation design whilst achieving dual satellite diversity statistics. Furthermore a new strategy of dynamic channel allocation is proposed using a genetic algorithm for use in MSS networks. The main idea behind this algorithm is to use minimum cost as a metric to provide optimum channel solutions for specified interference constraints. The frequency reuse condition for all spotbeams is investigated as a function of time. The update interval time and the sampling time are introduced in order to track time valiant coefficients and constraints of the algorithm. The method is demonstrated for S-UMTS based on a MEO satellite constellation. Using this algorithm, it is shown that the proposed model outperforms conventional DCA schemes in terms of capacity of the system and Quality of Service (QoS).We show in the thesis that the genetic algorithm is a robust method for calculation of dynamic variations in satellite constellation design and provides resource allocation improvements over DCA in MSS system networks.

This thesis describes the definition, implementation, and in-orbit testing of an autonomous navigation unit based upon a GPS receiver for use on board a small satellite in low Earth orbit. It explains the motivation for the use of GPS to provide this function, and describes the practical application and integration of this technology into an existing microsatellite system. Until now, the technology for any satellite to track itself has not existed. Space agencies spend significant funds supporting a network of tracking stations around the world for orbit determination. With the recent realisation of the Global Positioning System and the availability of inexpensive receiver hardware, it has become a practical proposition to include a GPS receiver within the demanding constraints of a small satellite. A GPS receiver on-board a satellite can eliminate the necessity for ground-based tracking by providing an autonomous orbit determination capability. During the course of these studies, the requirements and constraints of a small satellite were identified by the author and matched with the capabilities of a GPS receiver. A GPS Navigation Unit was defined to provide autonomous services available oil demand for the satellite platform and payloads; position and velocity; time synchronisation; orbital elements; payload triggering and GPS data logging (for experimental and research purposes). The GPS Navigation Unit includes a processing facility capable of command and initialisation of the GPS receiver, and data processing to give orbit determination capability. When used on a microsatellite, the additional constraints of low power consumption necessitate the intermittent operation of the GPS receiver. To test the concept of the GPS Navigation Unit, a commercial Trimble TANS II GPS receiver system that had been modified for orbital velocities was integrated into the PoSAT-1 microsatellite which was launched into low Earth orbit in September 1993. A method for orbit determination was developed for use with the output from the GPS receiver, and the GPS Navigation Unit was implemented in software according to the constraints of the PoSAT-1 mission. The significant results from these studies include: The first use of a GPS receiver on a microsatellite, PoSAT-1. The implementation, test and validation of a GPS Navigation Unit in low Earth orbit. The first satellite mission to demonstrate the capability for autonomous orbit determination through the GPS Navigation Unit. The definition of the general-purpose interfaces between a small satellite and a satellite- borne GPS Navigation Unit.

No description available.

A computer-controlled tracking system has been designed and constructed for the two metre antenna of the 22 GHz radio telescope at Rhodes University. The control system has been tested and its step response has been analysed with a view to response time optimization. Computer programs for tracking the sun and the moon have been written. Initial results of tracking the sun have revealed linearity and temperature stability problems. These problems have been investigated and suggestions have been made as to how they might be removed

The influence of inertia, eccentricity and atmospheric forces on the attitude dynamics of gravity oriented, non-spinning, axi-symmetric satellites, executing general librational motion is investigated using analytical, numerical and analog techniques. The problem is studied in the increasing order of complexity. For the case of a circular orbit, the autonomous, conservative system represented by constant Hamiltonian yields zero-velocity curves and motion envelopes which identify regions of instability from conditional and guaranteed stable motion. The non-linear, coupled equations of motion are solved using approximate analytical techniques: Butenin’s variation of parameter method and invariant integral approach. A comparison with the numerical response, establishes their suitability in studies involving motion in the small. The invariant integral method maintains reasonable accuracy even for larger, predominantly planar, disturbances. However, for a general motion in the large, the analytical solutions provide only qualitative information and one is forced to resort to numerical, analogic or hybrid procedures. The analysis suggests strong dependence of system response on the in-plane disturbances and satellite inertia. The librational and orbital frequencies are of the same order of magnitude. It also shows that the stable solution, when represented in a three dimensional phase space may lead to 'regular', 'ergodic' or 'island' type regions. The limiting integral manifolds, given here for a few representative values of Hamiltonian, provide all possible combinations of initial conditions, which a satellite can withstand without tumbling. The results, for a range of satellite inertia, are condensed in the form of design plots, indicating allowable disturbances for stable motion. In general, the slender satellites exhibit better stability characteristics. The presence of aerodynamic torque destroys the symmetry properties of the integral manifolds. The stability of the equilibrium configuration, which now deviates from the local vertical, is established through Routh's as well as Liapunov's criteria. As the system is still autonomous and conservative, the Hamiltonian remains constant leading to the bounds of libration. Numerical analysis of the system response indicates increased sensitivity to planar disturbances. The distortion and contraction of the regular, ergodic and island type stability regions show the adverse effects of aerodynamic torque. The design plots suggest that the shorter satellites, normally not preferred from gravity-gradient considerations, could exhibit better stability characteristics in the presence of large aerodynamic torque. An alternate, economical approach to the dynamical analysis of the satellites is attempted using an analog computer. A comparison with the digital data establishes the suitability of the method for design purposes and real time simulation. As the regular surface represents the only usable stability region from design considerations, a detailed study to establish the bound between regular and ergodic type stability was undertaken. The periodic solutions, obtained numerically using variable secant iteration show their spinal character with the body of stability region built around them. Of particular significance is the fundamental periodic solution (two planar oscillations in one out-of- plane cycle) associated with the regular region, suitable for practical operation of a satellite. The remaining periodic solutions represent degeneration of the island-like areas surrounding the mainland. The results lead to a set of fundamental periodic solutions over a wide range of system parameters. Floquet's variational analysis is used to establish the critical disturbance [formula omitted], beyond which no stable motion can be expected. The periodic solutions together with the regular stability region are presented here as functions of Hamiltonian, satellite inertia and aerodynamic torque. The case study of GEOS-A satellite is also included. In elliptic orbit, the Butenin's analysis of coupled forced systems is found to give an approximate solution of good accuracy. However for this non-autonomous situation, where Hamiltonian is no longer a constant of the motion, the concept of integral manifold breaks down. Fortunately, the design plots can still be generated by direct utilization of the response characteristics. In general the stability region diminishes with increasing eccentricity and disappears completely for e > 0.35. The presence of atmosphere adds to the complex behaviour of this non-autonomous system, where even the equilibrium configuration now becomes periodic in character. The stability regions are further reduced with instabilities normally initiating in the planar degree of freedom. Finally, a possibility of using the atmospheric forces in attitude control is explored. The use of a set of horizontal flaps in conjunction with a semi-passive, velocity-sensitive controller appears to be promising. With a suitable choice of system parameters even a large disturbance can be damped in approximately two orbits. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The influence of the major environmental forces on the attitude response of gravity gradient satellites is investigated using analytical and numerical techniques. The study establishes not only the effect of these forces on system performance but also their relative importance. The problem is investigated in the order of increasing difficulty which corresponds to a systematic reduction in altitude. In general, the non-linear, non-autonomous nature of the system renders the determination of a closed form solution virtually impossible. Hence, numerical techniques are employed, in conjunction with invariant surfaces or integral manifolds, to analyse the system. For a given set of parameters, the largest such surface defines the bound of stable motion; on the other hand, the smallest surface that can be found (i.e., a line or set of lines) represents the dominant periodic solution with which these manifolds are associated. The analysis establishes the importance of periodic solutions as they provide the 'frame' about which stability charts are built. Furthermore, a variational stability analysis of these solutions, using Floquet theory, accurately determines the termination of the spikes and establishes the critical eccentricity for stable motion. Phase I investigates the attitude dynamics of satellites at high altitudes where gravity gradient and direct solar radiation constitute the predominant torques. The approximate closed form solution, obtained using the WKBJ and Harmonic Balance methods, was found to predict the librational response of a satellite with considerable accuracy. As the satellites requiring station keeping permit only small amplitude motion, the analytical results are of sufficient accuracy to be useful during preliminary design stages. The response and stability bounds of the system, obtained numerically, are shown through the use of 'system plots' and 'stability charts'. The results indicate a considerable effect due to solar radiation on the attitude dynamics of a satellite. The use of solar radiation in controlling the satellite attitude is explored. The optimized results show this system to be quite effective, being capable of providing a pointing accuracy of 0-5° depending on orbit eccentricity. The extension of the analysis to the intermediate altitude ranges, where direct earth radiation, its albedo and shadow become significant, is undertaken in phase II. A comprehensive investigation was made possible by the determination of closed form expressions for earth radiation forces. This was accomplished through the concept of cutting plane distance ratios. The analysis shows only local variations due to earth radiations without substantially affecting the maximum librational amplitude or mainland stability area. Hence, for all practical purposes, direct earth radiation, its albedo and shadow can be neglected in such studies. Phase III investigates the dynamics of close earth satellites in the presence of aerodynamic and radiation forces, thus covering the remaining altitude range. The results show that a precise dynamic analysis requires the consideration of both aerodynamic and direct solar radiation forces. The investigation helps in establishing an altitude range in which a pure gravity gradient analysis is likely to be most applicable. The application of this analysis to the representative gravity gradient satellite, GEOS-A, over the entire altitude range, exemplifies the findings of the parametric study. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The dynamics of slowly spinning axisymmetric satellites under the influence of gravity gradient torque is investigated using analytical and numerical techniques. Particular emphasis is on motion near the equilibrium position in which the spin axis is normal to the orbital plane. The problem is studied in increasing orders of difficulty. Phase I deals with the response and stability of a simplified model free to librate in roll while the more general problem is treated in Phase II. Phase I serves as a proving ground for techniques to be used in subsequent analysis. A closed form solution is obtained in terms of elliptic functions for the autonomous case. In general, for non-circular orbits, motion in the large is studied using the concept of the invariant solution surface. These surfaces, obtained numerically, reveal the nature of motion in the large in terms of the dominant periodic solutions and allow one to determine the limits of oscillatory motion in terms of the state parameters. Floquet theory is employed in conjunction with numerical solutions of the linearized equations of motion to study stability in the small. This technique is extended to assess the variational stability of the dominant periodic motions in the large. Phase II investigates a more general model with three degrees of freedom in attitude motion. The presence of an ignorable coordinate gives a fourth order, non-autonomous system for an elliptic trajectory. Motion in the small is studied extensively, again using Floquet theory, and stability charts suitable for design purposes are presented. The invariant surface concept is successfully extended to the study of the autonomous case in the large. Methods are developed for determining the maximum response to a given disturbance resulting in a set of charts which are useful in assessing the effects of non-linearities and the validity of the analysis in the small. Procedures are explained for determining periodic solutions of the problem, as well as their stability, for arbitrary eccentricity. The analysis suggests the possibility of attitude instability during spin-up operations. It is shown that stable motion can be established by providing either a positive or negative spin to the satellite with the former preferrable. Given sufficient spin any configuration, even those with an adverse gravity gradient effect, can be stabilized. Eccentricity affects the attitude motion of a satellite adversely as regions of unstable motion increase in size and number with it. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate