The central question which will be addressed in this paper is: can we know the true geometry of space? My answer will be in the negative, but not first without heavy qualification. The thesis concerns the notion of truth in mathematical science, i.e. physical science for which mathematics (particularly geometry) is integral, and will ask whether we can know with certainty, or via some empirical test, which geometry is an accurate description of the actual universe. It will be a fairly historical approach, but hopefully not entirely so. We will begin with a 17th century debate on the nature of space between Newton and Leibniz and how Kant proposed to resolve the debate, and then move on to the views of the late 19th century mathematician Poincaré, but we will end with Einstein's Theory of Relativity - a theory which uses a very different geometry to which most of us are perhaps accustomed. In general, the goal will be to better understand the nature of geometry and its role in scientific theory; specifically, however, it will be an attempt to answer, in the negative, the central question before us. / Graduate

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Prior to their retrieval from low Earth orbit (LEO), the individual solar cells that make up the 'V2' solar array panel from the Huhble Space Telescope (HST) were prone to hypervelocity (>5 km/s ) impact damage from micrometeoroids and space debris. The analysis of such passive collector surfaces allows sampling of micrometeoroids that have not undergone any terrestrial atmospheric alteration and better defines the population of space debris particles below the lmm size range. Herein a new approach has been taken to try and identify the nature atid origin of impact derived residues generated in the individual solar cells from the HST. A total of 25 solar cells were selected on the basis that they contained impact craters (100-1000?n diameter) rather than larger impact holes (1-3mm diameter), as preliminary studies indicated that they were more likely to retain impact residues. These were subsequently analysed using digitised hack-scattered electron imaging, coupled with digitised x-ray elemental mapping and micro-spot analysis to locate, identify and classify the residues. 29 impact craters were located on solar cells. In the analysis of the residues; 3 were identified residues as space debris in origin, 6 unclassified and 20 as micrometeoroid. The space debris derived residues were identified as remnants of a paint fragment, a stainless steel particle and a fragment of a printed circuit board. The micrometeoroid derived residues were sub-classified in terms of mineral chemistry, with apparent mafic- and phyllo- silicates being the dominant components, with minor iron-nickel metal and iron sulfides, suggesting a broadly chondritic origin. Fe-Ni rich residue was also identified that would appear to belong to a group of non-chondritic particles previously unrecognised. Possible refractory or Ca/Al rich inclusions from a primitive micrometeoroid were also observed as near intact Ca-rich fragments, the textures of the individual grains suggested that they were not merely terrestrial contamination. Laboratory impact studies, using a light-gas-gun to accelerate small fragments (125- 250?m) of known meteorite mineralogies up to 5km/s, and then impact them into solar cells have generated a suite of residues that are analogues of those observed from LEO studies. The silicate minerals generated residues that were intimately associated with the host melt glass. Metallic sulfides and metals generated surface and sub-surface immiscible droplets. Several craters also contained near-intact fragments of minerals. Overall. despite the small sample set examined. the observed dominance of micrometeoroid to space debris residue chemistry (correlating to particle size range of 8-80 ?m) corresponds well to the accepted flux models.

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