IAO 2008, Практически тур, Група α — Задача 7. The Roemer’s experiment.

Practical round. Problems to solve · 13 октомври 2008 г.

Source availability

The original archive contains answer sheet2, reproduced in full. Separate answer sheets1 and3 were not found in the full16-file year inventory; the lightcurve and eclipse table printed on the question sheet are retained. No official practical solution or rubric was found. Unsigned handwritten annotations on the Bulgarian versions of these same questions are preserved as incomplete archive answers; they are not an official key. The transit annotations reach the photographed bottom edge and are partially cut off.

Условие

The first historical attempt to derive the speed of light from astronomical observations was performed by the Danish astronomer Ole Roemer in 1675. He observed many eclipses of the jovian moon Io by the Jupiter’s shadow, and noted that they did not occur at regular times. This phenomenon was interpreted as a consequence of the finite speed of light, which takes therefore different times to reach the Earth placed at different positions along its orbit during the year. The speed of light was also estimated by Roemer based on the deviation of the measured eclipse times from the expected ones.

Io’s observations can be performed at any time. The table reports some measured start times $T_m$ of Io’s eclipses in 2004, with the corresponding number of orbits elapsed since the first measurement. Since Io completes a revolution around Jupiter every 1.76979 days, complete the table (on answer sheet 3) with the expected start times $T_e$ and the resulting deviation from the measured ones, $\Delta T=T_m-T_e$. Report on a diagram these deviations as a function of the measured times and mark on the graph the points where Jupiter is at opposition with the letter O, at conjunction with C and at quadrature with Q. Finally, give an estimate of the light speed based on these data, as made by Roemer.

Io Eclipses start times

Date	$T_m$	$T_e$	Rev. Nr.	$\Delta T$ (min)
30/01/2004	00:55	00:55	0
14/02/2004	23:10		9
29/02/2004	02:57		17
17/03/2004	19:42		27
30/03/2004	05:03		34
16/04/2004	21:49		44
16/05/2004	23:56		61
17/06/2004	20:33		79
16/07/2004	04:12		95
17/08/2004	00:48		113
16/09/2004	02:55		130
30/09/2004	06:44		138
16/10/2004	05:00		147
30/10/2004	08:48		155
17/11/2004	01:32		165

Решение

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Оригинал в Архива: alphapract.png · допълнителни данни: practdata.png · допълнителни данни: bgbetapract1.pdf · допълнителни данни: bgbetapract2.pdf