As the ship leaves Earth further and further in its wake, Amy wonders whether this was the right decision: she is a mother. She wonders how many once-in-a-lifetime moments she'll miss. She wonders (half-laughingly) whether her husband can handle it by himself. She can't stop thinking about a small, broken music box that her child absolutely adores. This box plays Frere Jacques in a round. Eventually, the humming and noise of the ship work itself into the music as well.
The Frere Jacques comes from an actual broken music box that I have had for as long as I can remember. Getting it to play even roughly in time was a nightmare.