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4 Conclusion

Solar diameter measurements performed at Calern Observatory astrolabe during two solar cycles (22 years) shows variations. These variations leaded to many studies and one cause often advanced is the Earth atmosphere. It is then in order to quantify how the atmospheric turbulence effects contribute to the error in the solar diameter estimations that the present work was developed. It is based around a numerical simulation of the measurements at the solar astrolabe in various observation conditions. The first step was to simulate images of the Sun as those observed at the solar astrolabe through the Earth atmosphere. A synthetic image of the Sun was then needed. It was built using a model of the limb darkening function. A fractal model was after used to generate wavefronts randomly perturbed by the atmospheric turbulence and therefore optical responses of the whole system atmosphere and instrument. They were generated for various observation conditions and used to obtain the solar images. The second step was to simulate the astrolabe experiment and to define the needed parameters for the diameter measurements. The observed trajectories of both direct and reflected images are then built for various observation conditions. These are defined by the Fried's parameter, the spatial coherence outer scale of wavefronts and the ratio of the exposure time to the atmospheric characteristic time. The intersection point of the trajectories corresponding to the Sun transit time by the small circle, was then determined linked to the observation conditions. The study of the error due to atmospheric turbulence effects was developed around the transit time behavior with the observation conditions. Results show a decrease of the error with good seeing conditions whatever the used exposure times. The precision is however better in case of short exposure times than for long ones. A growth of the error is observed with the values of spatial coherence outer scale. It is significant only for small values of the outer scale and limited after by the error induced by the seeing. The error behavior is more critical with the exposure time relatively to the turbulence characteristic time. The error increases rapidly with the time ratio in order to reach a limit value. Thus, to have at least the same accuracy on the diameter measurement in poor seeing conditions that what we have with good seeing but using long exposure frames, this parameter needs to be less than a factor 5. This ratio seems then to be fundamental for the precision of the measurements with the solar astrolabe. To improve measurement diameter accuracy with the solar astrolabe, knowledge of time turbulence properties is suitable to adjust experimental parameters.

Acknowledgements

This work has been performed with support of the Observatoire d'Alger (C.R.A.A.G) and the French Foreign affair Ministry in the framework of scientific cooperation between France and Algeria (contract 96 MDU 357).


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