They dance to feed the engine, to be honest.
If the engine isn’t fed, then the ship will stop moving. And it’s a forty year mission – if the engine stops moving, the ship will stop, and if the ship stops they’ll be easy pickings or sitting ducks.
Captain Terpsichore raised his daughters to be bright, bold, brave – and not stupid. If he knew their dancing is powering the reactor core he’d pull them off the mission and cut their funding. Lianna will not allow that – so she encourages her sister to dance all night, rise late in the afternoon, and be the most competent team possible in the hours between.
So their feet blister and their smiles freeze. Their best dresses grow frayed and worn. They will be here until they make a breakthrough and make contact with alien life.
Until then they will be at the mercy of fate, their own rescue hanging suspended in the air, tantalizing them with the promise of release.