The figure of the earth, determined from observations made by order of the French King, at the polar circle: by Messrs de Maupertuis, Camus, Clairaut, Le Monnier, members of the Royal Academy of Sciences, the abbé Outhier, correspondent of the Academy, and Mr. Celsius, professor of astronomy at Upsal : translated from the French of M. de Maupertuis.

Digital reproduction, The National Library of Finland, Centre for Preservation and Digitisation, Mikkeli

Multidata inverse problems and Bayesian solution methods in astronomy

Statistical analyses of measurements that can be described by statistical models are of essence in astronomy and in scientific inquiry in general. The sensitivity of such analyses, modelling approaches, and the consequent predictions, is sometimes highly dependent on the exact techniques applied, and improvements therein can result in significantly better understanding of the observed system of interest. Particularly, optimising the sensitivity of statistical techniques in detecting the faint signatures of low-mass planets orbiting the nearby stars is, together with improvements in instrumentation, essential in estimating the properties of the population of such planets, and in the race to detect Earth-analogs, i.e. planets that could support liquid water and, perhaps, life on their surfaces. We review the developments in Bayesian statistical techniques applicable to detections planets orbiting nearby stars and astronomical data analysis problems in general. We also discuss these techniques and demonstrate their usefulness by using various examples and detailed descriptions of the respective mathematics involved. We demonstrate the practical aspects of Bayesian statistical techniques by describing several algorithms and numerical techniques, as well as theoretical constructions, in the estimation of model parameters and in hypothesis testing. We also apply these algorithms to Doppler measurements of nearby stars to show how they can be used in practice to obtain as much information from the noisy data as possible. Bayesian statistical techniques are powerful tools in analysing and interpreting noisy data and should be preferred in practice whenever computational limitations are not too restrictive.

Dynamic Analysis Model of Spherical Roller Bearings with Defects

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant seeing increasing use, because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This doctoral dissertation introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to nonlinear Hertzian contact theory. The results reveal how some of the more important parameters; such as diametral clearance, the number of rollers, and osculation number; influence ultimate bearing performance. Distributed defects, such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. Simulation results were verified with results obtained by applying the formula for the spherical roller bearing radial deflection and the commercial bearing analysis software. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis. Accuracy of the model was verified by comparing measured to predicted behaviors for equivalent systems.