Star Trek: The Next Generation (1987)

Answer: Prior to the supernova, English script "three point eight billion kilometers", German script "3.8 Milliarden km" speed of light in vacuum c = 299,792,458 m/s 3.8 billion km = 3,800,000,000 km = 3,800,000,000,000 m (3,800 = 3.8 thousand, 3,800,000 = 3.8 million, 3,800,000,000 = 3.8 billion) in physics formula c represents speed aka. Velocity = v, s means distance (abbreviation not known to me), t = time v = s/t v * t = s t = s/v v = 299,792,458 m/s s = 3,800,000,000,000 m 3,800,000,000,000 m / 299,792,458 m/s = 12,675.435617529778 s = 3.5 hours The impression in the scene could be convincing of 1-5 minutes prior to seeing the supernova, and not 3.5 hours. I would argue in order to give them the benefit of the doubt they would have to be either less specific about the distance travelled or more respectful of c. The movement of the spaceship aka. Matter in this case being faster than c is implied to be part of the fictional part of sci-fi and not a logical oversight on my end. c is constant.

Answer: Yes. The doors to the holodecks can be locked when in use by anyone aboard the Enterprise so they couldn't be disturbed. However, high ranking officers like Captain Picard could override the doors as it's seen that overrides are in use even for the crews quarters. Even Barclay, when he's indulging in one of his fantasies could have the doors to the holodeck unlocked by an override code.