Blink of an Eye: Voyager is caught in orbit over a planet on which time passes much faster than the rest of the galaxy.
Voyager drifts in to what looks like a fast-spinning doughnut and goes into high orbit, where they get caught. Meanwhile, down on the planet, primitive tribesmen experience earthquakes and see a new bright star in the sky. Then Voyager flies past a sun, and - oh, wait, that's the main titles.
The tribesmen discuss the new star and decide to start worshipping it. The Voyager crew discuss how they've become stuck. Seven says the planet has a "tachyon core" - the field has trapped Voyager and has created a "time differential" on the planet which is a fancy way of saying time passes faster on the planet. Chakotay is keen on studying the resident life form's development.
Down on the planet, the people have reached the "middle ages" stage. A young man discusses the nature of the stars with his aged mentor. The young man is using a wee hot-air balloon to send a letter up to the Voyager star.
Chakotay and Torres observe scans from a probe - the people on the planet have progressed to the industrial age. On the planet, a couple of people are observing Voyager through a telescope and sending a message by radio.
Y'know, since time passes faster on the planet, the sky should be black. Any light from stars to reach them would be too weak once its across the time differential to be visible to the named eye. Ditto for any light from their sun, yet there is light, and apparently enough solar energy to allow plants to grow and bear fruit. But I digress.
The people discuss the nature of Voyager and fail to get a response to their message. They don't think Voyager is causing the tremors on purpose though.
Seven detects the radio transmission and she and Chakotay slow it down and hear the two people. Tuvok says the prime directive applies, and they shouldn't radio back to apologise. Chakotay points out they've already interfered in their society. Janeway decides to send HoloDoc down as an observer. They beam him down for three seconds, but there's trouble getting him back and he's stuck down there and he's down there for three years planetary time.
HoloDoc says Voyager has encouraged much progress in order to contact Voyager, and warns that some people want to attack the ship. Naomi bugs Seven in Astrometrics again. With the new info from the HoloDoc, Voyager attempts to leave orbit, but Seven says the attempt is increasing seismic damage on the planet.
A manned spacecraft from the planet docks with Voyager and two people board the ship, one of them whom is Daniel Dae Kim. They find the crew seemingly frozen in time, cause they're still running fast. Reaching the bridge, they suddenly switch to Voyager time and collapse. One of the pair doesn't make it, but the pilot does and Janeway asks him for help in finding a way to get Voyager out of orbit. HoloDoc and the pilot discuss sports, and then the pilot helps Seven interpret the data HoloDoc gathered.
Voyager starts detecting antimatter explosions on the planet, then the people down there start lobbing antimatter torpedoes at the ship. Janeway sends Daniel Dae Kim back to the planet to talk to them. HoloDoc reveals that he had a son while he was down there. "Long story."
Voyager's shields are down, but Tuvok detects a new launch. Two ships tractor Voyager out of orbit, and a hologram of the pilot appears and talks to Janeway. On the planet, the now-elderly pilot watches Voyager disappear from the sky. The end.