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I assume that if a ship runs into particles without a deflector, this would amount to drag on the ship's forward motion.

However, a deflector field presumably moves particles sideways (perpendicular to the ship's forward path).

Would the particles still impart drag on the ship's forward motion? If not, what effect would they have?

(For the purposes of this question, let's please ignore the fact that particles colliding with the ship at relativistic speeds would be devastating. I am just interested in whatever action-reaction force is going on here.)

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@Close voters: you're missing the "star-trek" tag on this question; it does relate to a cited work of fiction and therefore is not off-topic per your selected reason. –  Jimmy Shelter Feb 5 at 13:33
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3 Answers

To answer this question, it's important to note that Star Trek physics often aren't very consistent or accurate or anything. But I guess most fans consider this as a fact and ignore it, so let's ignore that for now as well.

The short answer already mentioned by you: action-reaction force (or more specific: actio = reactio); so... yes, there's some impact.

First (or more specific second part) of the question:

Would there be any difference with the deflector field being off?

Sure there would! But in a bit different way. The intention of the deflector is right in its name: It's there to deflect anything that's in the way, no matter whether we're talking about particles, dust, scrap, or anything else. Without that, there'd definitely be some difference, even if we're just talking about space particles crashing into the ship's hull. Given the Star Trek typical vulnerability of the engines, this would most likely kill the ship instantly anyway (unless the deflector fails for some added dramatic effect).

So would there be some difference? Definitely. You have to consider that the deflector field essentially changes the overall "shape" of the ship (bare ship exteriors vs. "bubble"). Starting from there it should be easy to assume that there will be differences in friction/drag/etc. (while ignoring catastrophic impacts etc.).

But is there an in-universe explanation or example?

Of course, there are, lots of them actually.

Excuse me for not having all episodes (and especially their names) in my head, but there are lots of different examples where external forces are applied to a ship despite the deflector shields fully working:

  • More than once a ship is shown being steered into some kind of shockwave to "ride" on it and/or to prevent damages. This can be seen several times in TNG as well as VOY and ENT (and possibly others as well). If the deflector field would just neutralize all drag/push/whatever, this wouldn't be necessary nor possible.

  • There are at least two episodes (TNG and VOY), where the ship is stuck "swimming" with a swarm of aliens that will simply drag the ship with them. Once again, if the deflector would neutralize external influences, this wouldn't be possible.

So back to the initial question:

Would the deflector/particle drag impact the movement of the ship?

Yes it would (even if just very, very tiny and possibly neglectable). Just imagine a small ship in a bath tub. Whenever you apply external force (waves), it will react to it. No matter whether the shape of the "ship" is round, a classic ship form, a rectangle, etc. The shape doesn't matter unless it's magically able to negate all outer influences.

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I think there is some limit to what a deflector field can deflect. Otherwise, the ship would be able to dodge all torpedoes and such. I have seen some episodes where ships have impacted debris. I'm pretty sure the deflector field can only move very small particles. –  Lakey Feb 6 at 0:32
    
I appreciate your answer and the wave analogy. I'm not sure the deflector field is bubble-shaped though. It's not the same type of energy as is projected by the shield emitters. –  Lakey Feb 6 at 0:34
    
The bubble just has been an estimated example. It could also be more cylindrical with a rounded front or even some sort of prism. That doesn't really matter however, the important part is the "shape" pushing particles is changed (ship hull outlines vs. whatever form/shield). And yes, the size of objects being deflected is obviously limited since it definitely isn't able to apply infinite force to objects trying to pass it. Otherwise this would be some kind of "invulnerability effect". –  Mario Feb 6 at 9:21
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Yes, but "space particles" [1] are so light and rarefied that they would have no noticeable effect on the speed of the ship. By definition, it's some kind of gas or dust cloud that is in reality, quite low density when compared to a planet's atmosphere. Even dark and dense nebulae are quite close to a complete vacuum compared to Earth's atmosphere.

Now, that said, in order to impart any kind of force on any kind of mass, that force produces an equal and opposite reaction force, and it doesn't matter what kind of force it is, whether it's electro-magnetic, gravitational, or the strong forces that keep matter together. Gravitational forces like the ones that are supposed to make deflection shields work (they say that they bend space-time to make this happen, but that's exactly how gravity works), still create opposing forces. For example, in the Earth-moon system (or the sun-earth system, for that matter), both bodies pull on each other such that the moon doesn't so much revolve around the earth as they both orbit a common centre of mass - which just happens to be quite close to the Earth's centre as well. You can create the same effect by spinning a hula hoop around your waist. As the hoop spins around you, it pulls your hips outwards towards the far end of the hoop. It's just that in the Earth-moon system, gravity is the force that does the pulling between each body.

I think that the only difference between whether the deflection shield is on or off would be the jolt that would come from a bit of rock impacting the surface of the ship (brought to you by the electromagnetic force that holds molecules together), as opposed to the gentle nudge of gravity, which is a much weaker force. The latter would create a much smaller acceleration over a longer period of time.

[1] I'm going to take a wild stab and say you're referencing the title sequence of Voyager, where we see the ship making a wake in the rings of a planet.

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According to the Star Trek TNG Technical Manual, the deflector shields work by bending space around the ship, causing incoming attacks or debris to miss the ship entirely.

Field energy is concentrated at the point of impact, creating an intense, localized spatial distortion. To an observer aboard the starship, it appears that the intruding object has "bounced off" the shield. A zero-dimensional observer on the intruding object would, however, perceive that his/her trajectory is unaffected, but that the location of the starship has suddenly changed.

The incoming particle never actually contacts the shield or the ship, so its own kinetic energy is unaffected - therefore, there is no direct change to the ship's kinetic energy.

But what about the action of the shield on the fabric of space itself? The deflection is achieved by bending space for a brief moment, so does that action cause a reaction on the ship? Since we often see the ship shake when attacks hit the shields, it's reasonable to assume that creating these spatial distortions pushes back on the ship to some extent. This also explains why pure energy attacks, like phaser fire, can make the ship shake - the shaking isn't caused by the impact of the phaser beam, it's caused by the shields pushing against space to distort the path of the beam.

So it seems plausible that particles hitting the deflector would have some small, indirect effect on the ship during flight, due to the action of the deflector bending space. However, these tiny forces would most likely be smoothed out by automatic microadjustments to the warp field or the inertial dampeners.

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You almost got a +1 for me, but then you brought shields into the equation and leapt to the wrong conclusion. If space is bent, there is no impact, and the effect of a particle diverted by the distortion is identical to the effect of a terrestrial hurricane on an orbiting spacestation. –  DougM Feb 5 at 19:11
    
@DougM What I'm saying is that creating the spatial distortion in the first place is likely to require some type of force exerted by the shield emitters, which would be accompanied by an equal and opposite force on the ship as per Newton's third law. The nature of this force is never addressed in canon to my knowledge, but since we know that shield damage often causes the ship to shake, I think it seems reasonable to assume that this would be a physical force of some kind. –  Sandblaster Feb 5 at 20:52
    
Newtonian physics don't come into play when you're warping space. The deflector field itself may impose some drag, but an individual particle wouldn't add to that drag, since there's no interaction to speak of, –  DougM Feb 5 at 21:28
    
"According to the Star Trek TNG Technical Manual, the deflector shields work by bending space around the ship, causing incoming attacks or debris to miss the ship entirely." How does this relate to/interact with attacks that penetrate/ignore shields (e.g. energy weapons using the correct modulation/frequency)? –  Mario Feb 5 at 22:48
    
Sandblaster, thanks for the thorough response including an excerpt from the Technical Manual. However, I don't think the deflector array produces the same type of energy field as the shield emitters. Shields are clearly seen in the show to be hard bubbles. When an object hits the shields, it clearly stops (or explodes). This is different from the deflector field which, as you said, doesn't affect objects. –  Lakey Feb 6 at 0:27
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