They implied they avoided that because warping into a gravity well would cause some vague catastrophe.
Of course, the real reason was far more sinister: it’s way more dramatic to slowly creep up on the planet while listening to the captain’s log monologue to start the episode.
If nothing else, if you miss just a little dropping out of warp inside a planet, must be a Very Bad Thing in-universe. The ramifications would be seen even out-of-universe. ;-)
Sure, if your probability distribution looks at every point in the universe equally. But we're talking about introducing error in a situation where you're _trying_ to drop yourself right next to a planet, so the areas nearest to your target have a much greater probability.
The volume of space up to only geostationary orbit is about 177 times bigger than the volume of the earth.
Given that Star Trek's impulse drives are already traveling at up to around 0.9c, parking somewhere between the earth and the moon (which is about 1 light-second out), the ratio of space to volume of earth becomes 219,648.
That ratio growth with the cube of the distance to the planet.
If we’re talking about the known universe, the odds of your near-light navigation accidentally clipping a not-mapped-yet planet are certainly not zero.
Our gaze into the heavens is much better at spotting stars than their dark orbiting bodies, and we have fingers left over from one hand counting the number of observation platforms observing deep space from above our shimmering atmosphere.
Indeed. We can't even agree on whether or not there's an extra Neptune-sized gas giant out beyond the orbit of Pluto, and that's right here in our OWN solar system!
So? Even ten extra Jupiters or thousand extra suns would take up only a tiny amount of space compared to the size of the solar system out to Pluto:
The distance from the sun to Pluto is about 5.9 billion km. The radius of the sun is about 696,340 km. The ratio of radii is about 8,473. Cube that to get the ratio of volumes, and you get 608,263,848,559 for the ratio of volume in a sphere out to Pluto vs volume of the sun.
(Doing the numbers, I'm actually surprised: I had expected the ratio of radii to be bigger than 8,473. But I'm not surprised that the sun barely takes up any space.)
Arguably, the entire heliosphere is part of the Sun's atmosphere, and it reaches well beyond Pluto. If I were in a relativistic spaceship, I think I'd want to apply the brakes well before slamming into the heliosphere.
What do you call the heliosphere of a star that isn't the Sun? The stellosphere?
"Stellosphere" is wrong, because "stella" is Latin, and "sphere" is from Greek. It should be "asterosphere", but that's a word I've never seen nor heard.
> If we’re talking about the known universe, the odds of your near-light navigation accidentally clipping a not-mapped-yet planet are certainly not zero.
If we're still talking about Star Trek, then on a solar scale those ships can stop on a dime. They're not going to hit an unmapped planet while putting around.
It doesn't matter whether we can see those dark orbiting bodies: we observe minuscule gravitational impact on the stars, and that places a very sharp upper limit on the amount of mass that's outside of the star in a solar system.
The sun contains roughly 99.8% of the mass of the solar system, and is by far the largest object in it. But you wouldn't hit the sun randomly either. Space is just so damn large.
They implied they avoided that because warping into a gravity well would cause some vague catastrophe.
Of course, the real reason was far more sinister: it’s way more dramatic to slowly creep up on the planet while listening to the captain’s log monologue to start the episode.