In 1801, the year of the discovery of Ceres, Johann Georg von Soldner calculated with classical means the gravitational deflection of a lightray grazing the surface of the Sun as 0.84”. According to General Relativity (GR) and using present-day data the deflection amounts to 1.75”. The formula for the deflection is derived with a classical method, with GR and as done by Soldner. The GR formula gives twice as large a deflection as the classical formula. It is shown that the formula of Soldner is equivalent to the classical one. Soldner’s numerical calculation of the classical deflection by the Earth comes out a factor 6.9 larger than using present-day data. This discrepancy is for a factor 6.25 due to a mistaken value for the velocity of the grazing lightray. This factor 6.25 can numerically be accounted for by assuming Soldner made a conceptual mistake related to the Axial Tilt of the Earth. The remaining discrepancy is due to the use of data less accurate than the present-day data. Soldner’s numerical calculation of the deflection by the Sun comes out correctly to the data of those days. In case of the Sun he did not give any further information regarding the data he used. A reconstruction reveals that for the surface gravity of the Sun he used a value close to the present-day value.
References
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