So I had a thought earlier regarding the moment just before the big bang, when the universe was infinitely small and infinitely dense, while still maintaining the estimated mass of 1.6 x 10^{60}. Using the formula for gravitational force, my mass (68.2 kg) and the force holding me on Earth (668.6N), I calculated the furthest distance from such an object that I could stand and be sucked in - no questions asked. That distance came out to about 348,639,456 light years. My question for you all is simply: What is the most about of force (in Newtons per Kg) that gravity could put on an object without actually attracting it. Earth pulls me in (or I push on Earth) with 668.6N, but how many Newtons could I exert of Earth without actually being held to it? I hope I'm being clear. I would like to know so that I can calculate the smallest safe distance I would be able to stand from such an object. Obviously, this is all just for mental exercise and completely trivial, so please don't rant about that. Thanks in advance, Pete
"before the big bang" does not have any meaning in current models. The singularity is of unknown characteristics. The "Big Bang Model" starts AFTER the singularity. Also, your estimate of the mass must be for the observable universe because "the universe" is and has been of unknown size/mass. MIGHT be infinite, might not be.
That all is implied. This is simply a trivial thought experiment. Disclaimer to anyone else looking to post: If you plan on exercising your egocentrism and "correcting" me, don't bother. Attempt to be helpful.
Why would you think there is some maximum distance? Gravity extends to infinity. If you and the singularity are all there are, there IS no minimum distance.
What calculation did you do exactly, why did you choose those numbers? A gravitational force implies attraction. You can't have a force on a object without being attracted to it. Even your computer is pulling on you, but the force is negligible because gravity is such a weak force (you wouldn't "feel" an ant trying to pick you up, would you?) I'm sorry, but I have to "rant" about your experiment, because it's founded on the belief that you can be far enough away from an object and feel zero gravity. But if you insist on knowing what that distance would be, it's infinity. Also since gravity is a central force, you're more likely to orbit an object in instead of geting "sucked in." Also Newtonian gravity wouldn't apply before/during/immediately after the big bang since and that time the forces would have been united.
I chose those numbers simply because, given the equation that I linked into "gravitational force", they made the most sense. I don't mind ranting that offers some actual insight; that's called constructive criticism. However, in this thought experiment, I'm assuming that Newtonian gravity would apply because I'm not actually talking about the moment just before the big bang. Rather, I'm using that image of everything being so condensed to describe an object that would be similar. Assuming that everything else around it wasn't affected, only me, in an imaginary and infinitely large lab. I'm trying to determine the distance I could be from such an object so that its gravitational field wouldn't affect me in any observable way. To use Earth as an example instead of this pre-big-bang-pea: If an object (with a mass of 68.2 kg) were hovering just outside of Earth's orbit in a way that if it were to move just a little closer it would begin to descend to Earth's surface, what would that distance have to be? (Forget the Moon is there, and don't worry about colliding with any asteroids or comets) Now, what if Earth's mass were that of the entire universe? How far would the object have to be from it to hover as it did in the previous example? Does this help clarify things? I'm being vague because, like I said earlier, this is just a trivial thought experiment and nothing to split hairs about.
Infinity. [tex]lim_{r\rightarrow∞} \frac{Gm_{1}m_{2}}{r^2} = 0[/tex] Anything less than infinity and you get a finite, positive number for the force of gravity.
Ah maybe it'll help to add to the large lab idea that I'm looking for the least distance from the object in which the force of gravity pulling me to the floor of the lab overpowers the force of attraction produced by the massive object.
I understood clearly, and know clearly, but don't feel the need to clarify as we all are intelligent enough to understand what I'm implying.
Thank you. I think I'm going to just use the formula that I had before but substitute where I used my force on Earth (668.6N) for 1/3 of that, to show that I'm still in the gravitational field of the object but experience a greater attraction to the floor of my very large lab.
All you have to do is figure out the force the lab is exerting on you then solve for the distance the massive object would have to be away in order to equal it exactly. if you're further away than that distance, you'll stick to the lab instead of the "planet." However, the planet will end up being drawn towards you and the lab after any amount of time so...
For fun you could try and find the distance you have to be from each of the planets (the lab is now a planet) so you float in the middle without moving as they slowly move in to crush you. This is a more sensible and instructive problem, I think.