Deep in the Delta Quadrant, the starship Voyager approaches an alien world which exhibits unique properties. The planet's oddly squashed, toroidal shape is inconsistent with recognized theories on planet structure. It is discovered that the planet is enveloped in a tachyon field, suggesting that the planet's rapid rotation may be due to temporal effects. The crew of Voyager becomes fascinated by the strange world, and in an effort to learn more about it, Captain Kathryn Janeway orders the ship to move closer. However, the ship quickly becomes enmeshed in severe gravity distortions and is pulled towards the planet. Helmsman Tom Paris attempts to maneuver the ship out of orbit, but is unsuccessful, and the crew watch in horror as the ship plummets on a collision course directly towards the planet's surface.
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 occasion, however, is interrupted by Voyager's sudden appearance in the sky as a bright star and by a resulting earthquake. Assuming that the new star is a god, the villagers prepare a new religious altar for it.
In orbit, Voyager crew members 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. Chakotay 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.
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 (akin to a form of alien SETI) is broadcast at Voyager.
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. 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, simply by its presence, has encouraged art, music, architecture, literature, religion, and, crucially, 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 the 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. 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.
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, now 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 programs, and the capsule succeeds in docking with Voyager. Tureena and Gotana-Retz, the capsule's humanoid astronauts, board 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 synchronize 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 apologizes for the attack, but Janeway counters that his people have every right to defend themselves against the earthquakes which still shake their planet. As the antimatter blasts weaken Voyager's shields, Janeway urges Gotana-Retz to return to the planet and convince his government to cease the attack. Gotana-Retz returns to the planet, and, as Voyager's shields approach collapse, convinces his superiors to stop the bombardment.
As the crew sigh in relief, two immense starships appear 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 civilization, they will continue to develop technology in order to follow Voyager into space.
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. The episode ends on the same altar the humanoids built at the beginning, only that it is now a glittering high-tech metropolis, testimony to the lasting effects of Voyager on the planet below.