Two Structures Adrift In Space

Question

There are 2 planet sized structures that are artificially made with no means of propulsion. Each structure has the approximate mass of Earth but are hollow inside. The inside area is where the people live.

The 2 structures are adrift in interstellar space. There are no significant celestial bodies for more than 1 light year away.

The skin of the structure is made of fused rock (the consistency of cooled lava). The skin is about 200 miles thick to partially offset any outside cosmic radiation.

The inside of the structures are hollow. Think of the inside of a skyscraper. Each of the floors is 5km below the one above with the top floor being about 5km below the "ceiling". The people live on each of the floors.

Based on other answers in WB I've seen, I assume that a size of 5X to 7X the diameter of the Earth would work if the insides of the structure were not very dense. So a ballpark of 60km diameter for the structures would yield about 10 - 12 floors.

In these structures, would it be safe to assume that the people experience reasonably close to 1 Earth gravity?

Answer 1

You are talking about planets that are near each other somehow, so I'm going to draw your attention to this concept. A roche limit is the distance within which a celestial body, held together only by its own force of gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction. There's several useful equations on that link and others that can provide you with handy equations on how far apart you can put 2 big objects.

Because I'm vain that way I'd also like to present this link because you suggested hollow planets. That question was put on hold and my answer as you can see was accepted but not exactly popular. To have a single hollow planet (which was what the question asked about) was already infeasible so the OP invented some attractive-but-repulsive force to get around accepted physics.

Now you're asking not only about hollow planets but people living on the inside of them. According to physics, no, your people cannot stand up like we do on Earth. BUT you can get around this. Just to create such a megastructure requires technology that doesn't exist - you need materials we straight up don't have. Diamonds, carbon nanotubes - nothing we can do right now will give you what you need. But assuming that we did have some sort of ultra-nanotube technology, why not run a whole lot of current through it? If you're familiar with electricity, you'll know that a wire of current generates a magnetic field around it. Check out this site for homework! So, if somehow you were running a whole lot of these magnetic fields (equally, symmetrically, on all parts of such a hollow planet), you could induce a magnetic field, and therefore some level of 'gravity' using Faraday's Law at its most extreme.

TLDR: A hollow sphere with a perfectly even mass-distribution on its own has no gravity on the inside of it, so maybe running current through the entire structure perfectly symmetrically would get around this.

EDIT1: Check out this link! It discusses the possible merging of 2 planets into one and goes through Roche limits too. Has an answer by me to endorse my own vanity lol.

I hope this helps!

Answer 2

The people inside each hollow Earth will experience no gravity. This is due to the Shell Theorem. A non-hollow planet does not suffer this effect.

In simple terms: in a non-hollow planet, as long as you are not on the mass center, there is always more mass pulling you to the mass center than otherwise. On a hollow, symmetrical planet, if you calculate the different pull from each point of the shell they all cancel out as long as you are in the inside.

As for the distance, as long as there are no other stronger gravity pulls (i.e.: from a galaxy, or nearby black hole) the planets will eventually collide. It's just a matter of time. Depending on the distance between them it could be seconds or a time longer than the current age of the universe. This is not a good way to ask this; Rather, calculate in how much time they will collide based on a given distance, then adjust as much as you like. The formula for the force of attraction due to gravity between any two bodies in space is:

$$F = G\frac{m_1m_2}{d^2}$$

Where $F$ is the force, $G$ is the gravity constant, $m_1$ and $m_2$ are the masses involved and $d$ is the distance.

And the formula for acceleration, time and distance is:

$$s = v_it + \frac{at^2}{2}$$

Where $s$ is the distance, $v_i$ is the initial speed, $t$ is the time, and $a$ is the acceleration.

Also remember that $F = ma$.

If the distances and speeds are too great you may need to add relativity into your process.

Answer 3

According to the Shell Theorem, a spherically symmetric hollow sphere will always have zero gravity inside, so the people experience no gravity at all, unless they live on the outside or within the shell itself (where gravity will linearly fall off going inside).

On the outside, gravity will be far below earth normal, because a hollow sphere of earth mass will necessarily have a larger diameter than earth.

Any two masses will, without outside influence, always attract each other, and, falling in from "infinity", crash with their combined escape velocities. So, the answer to pt. 2 is, any distance but directly touching will be catastrophic, and even when touching standing still, the gravitational stresses will probably squish them.

Answer 4

So the short answer is that any hollowed out object no matter how big will have zero gravity on the inside (even with an atmosphere on the inside).

And no matter how distant the two structures are, over a LONG period of time, they will eventually impact each other.

Thanks for you help.

Answer 5

1. It depends upon the the contents of the structure, but the shell will not exert any net force on objects inside. but as you go down towards the centre the gravitational force would decrease proportionaly.

2. If the bodies are stationary with respect to each other then there is no safe distance, it would just be a matter of time. That could even be millions of years if the distance was great enough but there is no totally safe distance.

If the bodies are moving with respect to each other and in a stable orbit around their common centre of mass then they could approach very closely indeed. Depending on the exact structure almost to touching, although this would be highly dangerous as slight mass shifts such as people and equipment moving around inside would be likely to destabilize the system leading to a catastrophic collision and total destruction of both structures. Better to have them thousands of miles appart.

Answer 6

Let's make your planets more complicated:

Each one is a hollow sphere, but with a sphere of inside it. Think tennis ball inside a softball, but probably closer in size.

The shell then has the job of contain the atmosphere.

This allows you do do some cool things:

• The visual distance in air at sea level pressure is 50-100 miles max. So if the space between the planet and the shell is more than 100 miles, it has no distinguishable features.

• If you make the planet small enough, people have a high enough strength to weight ratio to fly. Or dragons can fly more realistically. Low gravity makes all sorts of interesting thing: Waves move more slowly. While you can carry more, you still have momentum. You have to lean in to corners. Traction is a problem.

• Living inside a ball you have problems of illumination. If you are a light year from the nearest star, even a regular planet gets cold. Make the shell out of a lattice of carbon nanotubes and diamond windows. Or make it from scrith -- the material used by Niven to build the Ring World.

• Not sure how weather would work. You would still have a gravity gradient and a temperature gradient, but essentially no vertical pressure gradient.