The purpose of the spacecraft known as Rosetta is to study a comet and track its changes. This option is the correct answer.

Option 1, to detect any asteroid fast approaching Earth, is not the correct answer. While it is important to detect and track asteroids that may pose a threat to Earth, Rosetta is specifically designed to study comets, not asteroids.

Option 3, to identify any traces of water on the moon, is also not the correct answer. Rosetta is not designed to study the moon or identify traces of water on it. Its main objective is to study comets and their composition, not the moon or its resources.

Option 4, to probe the space outside the solar system, is not the correct answer. Rosetta is not designed to go beyond the solar system. Its mission is focused on studying comets within our own solar system, particularly the comet 67P/Churyumov–Gerasimenko.

In summary, Rosetta is specifically designed to study a comet and track its changes, making option 2 the correct answer.