Clinical psychologist Dr. Chris Kelvin is approached by emissaries for DBA, a corporation operating a space station orbiting the planet Solaris, who relay a message sent from his scientist friend Dr. Gibarian. Gibarian requests that Kelvin come to the station to help understand an unusual phenomenon but is unwilling to explain more. DBA is unsure how to proceed, as the mission to study Solaris has been sidetracked and none of the astronauts want to return home. In addition, DBA has lost contact with the security patrol recently dispatched to the station. Kelvin agrees to a solo mission to Solaris as a last attempt to bring the crew home safely.
Upon arriving at Solaris Station, Kelvin learns that Gibarian has committed suicide and most of the crew have either died or disappeared under bizarre circumstances. Both surviving crew members, Snow and Dr. Gordon, are reluctant to explain the situation at hand. Once alone in his quarters, Kelvin dreams about his dead wife Rheya â reliving when they first met and some of their most romantic and intimate moments. He awakens shocked and terrified to encounter Rheya, apparently alive again beside him in bed, and he leads her into an escape pod and jettisons it into space. Kelvin confides his actions to Snow and comes to understand that replicas of the crew's loved ones have been mysteriously appearing. When Rheya manifests a second time Kelvin lets her stay, but she admits she does not feel human; her memories feel artificial, in that she lacks the emotional attachment that comes with actually having lived them.
Through numerous flashbacks, Kelvin and Rheya's meeting and courtship are explored, with hints as to her disturbed upbringing and emotional difficulties. It is also gradually revealed through these flashbacks that Rheya once terminated a pregnancy but did not tell Kelvin about it. When he discovered her choice he was distraught and walked out on her. Rheya then committed suicide and was later found by Kelvin when he returned for her.
Kelvin, Rheya, Snow and Gordon meet to discuss the situation and Gordon tells Rheya what Kelvin did to her previous replica. An appalled Rheya abandons the meeting. Kelvin confronts Gordon, who in turn chastises him for getting emotionally involved with something that is not really human and may eventually pose a threat to human beings on the station as well as on Earth. Later during a dream, Kelvin questions a replica of Gibarian as to what Solaris's motives are for providing the manifestations, but he is told "there are no answers, only choices." Kelvin wakes to find Rheya dead, having committed suicide by drinking liquid oxygen. But she quickly self-resurrects, and it is revealed that other manifestations who have 'died' have done the same.
Gordon develops an apparatus which can permanently destroy a replica but Kelvin objects to using it on Rheya. Driven by his own grief and guilt over the 'real' Rheya's death on Earth, he begins ingesting a chemical stimulant to stay awake in order to monitor Rheya, trying to avoid repeating the past and essentially abandoning her to suicide. Kelvin eventually falls asleep and Rheya successfully petitions Gordon to destroy her with the apparatus as she has done for her own replica(s). Traumatized, Kelvin confronts Dr. Gordon who maintains she merely facilitated in assisted suicide and only strives for the preservation of the humans on the station.
Kelvin and Gordon then discover Snow's body stashed away in a ceiling vent and realize that the Snow they have been interacting with is a replica. Snow admits to being a replica and explains that upon being dreamed into existence, he was attacked by his creator and thus killed the "original Snow" in self-defense. The Snow replica tells them that repeat usage of the apparatus has drained the ship's fuel cell reactor, making a return trip to Earth impossible. Furthermore, Solaris has reacted to the behavior of the humans by 'exponentially' increasing its mass, thereby gravitationally pulling the space station inexorably toward the planet. Gordon and Kelvin begin prepping a smaller space vehicle called Athena to escape.
Kelvin gives up the idea of boarding the lifeboat, and Doctor Gordon leaves him behind. As the plummeting space station rattles itself to pieces around him, a replica of Gibarian's young son appears and offers his hand in assistance. Kelvin is then shown struggling to return to normal life on Earth whilst ruminating on the idea that he "remembered her wrong" - that is, Rheya as being invariably suicidal. He accidentally cuts his finger while chopping vegetables in his kitchen, but the wound immediately heals, and he realises that he has only glimpsed a possible future and that he is still on Solaris, since an artificial environment has apparently been created by Solaris for his continued survival on the planet. Or maybe the original Kelvin died aboard the wrecked space station and has been replaced by a replica of himself without realising it. But even his perception of this home away from home could merely be a temporary convenience, because when Rheya appears to him yet again, she replies to a question of his with an implication that they have transcended the conventional meanings of 'life' and 'death' and that all they have done to each other is forgiven.

Question: Why can't the ship return to earth?
Answer: The ship's fuel cell reactor was drained.