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The solar diameter derived from Tobias Mayer's observations 1756-1761

 

Axel D. Wittmann, Göttingen

 

Abstract

Tobias Mayer (1726-1762), one of the leading astronomers of the 18th century, was particularly famous for the precision of his positional observations. In 1751 Mayer became director of Göttingen University Observatory, where he worked until his untimely death in 1762. Mayer's observations were made with a 6-ft. mural quadrant (D=5.0 cm, f=1.86 m, 96 partes = 90o) manufactured by John Bird/London. This instrument is one of the most accurate mural quadrants ever made and is still preserved in our institute.

Among Mayer's observations is a series of meridian transit times of the Sun which were observed across a 5-wire fiducial grid in the focalplane of the telescope (at about 30-fold magnification) and were timed using a precision pendulum clock designed by Franz Kampe. Although these observations have been analyzed several times before (Mayer, 1762 [published 1767]; Wittmann, 1980; Toulmonde, 1995) they still merit revisiting with regard to possible long-term variations of the solar diameter. From a recent analysis, using improved reduction techniques and as many as possible of Mayer's observations, the author has obtained the following results (where R is the angular solar semidiameter at 1 au):

1. The absolute time of meridian passage (transit of disk centre) was measured with an accuracy of typically ± 0.7 or 11" (note that in case of the Sun this must be inferred from the transit time of opposite limbs and that this also depends on the absolute accuracy of the clock).

2. The observations split into two distinctly different groups (with a gap in between). The first group (N=120, 1756-1758) is much more homogeneous and considerably more accurate than the second group (N=13, 1760-1761), and it may, therefore, be justified to completely disregard the second group:

1st group: R = (960.46 ± 0.11)" [N=120] 2nd group: R = (959.85 ± 0.72)" [N=13]

Both: R = (960.40 ± 0.12)" [N=133]

3. If, with due allowance for the accuracies involved, this is compared to recent drift timing results obtained during a joint project by A.D. Wittmann at Tenerife in 1981/1990-1997 (1st group) and by M. Bianda at Locarno in 1990-1997 (2nd group), viz.

1st group: R = (960.59 ± 0.03)" [N=7627] 2nd group: R = (960.59 ± 0.05)" [N=2244]

Both: R = (960.59 ± 0.02)" [N=9871]

we can conclude that there has been no significant secular change in the size of the Sun during the last 250 years, or that such a trend, if it exists, would not have exceeded +0.00086 "/yr.


Bibliographical details:

Axel D. Wittmann: The solar diameter derived from Tobias Mayer's observations 1756-1761. In: Peter Brosche, Wolfgang R. Dick, Oliver Schwarz, Roland Wielen (Eds.): The Message of the Angles - Astrometry from 1798 to 1998. Proceedings of the International Spring Meeting of the Astronomische Gesellschaft, Gotha, May 11-15, 1998. (Acta Historica Astronomiae ; 3). Thun ; Frankfurt am Main : Deutsch, 1998, p. 49-51.