Investigating the variation of the Sun\u2019s visual shape, atmospheric refraction and Einstein\u2019s special relativity considered

Abstract

By experimental measurements and theoretical analyses, this paper investigates the variation of the Sun’s visual shape and figures out the reasons for the variation of its shape. First, the method of image processing, the method of moments and the least-square method are combined to perform experimental measurements and calculations, and the features of the Sun’s visual shape are extracted from the photos of the Sun. Second, theoretical analyses are conducted based on atmospheric refraction and the Einstein’s special relativity theory. The relationship model is established between the zenith and azimuth angles of the Sun, the velocity of the Sun relative to the Earth, and the observation time and position; the refraction index of the atmosphere is expressed as a function of altitude and wavelength of light; an iterative algorithm is constructed to trace rays of light in the atmosphere; a set of formulas is derived to determine the contraction ratio and contraction direction of the Sun’s visual shape. Finally, the theoretical and experimental results are compared; their relative errors are less than 0.3%, which verifies the theoretical analyses. Both theoretically and experimentally, this research proves that the Sun’s visual shape is an ellipse; its shape variation mainly results from atmospheric refraction effects; and the length contraction effect of the Einstein’s special relativity also contributes a little, except at the time of sunrise and sunset.