# Newton's Third Law, Gravity, and the Planck Length

#### kmarinas86

If you have a object that is about 10^36 less massive than the earth (about 10^-12 kg) and say it exerts a force on the earth about 10^-11 newtons, this would cause the earth to accelerate about 10^-36 m/s^2. If this object was away from earth, and say if these objects were initial stationary towards each other, in one second, the earth would travel a distance of .5at^2, which would be .5*10^-36 m, less than the planck length? So does such a small mass affect the earth at all at a distance? Does the Earth move if the 10^-12 kg object does?

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#### vanesch

Staff Emeritus
Gold Member
I would say that given that this is not measureable by any standard in any near or not so near future, that the answer to your question is entirely hypothetical. As such, it depends on the paradigm in which you place yourself.

Of course, in classical physics, given that there is no minimum length scale in that paradigm, there's no problem assuming that the earth is moving over that distance. And, if not in classical physics, you enter in any case the twilight zone of speculation about gravity and quantum effects: I don't even think that string theorists, or LQG people, would be able to give you a precise answer in their speculative paradigms, or might even have several different views on the subject.

#### baryon

To answer your question k the earth would not move at all because you're talking about an immensely small mass versus one of gargantuan proportions. All that might happen is that, when that little object explodes due to an impact or something in space, some of the particles might make it to Earth.

#### pallidin

I consider this to be an exceptionally interesting question.
To be sure, if the "outcome" of a physical intervention is not permitted due to certain laws what, then, is to be made of the permitted initiating process? A catch-22, else one ends up with an action without a reaction in this case.

The reason I find this of interest is that I have been inspecting the potentially bizzare consequences of "forced violation"

I realise that these types of comments from me do not belong in this thread so I will stop here.

"Newton's Third Law, Gravity, and the Planck Length"

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