In Star Trek: Generations, Dr. Tolian Soran shoots a solar probe into the nearest star in order to
shift the Nexus.
So, if the star is approximately the same distance away from Earth, how fast would the probe actually have to be travelling to reach the star in the allotted time and is there any indication what allowed this speed to be reached?
The relevant scene described by the OP takes place at the Veridian system. According to the Star Trek: Star Charts (p. 65):
Veridian was classified as a G-class star.
All G-type stars have a mass of 0.84 to 1.15 solar masses and surface temperature of between 5,300 and 6,000 K, so we can safely assume that Veridian is roughly similar in mass and temperature to our Sun. Therefore, any habitable planets will be at a distance of roughly one astronomical unit (AU) or so, which corresponds to the "Goldilocks zone".
Then, assuming the distance from the planet to its star to be around 1AU, the probe should be travelling at warp ~3 in order to hit the star in around 10 secs.
The reason for this is that 1AU is ~8 light minutes or ~480 light seconds, so for the probe to cover the distance in say 10 secs it has to be travelling at a speed of 48c (c=speed of light). According to the wiki and the warp diagram from the TNG Technical Manual seen below, 48c is about warp 3.
Since Starfleet's Class 8 probes can reach warp 9 and are no bigger than a photon torpedo, it is certainly plausible for a small probe like the one used by Soren to reach warp 3 given the available tech at the time.
Assuming a similar distance from planet to star as that of Earth, eight light minutes, then the missile had to travel at approximately 50 times light-speed to arrive at the star in ten seconds. That is very much within the realms of Star Trek technology.
More importantly, though, the missile traveled at the speed of plot. Had this been a more suspense-driven plot element, or one the Enterprise crew were intended to have a reasonable opportunity to stop, the same missile fired from the same planet might have take half an hour or more to make the same trip.
It has to be traveling backwards in time.
It's a life sustaining planet in orbit around a star that's between white and yellow in color. This puts light-delay from the star surface to the planet somewhere around 6-9 minutes. We see the effect of the probe on the star from the planet's surface in ten seconds.
It took effect ten seconds after launch. Dude, Warp 10's not enough! It's gotta get there at least 6 minutes before it was launched. Ordinary speed definitions don't really apply anymore. And due to the limitations for how time travel works in Star Trek you've got a serious problem.
