Suddenly, Voyager abruptly stops, and hovers in orbit above the planet, trapped in a magnetic field from which the ship cannot escape. The crew quickly discovers that the ship's warp drive is off-line, and that attempts to break out of orbit could worsen the gravity situation. With no other option open to them, the crew are forced to simply wait, until an escape plan can be formulated. While conducting surveys of the strange planet, Seven of Nine determines that Voyager has become a third pole, and that the gravity waves which have trapped the ship in orbit are also causing occasional earthquakes on the planet. Voyager continues to scan the world, and makes an astonishing discovery: time passes at a much more rapid rate on the planet. For every second that passes on the ship, nearly a day goes by on the world below.
Meanwhile, on the planet, a tribe of primitive humanoids, in a paleolithic stage, gathers for a religious ceremony. The local medicine man prepares a sacrifice of native plants and other fruits to Tahal, one of the brightest stars in their sky, worshiped as a god by the natives. Suddenly, immense earthquakes occur, and a new star, even brighter than Tahal, appears in the sky. The medicine man is instructed to prepare a new altar dedicated to the new deity; which in truth, is Voyager.
In orbit, Voyager crew members are still no closer to finding a way of breaking out of orbit. They continue to observe sensor readings from the planet, watching the seasons come and go right before their eyes, and note the existence of a sentient humanoid species. Janeway notes that despite the ship's predicament, they have been offered the opportunity to observe the rise (and possible fall) of the humanoid societies emerging on the planet below. Sensor probes are launched, and make their way towards the planet, gathering information on the rapid progress of the humanoids.
Down on the planet, thousands of years have passed, and the inhabitants are now at a level approximating the European Middle Ages of Earth. A local Protector emerges from his castle and enlists the aid of an elderly Cleric in an attempt to contact the "sky ship" which has hovered in the sky since time immemorial. The two men write a note on parchment, beseeching the "sky ship" to stop the tremors which continue to shake their world. After placing the note into a leather hot air balloon and launching it toward the heavens, they wonder whether anyone will ever read their message.
On Voyager, Chakotay and B'Elanna Torres observe the changes which spring to life in seconds on the planet below. As hours on Voyager pass, centuries pass on the planet below. The humanoid inhabitants enter an Industrial Revolution equivalent to the early Victorian era of Earth's history. Chakotay notes that the humanoid cities, their complex road networks, and buildings, contain much more iron than would be expected of a species at their current level of technology; B'Elanna speculates that the mass usage of iron is an attempt to strengthen buildings and roads against the ongoing planet-wide earthquakes being caused by Voyager. Chakotay and B'Elanna note a rise in ammonia and carbon monoxide levels, and realize that the species has begun mass usage of the internal combustion engine. As the crew discusses the unusually rapid technological progress of the species, a radio message is intercepted, emanating from the planet.
On the planet below, society has developed technology similar to that possessed on Earth during the 1920s. Astronomers are seen attempting to contact Voyager, sending lists of prime numbers and other mathematical constants by radio, to demonstrate their intelligence. While doing so, the astronomers debate who the crew of the sky-ship might be, and proudly boast of the endless series of "sky ship friends" (toy replicas of Voyager) which they own. It is revealed that the species has known for some time that Voyager is in fact a spacecraft built by a more advanced species, and that culture across the planet is dominated by the sky-ship. After another quake, the astronomers attempt to send a voice message, which Voyager crew members manage to decipher and translate. Captain Janeway calls a meeting of the senior officers to debate what to do. Tom Paris wants to reply, arguing that the astronomer deserves an answer, but Tuvok points out that the man who sent the message is long dead. Paris persists in pressing his opinion, arguing that the species below has made first contact with the ship; however, Janeway counters that the species has still not developed warp technology, and that as a result, a reply from Voyager would be a violation of the Prime Directive. Instead, Janeway suggests a covert one-man mission to the planet, to observe the species and its development.
As humans would be unable to transport safely to the planet's rapidly revolving surface, the Doctor, being a hologram, volunteers for the mission, as his structure will be unaffected by the sudden change in the passage of time. The Doctor intends to remain there for only a few days, planet time, but after Voyager briefly loses contact with him, the Doctor is left on the surface for over three of its years. Upon returning to the ship (an absence of only a few minutes on board the ship), he enthusiastically reports on what he has seen. Voyager has had much more of an effect on the planet than anyone could have predicted. Voyager, simply by its presence, has encouraged art, music, architecture, literature, and even religion, all inspired by the ship in orbit. Crucially, Voyager's presence has encouraged unusually rapid technological development through the ages, as the humanoids develop increasingly sophisticated technology in an effort to contact the sky-ship. In addition, the Doctor explains that planet is divided into twenty-six sovereign nations, all engaged in a space race to see who can first make contact with the sky-ship. The Doctor sadly reports that while some of the strongest states strive to establish peaceful contact with Voyager, other states are pursuing more belligerent policies, and are developing increasingly powerful weaponry in an attempt to shoot down Voyager. He explains that during his three years on the planet, one of the belligerent countries attempted to shoot Voyager down using long-range artillery, but that the shells landed in a rival nation, and provoked a world war which went almost unnoticed by the crew of Voyager.
While the Doctor relates his tale, the species below develops technology sophisticated enough to send astronauts on a manned mission to make contact with the sky-ship. The species, apparently possessing technology similar to that seen on Earth in the 1960s and early 1970s launches a rocket, reminiscent of Earth's Gemini or Apollo space programmes, and the capsule succeeds in docking with Voyager. Tureena and Gotana-Retz, the capsule's humanoid astronauts, board the ship, but soon fall ill because of the shock of moving in the immensely slower time-line of the ship. As the two astronauts explore the ship, they pass crew members apparently frozen in time, and speculate that the crew are in a form of stasis. However, when they reach the ship's bridge, scenes of crew members performing everyday activities convince the astronauts that they are on different time-lines. As they survey the bridge, the two fall unconscious from the stress of adjusting to the time-lines, and their fallen bodies are seen by Voyager's crew just as Tuvok reports a rocket-launch from the planet and Kim warns that a capsule has just docked in the ship's cargo bay. With the astronauts' mission having taken place in a fraction of a second in the ship's time-line, the pair are taken to the ship's medical quarters to recover. Tureena dies in sickbay, but Gotana-Retz is successfully treated with a serum to synchronise his neural network to function on Voyager's timeline. Given an explanation of the situation by Janeway, Gotana-Retz tours the ship, gazing with awe at the ship which has been his peoples' goal for thousands of years. As Gotana-Retz explores the ship, Tuvok and Seven of Nine detect a series of increasingly controlled antimatter tests on the planet below, and within seconds, the ship is hit by a bombardment of antimatter artillery blasts. Gotana-Retz confirms the Doctor's earlier story, and explains that the attack is being launched by a rival nation. He apologises for the attack, but Janeway counters that his people have every right to defend themselves against the earthquakes which still shake their planet. Upon receiving news that the species below has developed warp technology, Janeway officially makes first contact with Gotana-Retz on behalf of the United Federation of Planets. As the antimatter blasts weaken Voyagers shields, Janeway urges Gotana-Retz to return to the planet and convince his government to cease the attack. As Gotana-Retz returns to the planet, he learns that many changes have already taken place (for instance, his former posting, 'Launch Control', is now called the 'Tactical Command Center'; the natives all think he is dead), and struggles to make contact with his superiors. As Voyagers shields approach collapse, the bombardment stops. As the crew sigh in relief, two immense starships appear alongside Voyager, revealing that the humanoids below have reached the same level of technology as Earth. The two ships line up alongside Voyager, and using tractor beams, tow the vessel to safety. Gotana-Retz briefly transports to Voyager, and Janeway thanks him and his people. Gotana-Retz speculates on the effect that Voyager's absence will have, as the driving force of his entire species has been establishing contact with the sky-ship, and fears that Voyager's departure will result in his species losing the will to continue their development and progress. Janeway replies that if Voyager has had such an immense influence on the civilisation, they will continue to develop technology in order to follow Voyager into space. Gotane-Retz replies that unfortunately, due to his planet's bizarre timeline, his species is still a long way from being able to conduct space missions on the timeline of the rest of the universe, but that this challenge will undoubtedly prompt further development on the planet. After bidding farewell to the crew, he teleports back aboard his ship.
Seconds later, Voyager is towed out of orbit by two "advanced" spaceships and successfully breaks orbit and sails away from the planet. On the surface, the same seconds pass as decades; an elderly Gotana-Retz, long returned from his experience in space, gazes wistfully into the sky as his people's beloved Sky Ship vanishes from the heavens. As the camera pulls back, we see that he is sitting on the same spot where, thousands of years ago, his primitive ancestors celebrated the Sky Ship's arrival. But now, a glittering high-tech metropolis sprawls to the horizon; testimony to the lasting effects of Voyager on the planet below.