The smallest shift

Adapted from IOAA 2007 (Chiang Mai), theory problem 1.5. We have restated it in our own words and kept the original data, adding values for the parsec and the astronomical unit. The solution was last checked on 14 October 2026.

An observer manages to measure the change in the direction to a star 100 parsecs away that is caused by Earth's motion around the Sun. What is the smallest angle, in arcseconds, that the observer must be able to measure? Take 1 parsec to be $3.086\times {10}^{16}$ m and 1 au to be $1.496\times {10}^{11}$ m.

AnswerThe observer must be able to measure about 0.02″.