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My understanding is that every Federation ship has a navigational deflector which is primarily used to deflect any objects that may collide with the ship while at warp or otherwise. From what I've seen of TNG and Enterprise, the deflector can be used for other means, including as a weapon to damage larger objects. These appear to be rare exceptions to its intended use.

During conventional use, for navigation and preventing collisions while on the move, is there an upper limit, be it in terms of size, mass or speed to what the main deflectors can protect the ship from? Given that ship-to-ship collisions have been shown throughout the series (even if one ship was relatively undamaged, I would assume they don't switch off the deflector at any point), I doubt it could stop a Galaxy-class ship from accidentally crashing into a parked shuttlecraft, but are there any examples throughout the series of the main deflector sparing the ship from collision with anything bigger than dust or small debris fields?

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    not really - if you can change the gravitational constant of the universe.....once, Geordi was able to use the deflector to push around a world killing asteroidal moon: "LAFORGE: You know, this might work. We can't change the gravitational constant of the universe, but if we wrap a low level warp field around that moon, we could reduce its gravitational constant. Make it lighter so we can push it. " - chakoteya.net/NextGen/161.htm – NKCampbell Dec 6 '18 at 14:14
  • An asteroid of 0.7 mass is apparently too big. Too bad they never stated in the movie what unit of measure does 0.7 refers to... 0.7 kilograms? 0.7 Earth mass? Something else? – Sava Dec 6 '18 at 20:24
  • It's probably more related to the power required for the deflection rather than the mass of the object. I.e. how much momentum change is necessary to avoid collision given the range of the deflector. So if a small shuttle is traveling at high impulse speed towards the Enterprise, the deflector dish may not be able to deflect it even if it were able to move a much larger shuttle that's more or less stationary relative to the Enterprise. – Lèse majesté Dec 6 '18 at 20:34
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There's no upper limit to the size of object the ship can move, but this is subject to the normal restriction that apply when applying force to large objects; the bigger they are, the harder it is to get them to move.

The TNG Technical Manual presents us with a wealth of information about the deflector system. In essence it consists of two main systems; a series of nested static fields that deflect interstellar dust and hydrogen and a secondary deflector/tractor-beam capable of moving larger objects out of the ship's path.

Although the density of the interstellar medium is extremely low, significant hazards to navigation exist, especially for a starship traveling at relativistic or warp velocities. Among these are micrometeoroid particulates, as well as the much rarer (but more hazardous) larger objects such as asteroids. Even the extremely tenuous stray hydrogen atoms of the interstellar medium itself can be a dangerous source of friction at sufficient velocities.

...

The navigational deflector, also controlled by the subspace field coils, is a powerful tractor/deflector that sweeps thousands of kilometers ahead of the ship, pushing aside larger objects that may present a collision hazard.

Although the active scanners are generally used to move the ship out of the path of very large objects, the deflectors are approximately twenty-four times as powerful as the ship's primary tractor beam, albeit subject to the same inverse square law degradation of their effect at distance.

(compare)

The heart of the navigational deflector system is three redundant high power graviton polarity source generators located on Deck 34. Each of these generators consists of a cluster of six 128 MW graviton polarity sources feeding a pair of 550 millicochrane subspace field distortion amplifiers. The flux energy output of these generators is directed and focused by a series of powerful subspace field coils.

[vs.]

The main tractor beam emitters are built around two variable phase 16 MW graviton polarity sources, each feeding two 450 millicochrane subspace field amplifiers. Phase accuracy is within 2.7 arc-seconds per millisecond, necessary for precise interference pattern control.

Assuming these calculations apply equally, the ship can deflect moderate-sized objects (in the range of tens of kilogrammes) sufficiently to make it worthwhile before the ship gets there. Anything larger wouldn't have moved far enough out of the way to bother and would be avoided through course-correction but there's nothing that stops the Enterprise from trying to deflect a planet, it just wouldn't move very far. Note also that unless you can entirely envelope the object, you also risk it being torn apart

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    Your answer explains how the deflector works in-universe, but doesn't reply to the question asked except through conjecture. That being said, I have doubts that there is a canon answer to the question. – Sava Dec 6 '18 at 20:26
  • @Sava - I'm pretty sure my answer does answer the question asked. It can move an object of any size, but if it's larger than a few kilogrammes, that object won't move very far or very fast – Valorum Dec 6 '18 at 20:30
  • I suppose it would be tough to find an example in the series of near-misses during conventional use, especially since we probably wouldn't find out the exact size or masses of the obstacles. Understanding more how they work helps though! – user107907 Jan 3 at 11:51

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