# Is the size of a portal going to limit the propagation of gravity through it?

It's a general question but my specific concern is whether different planets would crash into each other if a portal is made between them.

We're assuming bare, naked, "hole in space" portals.

This can be visualized like this: if you have two planets, and in between them is a wall that cancels and is not affected by gravity, and there's only a small hole in that wall, will the attraction between those two objects be less than if there's no wall.

If the answer is yes, what's the largest portal that could be opened in the immediate vicinity of two Earth-size planets without causing problems?

• Welcome to Worldbuilding.SE! We're glad you could join us! When you have a moment, please click here to learn more about our culture and take our tour. How big is the initial "test" portal? How far off the ground? Should we assume the two planets are both Earth-like? Thanks! – JBH Jan 31 at 0:51
• Properly speaking, I don't think anyone knows the answer to this, as nothing in nature has been proposed that would have that effect. I daresay you could say either it does, or it doesn't, and we could give you a rundown of the consequences. – Cadence Jan 31 at 0:52
• If you want a science based answer, you need to tell us the science behind the portal operation. – L.Dutch Jan 31 at 1:23
• We don't know of any substance that cancels gravity. I think that's the basis of some proposed future gravitational observatories which may see the big bang itself; as far as we know, gravitational propagation passes through everything. I think this question is solvable, but it would require a lot of math. I also think it's reasonable to assume some gravity would propagate through the hole, and if it does, then any size hole would eventually cause problems, drawing the planets nearer and nearer. – B.fox Jan 31 at 1:30
• Hard to answer with given data, but for most situations I would assume guidelines for safe use of an interplanetary portals would be to make it as short as possible or it is a good way to end said planets. – Artemijs Danilovs Jan 31 at 11:52

First off, let me start out with the disclaimer that the concept of a wall through which gravity cannot pass doesn't really mesh with any scientific description of gravity, so any answer you get is going to come with a large dose of interpretation.

That being said, the way I'm choosing to interpret this is analogous to the problem of what the electric field looks like if you put a metal plate with a hole in it in front of some electrostatic charge. You see, metal plates "block" electric charge-- more precisely, the electric field within one is always zero (alternatively, the voltage is always the same). The reason I'm talking about the electric field is that for charges that aren't moving, it works very similarly to how a gravitational field works.

In both cases you have some potential-- $$V$$ in the case of the electric field and $$\phi$$ in the case of the gravitational field-- whose rate of change tells you the strength and direction of the field. The only difference is that charge is the source of $$V$$, while mass is the source of $$\phi$$.

Now, if we have a planet on one side of the barrier and nothing on the other side, on the side with nothing, the gravitational potential will follow Laplace's equation:

$$\nabla^2 \phi = 0$$

Don't worry if you don't know what those symbols mean-- the important thing is that Laplace's equation has unique solutions. A fairly straightforward consequence of this is that if you have a solution to Laplace's equation for one set of boundary conditions, it can't be the same as the solution for different boundary conditions. But clearly, the setup with the gravity cancelling wall has different boundary conditions than those without it, since in the former every part of the gravity proof barrier has $$\phi = 0$$.

From this, we can definitively say that using the model you propose, the portal would affect gravity. As for the question of precisely how much, well, that depends on the shape of the portal and the mass distribution behind it. Even when specifying this, there likely isn't a closed form expression for any but the most simplistic limiting cases. To achieve any degree of accuracy, you would have to put in all this information to find boundary conditions at the barrier, and then use numerical methods to approximate a solution to Laplace's equation on the other side.

TL;DR There is a mathematical solution to what you propose, but it requires more information to calculate and a significant amount of effort.

I would say the gravitational influence exerted by the portal would be determined by the mass behind the portal. So assuming the gates are perpendicular to the surface of the planet (and there are no mountains between the gate and space the only gravitic force that would be exerted on each side is the mass of a cylinder of air with the diameter of the portal reaching out to the edge of atmosphere, not doing much more than creating a slight weather disturbance.

Disclaimer 1: As another answer points out, much 'interpretation' of the question is needed to provide any kind of answer, so here's my interpretation: The "wall" is actually nothing more than distance, and "visualizing" this distance as a wall is simply for convenience of understanding of the question itself, not an actual physical barrier to the gravity.

Disclaimer 2: I have no more than a wikipedia level of understanding of string theory, gravitons, and gravity.

As I understand it, and for the purposes of this question, Gravitons are effectively long straight lines (strings, as in "string" theory) radiating out in every direction from the mass object (in the case of the planet, they radiate out from each individual atom in the planet), and they affect anything they come in contact with, but the effect is lessened with distance. At the distances of the planets involved in this question, the effects can be considered negligible, all but non-existent, and effectively a 'wall' between them that reduces the gravitaional affect to (effectively) 0 ... Until you punch a "hole" in the "wall" with the portal.

Now, the size of the aperture would have a VERY significant influence on the gravitational effect, similar to a pinhole camera's effect on light. Yes, light from the entire facing surface of the sun can get through the pinhole, and create an image on the back wall of the camera. But that image is a VERY pale spectre compared to the massive amount of light from the original object, because only a very tiny fraction of the light coming off of any particular area of the surface of the sun will be headed in the right direction to get through the hole. Similarly, for a (relatively) small portal between planets, it will be a very tiny fraction of the total number of gravitons from the atoms of the planets that are actually pointed in the right direction to make it through the portal and affect the planet on the other side. So the gravitational effect felt through the portal would be a pale spectre of the full gravitational force of the original objects.

I lack the math skill and quantum physics knowledge to try and provide any sort of numbers or even estimates, but I think that (as far as this interpretation of the question is concerned) it's pretty clear that the size of the aperture is of HUGE importance to the size of the gravitational effect felt through it.

Lisa Randall asked the question how does a tiny refrigerator magnet overcome the entire gravitational force of the earth to lift a paper clip? In other words why is gravity so darned weak? Until she answered the question everyone thought gravity was leaking out of the universe. She showed that its the opposite and gravity is actually leaking into the universe.

So without speaking to your overall question, yes physicists seem to believe the size of the aperture would affect flow just like a window or a dike affects water or air because gravity like air and water is composed of small (elementary) particles (gravitons) that form waves.

Otherwise we would be crushed by all the gravity leaking in at once.

• Sorry, can you provide some reference to substantiate your statement? What do you mean with "leaking in" and "leaking out"? Where did you see that gravity is formed by particles? – L.Dutch Jan 31 at 14:24