^The only time I ever run real numbers is in time-of-travel calculations. Speed of plot annoys me. Also, for sublight, there a number of relativistic calculators available that make this a cinch. Anything beyond that is beyond my capabilities. More

than

I guess.
4) (And this one I'm still debating on) You seem to suggest another form of shockwave as a result of hitting relativistic velocities. I'm not sure I want to go with blowing off the entire planet's atmosphere, but is it possible for there to be a shockwave severe enough that you could be looking at meteorological disruptions for years after the event? (Is asteroid damage, such as the Cretaceous extinction event, a reasonable precedent or no?)
The question here is whether the impulse engine has such fine control that it can be regulated to produce just enough acceleration to throw a half-million ton starship into orbit (and this is still a tremendous amount of energy that should have local impact) or if it has a certain specific fusion point where the lowest possible power at which it could be operated is enough to create damage on a regional scale.
If your guys are running from something, this might not even matter, as they would simply order full impulse power without considering the impact on the planet.
Unfortunately, we don't know precisely how powerful impulse drive is. There is substantial evidence to show that it utilizes a low-powered warp field (the most critical piece of evidence, to my mind, is that the ship would need so much deuterium fuel to get up to relativistic speeds the deuterium need be either super-compressed or the ship super-huge). The contravening suggestion is that if they're using a warp field,
why bother with the impulse exhaust at all? We know warp fields are propulsive.
Actually, I know I said I didn't run the numbers, but if my reasoning is correct (it may not be), then a billion tons of starship would require 280 billion tons of deuterium fused at perfect efficiency to attain half the speed of light... yikes.
(For those interested, my reasoning is that the kinetic energy of a billion-ton starship at .5c is E = .5mv^2 is 7.5X10^25 Joules... and assuming a .03% mass-energy conversion of the deuterium, that amount of fuel would need be expended to feed that much kinetic energy into the ship. I might be approaching the problem from a flawed premise and would love to be corrected.)
This would require, for a fuel cell of 200,000 cubic meters, a density of 140 million kilograms per square meter... a tad less than ten times the density at the heart of the sun. But less than the density of a neutron star, so at least we wouldn't have to imagine they're keeping the fuel so compressed it's developing degeneracy pressure against the seal. But at such a density it's fusing all the time, unless in addition to being masters of gravity, Trek denizens are masters of the strong nuclear force.
But, of course I'm not factoring in the weight of fuel itself, which increases the weight of fuel required to push the fuel to be expended later! And... I've reached my limit for math for the evening.
On the plus side, we're not
sure that impulse = .5c. It could be far lower.
5) (Also debating this) It's been suggested the superheated exhaust itself could do damage on the ground in the immediate area of the maneuver.
That seems very reasonable, especially if the impulse engines are pointed directly at the ground.