In 2020, the Mars I spacecraft, en route to planet Mars, is commanded by Luke Graham (Don Cheadle) with fellow astronauts Nicholas Willis (Kavan Smith), Sergei Kirov (Peter Outerbridge), and RenĂŠe CotĂŠ (Jill Teed). Upon arrival, the team discovers a crystalline formation in the Cydonia region, which they suspect is an extrusion from a subsurface geothermal column of water, useful to future human colonization. After reporting this to the World Space Station, they hear a strange sound on their communications system, which they assume to be interference from their planetary rover. While they scan the formation with radar, a large vortex kills them.
After the vortex subsides, a large humanoid face is exposed in the adjacent mountain. ISS having received Luke's message, a second ship is readied for a rescue mission - the Mars II containing Commander Woody Blake (Tim Robbins), Co-Commander Jim McConnell (Gary Sinise), and mission specialists Terri Fisher (Connie Nielsen) and Phil Ohlmyer (Jerry O'Connell). As the ship enters Mars orbit, micrometeoroids breach the hull. During repair, the external fuel tanks are overlooked, causing a leak and later explosion. The crew then board the REMO ("Resupply Module") orbiting Mars. Tethered to the others, Woody launches himself at the module, but he is unable to properly land on it. Terri tries to rescue Woody, who is her husband; but, knowing she would run out of fuel before reaching him, Woody removes his helmet, killing himself to save her. When the survivors arrive on the surface of Mars, they find Luke living on the produce of a greenhouse, whereupon he reveals that the crystalline structure looks humanoid and that the noise represents a map of human DNA in XYZ coordinates, but missing a pair of chromosomes. To complete the sequence, the crew dispatches a robotic rover to reproduce the completed signal. Following the transmission, an opening appears in the side of the mountain, which Jim, Terri, and Luke enter, while Phil remains at the repaired emergency return vehicle with orders to launch, with or without them, at the agreed time.
The opening seals behind them, disrupting radio communication with Phil, and a three-dimensional projection depicts the planet Mars, covered with water, being struck by a large asteroid and rendered uninhabitable. A Martian then reveals that the natives of Mars evacuated their world in spacecraft, one of which landed on Earth to create humans, who could one day land on Mars and be recognized as descendants. An invitation is offered to one astronaut to follow the Martians to their new home. Jim accepts the invitation and is launched in an oxygenated capsule, while the others return to Phil, and subsequently to Earth.

Question: What is the name of the ship the first crew was aboard?
Answer: Mars I
Alternative answer: The Mars I spacecraft.