An annular eclipse on film

Adapted from IOAA 2008 (Bandung), theory problem S11. We have restated it in our own words and kept the original data. The official solution takes the diameters of the Sun and the Moon as 1 392 000 km and 3476 km, which we state. The solution was last checked on 23 October 2026.

A photograph of the annular eclipse of 22 August 1998, seen from Dumai in Indonesia, was taken on 35 mm film through a telescope of aperture 10 cm and focal ratio 15. On the film the Sun's disc is 13.817 mm across and the Moon's is 13.235 mm. Taking the diameters of the Sun and the Moon as 1 392 000 km and 3476 km, find the distances of the Sun and the Moon from the observer, and the percentage of the Sun's disc covered by the Moon at mid-eclipse.

AnswerThe Sun was $1.511\times {10}^8$ km away and the Moon about 394 000 km away, and the Moon covered 91.75% of the Sun's disc.