Computer analysis of the lineaments of Nepal

Various information has been obtained by computer analysis of the lineaments of Nepal. The data were carefully studied and correlated to establish the relationships of lineaments with geological units, structure, mineralization, etc. The lineament map of Nepal was prepared during 1977–1978; the lineament data were digitized in 1982—using a Hewlett Packard system 45 desktop computer—separated by area (east, central and west Nepal) and also according to geological units. By trial and error and using all variables, the different preferred orientation classes were identified for east, central and west Nepal. Lineaments were grouped according to length into less than 10 km, 10–20 km, 20–30 km and more than 30 km, for the entire country and also for major geological units, i.e., Siwalik (sub-Himalaya), Lesser Himalaya (midlands) and Higher Himalaya. Various rose diagrams and histograms showing frequency and lengths of lineaments were plotted for the different geological units and the different sectors. Lineaments associated with granites of major subdivisions were plotted separately and analysed.     

A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite’s location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth’s oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM_atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM_atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM_atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the “truth”, the relative error in PPM_atm is ?0.79% while the SECM 11.07%. The influence of the PPM_atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM_atm can reduce the radial orbit error RMS by 5.6?cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction.     

Fast solar radiation pressure modelling with ray tracing and multiple reflections

Physics based SRP (Solar Radiation Pressure) models using ray tracing methods are powerful tools when modelling the forces on complex real world space vehicles. Currently high resolution (1?mm) ray tracing with secondary intersections is done on high performance computers at UCL (University College London). This study introduces the BVH (Bounding Volume Hierarchy) into the ray tracing approach for physics based SRP modelling and makes it possible to run high resolution analysis on personal computers. The ray tracer is both general and efficient enough to cope with the complex shape of satellites and multiple reflections (three or more, with no upper limit). In this study, the traditional ray tracing technique is introduced in the first place and then the BVH is integrated into the ray tracing. Four aspects of the ray tracer were tested for investigating the performance including runtime, accuracy, the effects of multiple reflections and the effects of pixel array resolution.Test results in runtime on GPS IIR and Galileo IOV (In Orbit Validation) satellites show that the BVH can make the force model computation 30–50 times faster. The ray tracer has an absolute accuracy of several nanonewtons by comparing the test results for spheres and planes with the analytical computations. The multiple reflection effects are investigated both in the intersection number and acceleration on GPS IIR, Galileo IOV and Sentinel-1 spacecraft. Considering the number of intersections, the 3rd reflection can capture $99.12\%\text{,}99.14\%$, and $91.34\%$ of the total reflections for GPS IIR, Galileo IOV satellite bus and the Sentinel-1 spacecraft respectively. In terms of the multiple reflection effects on the acceleration, the secondary reflection effect for Galileo IOV satellite and Sentinel-1 can reach 0.2?$\text{nm}/{\text{s}}^2$ and 0.4?$\text{nm}/{\text{s}}^2$ respectively. The error percentage in the accelerations magnitude results show that the 3rd reflection should be considered in order to make it less than $0.035\%$. The pixel array resolution tests show that the dimensions of the components have to be considered when choosing the spacing of the pixel in order not to miss some components of the satellite in ray tracing. This paper presents the first systematic and quantitative study of the secondary and higher order intersection effects. It shows conclusively the effect is non-negligible for certain classes of misson.