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Now the purpose of the deflector dish on a starship is to push aside debris and objects in the ships path so that when the ship is moving it doesn't plow through this debris and destroy the ship. This debris that gets flung aside is subject to the laws of physics in space and will keep moving, eventually becoming subject to other forces.

As we are learning, space is not nearly so empty as we used to believe. With millions of ships throughout the galaxy flinging debris in every direction, would not this near infinitesimal amount of debris being flung about become an extreme hazard to other ships, space stations and inhabited worlds? Technologically advanced worlds would have various defenses to protect them from this, but most of the inhabited worlds in the Star Trek universe have not developed to the point of having such advanced space based technology.

So would this not be danger to them? And has this potential danger ever been addressed in any of the stories? I'm pretty sure it was never discussed in any of the tv series, but perhaps one of the books?

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"As we are learning, space is not nearly so empty as we used to believe" -- what are you referring to here? I think it's still agreed that interstellar space is basically empty of anything except individual hydrogen/helium atoms and microscopic dust particles, see www-ssg.sr.unh.edu/ism/what1.html –  Hypnosifl Apr 3 at 13:32
    
I agree with Hypnosifl. Could you be more specific about what particles you're worried about? –  Zibbobz Apr 3 at 13:40
    
For example, around the time of TOS, we really had no concept of the Ort cloud. We knew that comets orbited way out there, but we really didn't understand that it contained so many rocks and ice and asteroids and planets/planetoids as well as comets. Even through the vast void between star systems there are rocks, planetoids, rogue comets, etc. A ship traveling, especially at warp speeds, is likely to have its deflector field push objects out of it's path at some point, changing their natural orbits and trajectories. Not frequently, but it would likely occur. –  BBlake Apr 3 at 13:50
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According to the page at apps.usd.edu/esci/creation/age/content/creationist_clocks/… "Even with the immense number of comets, the volume they occupy is so large that they rarely come into contact with each other. The average distance between them is approximately 20 A.U. (Druyan and Sagan 1985:197)." 1 A.U. is the distance between the Earth and Sun, so that's an average of 3 billion kilometers between comets, which are small objects themselves...I think the chance of a ship's deflectors hitting one would be tiny, even if they didn't try to avoid Oort clouds. –  Hypnosifl Apr 3 at 14:04
    
I have a new theory for the "Wow! signal" –  Tim S. Apr 3 at 14:57
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I think you're overestimating the size of particles that were deflected by the deflector dish. At high impulse, even a grain of dust could pose a serious threat, but a whole asteroid could never be deflected.

So, you're right that the deflector dish is for pushing stuff aside, but the kinds of things it's pushing aside are so small as to be totally unnoticed when entering the atmosphere.

Anything larger than this has to be avoided.

Furthermore, at the distances we're talking about (billions of km), even the slightest difference in angle will mean the difference between hitting a distant planet and missing it entirely, which means that there's really very little danger of even one particle having just the right trajectory to reach that planet, let alone several.

Space is, after all, mostly space.

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I think this, combined with my answer, creates the full picture of why planets really don't have to worry about this sort of thing, even with Warp Fields creating complications (warp fields dissipate after a certain distance anyway) –  Zibbobz Apr 3 at 15:01
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I think you're underestimating the amount of space debris that already get flung around on a regular basis in space, without starships to worry about.

Massive plasma emissions from the sun, particles moving at near-light speed , and other cosmic rays impact Earth all the time without incident.

Not to mention that Warp Speeds near a habitable planet are very rarely used, so fear of faster-than-light particles is less worrisome.

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I don't remember reading about this in any book (although the movie Gravity uses this theme). Ships without deflector shields would be subject to impact, although the ship is already moving, even a stationary object would be dangerous.

Unless the debris is asteroid sized, it would be burned up when entering a planet with an atmosphere.

So, one could argue that a ship with a deflector shield will actually help clear debris by putting it into motion where it will eventually be pulled in by the gravity of a planet or star.

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With star systems being so far apart, it won't make that much of a difference unless it happens upon a rogue planet. –  nitind Apr 3 at 22:07
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The deflector dish was used for more than just deflecting particles (or, indeed, objects of greater mass such as asteroids - TOS episode Mudd's Women shows that). It was more of a general purpose energy modulation field that frequently caused subspace distortion (so says TNG Technical Manual). One could imagine that the force beams (steered by navigational sensors, again according to the TNG Technical Manual) simply steered objects around the ship in travel and deposited said objects with their original velocity behind the craft in motion.

At superluminal velocities, since they are not actually traveling through space at speeds exceeding the speed of light, the navigational sensors (which operate in subspace frequencies) would see the objects in the space-time far enough in advance that the navigational deflector could steer the object by the time the object was within the warp "bubble".

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This doesn't really address the risk to the environment –  Richard Apr 3 at 19:28
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There are at least two instances in which it was mentioned that it is dangerous to go to warp within the solar system. In ST:TMP, In Star Trek: The Motion Picture, Captain Kirk had to risk jumping to warp inside Earth's solar system to intercept V'Ger as soon as possible.

In "By Inferno's Light" Dax is hesitant to go to warp in a runabout in the Bajoran system, but it is ultimately decided that the alternative (letting the founder detonate the Bajoran star) is worse.

It has been claimed that this is because of the danger to the ship of running into a large object such as an astroid or planet. However, on at least one occasion (having trouble remembering the episode, but it was at least TNG era) it is said that the computer can be programmed to perform a series of warp jumps far faster than a human, and it seems unlikely that technology would not have advanced that far between Kirk's time and Picard's.

The density of particles in space is greater within a star system than in the interstellar medium. Thus the prohibition (except in case of emergency) against going to warp, as well as the standard procedure seen in many episodes of coming out of warp upon reaching a star system (for instance, the Enterprise D chased the Borg cube at impulse in the solar system), specifically for the reason you mentioned. Within the solar system the higher particle density would indeed create random currents of potentially lethal high energy particles.

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"it is said that the computer can be programmed to perform a series of warp jumps far faster than a human" Voyager touches on that, by a statement in Fury that "We could preprogram every kilometer. That way we'd only spend a second or two at impulse every time the computer executed a turn. ... The neural gel packs can calculate vectors a little faster than you can". –  Michael Kjörling Apr 4 at 12:05
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