The ship was propelled by a device called a quantum rod, which tunneled through spacetime by attracting together related matter which emerged from the Big Bang. The derelict is also the likely origin of Pree, the predictive computer that Kryten and Rimmer attempt to install as the new main computer on Red Dwarf, with disastrous consequences.
The Trojan was left derelict in space and was eventually discovered by the crew of Red Dwarf. Rimmer's brothers had all served on similar ships and he was very glad to have a similar vessel, despite the fact that it could not move under its own power.
When they made contact with Howard Rimmer aboard the Columbus 3, Rimmer convinced his friends to pretend to be the crew of the Trojan. He dressed himself in the captain's uniform and the rest of the Dwarfers as officers to convince his brother that he was a successful space adventurer. In fact, the ship was being towed by Red Dwarf and the crew had to pretend to work her controls, even leaning to mimic a change of course.