Spoilers about the first episode of season 4 ahead.
How did Starbuck get to Earth and back in only six hours?
The first episode of the fourth season presents us with an interesting physics problem. Starbuck returns two months after the destruction of her Viper with a brand new ship, claiming to have been to Earth. She thinks she's been away only six hours. What's going on? Some possibilities:
Starbuck discovered a wormhole network between gas giant planets in various planetary systems.
Buried deep in gas giant atmospheres, wormholes could permit instantaneous travel between widely separated points in the universe. Starbuck says she remembers seeing a gas giant planet with rings; without a telescope (even with a pilot's sharp eyes), she'd have to be very close to Saturn to see its rings. Perhaps our solar system's end of the wormhole is located at Saturn.
Starbuck's still got to get from Saturn to Earth and back again. In the Miniseries, it was determined that Colonial One can travel at about 1/10 the speed of light. Taking a wild guess that a military fighter can travel at twice that speed, it would take a viper at full throttle 178 minutes to travel the most likely distance between the Earth and Saturn (it could be 161 minutes, it could be 196 minutes, or any value in between). With relativistic time dilation caused by traveling at 20% of the speed of light, the 178 minutes would seem to Starbuck (and the clock in Starbuck's viper) like 175. It is just possible for Starbuck to travel from Saturn to Earth, take some quick pictures, travel back to Saturn, and traverse the wormhole.
But she came back at a different place from where she left. That implies a second wormhole in our solar system, leading to a second destination. If the new wormhole is at Jupiter, say, then Starbuck had time for a quick orbit of the Earth (which is what she said she did) before traveling to the second wormhole.
Of course, the big unanswered questions with this scenario are: how did she know where Earth was in relation to Saturn, and how did she know where the return wormhole was?
Some agency managed to accelerate her Viper it to 99.99132% of the speed of light.
At that speed, the relativistic time dilation effect would make her feel as though 6 hours had passed while two months has elapsed for the Fleet. (Of course, the fleet is moving at about 1/10 the speed of light itself, but this time dilation is negligible). If this is what happened, then the colonists have the answer they've been searching for: the the round trip distance to Earth.
But it's an answer that's meaningless. At 99.999132% the speed of light, a one month outbound trip covers 482.7 billion miles – about 1/12 of a light year. (Makes sense: one month is 1/12th of a year). This is 1/50th the distance between the Sun and Alpha Centauri, and about half the distance between the Sun as the Oort cloud. If the fleet were that close to the Sun, they'd certainly be able to detect its planets, and possibly be able to observe Earth directly.
It's not Starbuck.
Starbuck died in a vortex of a gas giant planet. The thing that returned is some sort of replica, created in the image of the real Starbuck by some unknown agency, flying a showroom-new viper to replace the one that got destroyed.
This is the simplest answer and the most unscientific. At our present level of understanding, a technology that could do such things is indistinguishable from magic.
Repeat to yourself it's just a show, I should really just relax.
