# Would a spacecrafts artificial gravity give it an atmosphere?

Artificial gravity is a staple concept of science fiction. Not much focus is ever put into explaining it for time and convenience as it would distract the audience from the story. Realistic sci-fi commonly uses centrifugal force to get their gravity while others prefer the good old gravity generator. The latter only affects the inside of the ship for some reason. You can tell that as a writer I’m quite discontent with that logic.

With that in mind my spacecraft has a gravitational center that generates an earth like pull of 1g (9.8 m/s²). Due to the pull being unidirectional the ship is designed accordingly, with no true up or down meaning you could walk on opposing sides of the ship. This system is only used in deep space to avoid messing with any planets gravity and causing unwanted harm. But the thing I’m wandering about is if the ship would end up with its own mini-atmosphere due to the gravity pulling in gases. A small percentage of the exhaust fumes could end up wafting around the hull (mine uses hydrogen plasma as a propellant). It would by no means be enough to stop debris from hitting the ships hull and probably won’t be breathable either. Things might even start orbiting the ship.

This raises many questions about how the gravity would work. Would these things happen? Would they be an issue? Is it just an asset in disguise?

• As far as I know a gravity force is inversely proportional to the square of the distance. Suppose your gravity machine acts like a point mass in space. On a small distance, the mass causing the gravity can be smaller. The gravity machine of your ship should support that. Suppose it does, the smaller your ship, the less harm it will do to the surroundings and the denser your artificial mass needs to be. A relatively small but very dense artificial mass is sufficient, to cause earth-like gravitation on that distance. On a distance in space, affecting surroundings, the mass could be irrelevant. Sep 18, 2021 at 23:11
• consider your ship might end up quickly surrounded by a dense field of exhaust gasses, particle collision will rob a decent amount of your exhaust gasses of sufficient velocity to escape.
– John
Sep 18, 2021 at 23:32
• @John if they have artificial gravity, they might not have exhaust fumes. Sep 19, 2021 at 0:46
• How big is the ship? Sep 19, 2021 at 0:51
• Just a note, but 9.807 m/s^2 is absurdly specific. Gravity can vary by as much as 0.5 percent across the surface of the earth, so using more significant digits than 9.8 m/s^2 is only useful if you want to describe the gravity in a specific place or area. Or is 9.807 a rounding of the "standard gravity" of 9.80665? Sep 20, 2021 at 10:19

## Yes it could.

If your gravity is 1g around a 'gravitational centre', presumably your ship is a sphere, so your crew and passengers are being pulled at 1g to your 'centre'. Could in fact your spaceship be a planet?

If it is physically smaller than a planet, then the radius determines how much 'artificial gravity' you need, or does it? An ultra dense material would create a gravitation field with a 'centre', and perhaps a small black hole would also accomplish what you seek. These are known concepts so do not necessarily require your 'artificial gravity' to exist.

Say your ship is 50m in radius, the mass of your 'gravitational centre', using Newtons equation your centre needs to have a mass of 367 x 10^12 kg's, so that a 70kg person feels a 1g pull on (let's call it) Deck 01.

Of course, this would also form an 'atmosphere' as it pulls any floating particles around it towards it too, and the fall off would be similar to planet Earth's, as the rate of fall off is a simple relationship to radius. For all intents and purposes then, it is a 'mini-Earth'. Keep in mind though that the pressure is not, unless you want it to, and you could have a mini-Earth with hardly any atmosphere (such as mercury or mars).

However, moving your spaceship is a variable you must consider. If your ship suddenly accelerates to a new speed, it is easily conceivable that your atmosphere will not come along with the ship as you would want depending on your speed. This also affects your passengers and crew - your ship may not be as useful as originally thought.

Also, moving your ship through a typical solar system will affect orbits of other planets - imagine having all the effects of moving the Earth around, but just one that has a small physical size. It could be quite disruptive.

• Your last paragraph is inaccurate, at least for the size of ship you hypothesize earlier in your answer (367 x 10^12 kg). The mass of the Earth is ~5.972 × 10^24 kg, which is many orders of magnitude higher. Even the [estimated mass of the Chicxulub meteor, 6.82×10^15 kg, is an order of magnitude higher. The ship you've hypothesized is equivalent to a medium size asteroid, so it moving around the solar system for "normal operations" will have little or no impact on the planets. Sep 19, 2021 at 19:52
• @Makyen - That depends on how the ship generates the gravity. It's possible that the ship has an effective mass of a planet, which would. Sep 19, 2021 at 22:33

No. The problem is that holding onto atmosphere is not a function of the gravitational field, but of the escape velocity.

In a normal planetary situation escape velocity and gravity are related--a planet with Earth-normal gravity will have no problem holding an atmosphere unless it's roasting.

However, in situations like this the relationship is severed. Your ship has 1g on the surface but the gravity drops off much faster than on Earth--the atmosphere departs quickly.

If I haven't dropped a zero somewhere: 100m radius with 1g at the surface has an escape velocity of 140 m/s. Oops--the average particle (all the important ones are reasonably close in mass) in Earth's atmosphere is moving 500 m/s. Your atmosphere departs nearly instantly.

Size and weight of the ship

Below answer assumes the artificial gravity behaves as a point mass in space, keeping the spherical ship's human inhabitants residing on the surface upright, with comfortable Earth-like gravity. It also assumes the ship is quite big, that is a several hundred meters in diameter. This is to prevent dizziness and balance issues for people, when walking around on the ship.

Suppose the ship is sphere-shaped, then its surface is proportional to R squared, like gravity is proportional to R squared. Consequently, if you know the diameter of the ship, a simple linear scaling can be used. The weight of the ship would be earth's mass times the surfaces divided.

Calculation example: Take earth's mass 6e24 kg, times the ship's surface in m² divided by earth's surface 5.1e14 m². If your ship is 400 meters in diameter, its radius is 200 meters.. the ships surface will be

4π * 200m * 200m = 502.654 m²

The weight of the ship will be earth mass times surfaces ratio,

mShip = 6e24 * 502.654 m²/ 5.1e14 m² = 6.0e15 kg

On 200 m distance from center of this mass, the ship's inhabitants will feel Earth gravity. An outside observer will feel the gravitational attraction also. This amount 6e15 kg seems a lot, but it is about the same mass of the asteroid that killed the dinosaurs (6.82e15 kg) . So the ship, as an object, will not relevantly affect anything far in space.

Atmosphere

Anything about 200m distance will feel the same gravity as humans on earth, so when gases are released, they will stay as easily near the surface as would happen on Earth. It won't be a thick atmosphere though.. the nearer the central point of gravity will be, the steeper the gradient of gravity decay near that 200 meters. But suppose the atmosphere would hold about 1000 meters thickness, I did not calculate that, but it may be enough to breathe in and keep an ecosystem alive. The ship will also attract near dust and particles, and near asteroids..

But.. how to travel ?

So far so good, a little dust won't harm. Only trouble is.. how to move a ship like this ? the energy required would be enormous.

• Idk the reason for downvote, but calculations are not wrong, it flow of gravitional field trough enclosed surface, and equilibrium of density of field trough those surfaces Sep 19, 2021 at 10:55
• Atmosphere part however take look at Loren answer. Also if you do not worry which kind of black hole holds that mass and not dive in black hole matter then that move energy problem probably not worty of mentioning. Sep 19, 2021 at 11:04

Remember Oumuamua

Darrel S Rivers 2021, via technostalls.com, fair usage.

Well, the humble caddisfly larva has a neat trick to hide itself from hungry dragonfly larvae and fish:

Joyce Gross 2021 fair usage.

Of course the tube is open at both ends to allow feeding and respiration at the tail end. I figure your ship should be able to navigate, and propel itself equally.

As pointed out in the comments, gravity decreases according to the inverse of the square of the distance, meaning - well it depends how your gravity system works.

If you want the effect of a cocoon, then you can just say it's residual effects from "gravity leak" around the hull, the effect could be quite weak. This would naturally mean that to hold on to the camouflage, no sudden maneuvers or strong acceleration can be attempted. If the effect is intentional and under control, then its strength is up to what the crew can endure.

It could also have the advantage off protecting the ship from meteor showers, debris fields that must be traversed and coronal mass ejections that might otherwise cause severe issues (in the latter case, it'd still be wise to switch-off all the electrics 'till it passed).

As to an atmosphere, you'd need to wack the field-strength way up (to lethal levels) to hold onto anything with a vapor-pressure. A solution might be to release a cloud of water micro-droplets. It wouldn't give you anything breathable, but it would make you look like a comet, with the mist being blown in a trail away from the nearest star.

• It is definitely no good me writing answers when I'm half asleep, thanks @MolbOrg Edited. Sep 19, 2021 at 13:58

According to Habitable Planets for Man, Stephen H. Dole, 1964, a planet needs an escape velocity several times as great as the average speed of atmospheric particles in order to retain them for geological periods of time.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

According to table 5 on page page 35, the ability to retain atmospheric gases depends on the ratio of the escape velocity to the root-mean-square of the velocity of the atmospheric gas particles.

Where the ratio is 1, the lifetime of the atmosphere is zero. Where the ratio is 2, the lifetime is zero. Where the ratio is 3, the lifetime is a few weeks. Where the ratio is 4, thelifetimeof the atmosphere is several thousand years. Where the ratio is 5, the lifetime of the atmosphere is about a hundred million years. Where the ratio is 6, the lifetime of the atmosphere is infinite.

Of course your spaceship might not operate for geological periods of time, so a ratio of 3 or 4 might be sufficient tor the duration of the story.

Note that the ratio is the ratio of the escape velocity and not the surface gravity to the root-mean-square of the velocity of atmospheric particles.

The planet Earth has a surface gravity of 9.80665 meters per second per second,or 1 g, and an escape velocity of 11.186 kilometers per second.

The planet Jupiter has a surface gravity of 24.79 meters per second per second, 2.527 of Earth's, and an escape velocity of 59.5 kilometers per second, 5.319 of Earth's.

The moon Io has a surface gravity of 1.796 meters per second per second, 0.183 of Earth's, and an escape velocity of 2.558 kilometers per second, 0.228 of Earth's.

The moon Europa has a surface gravity of 1.314 meters per second per second, 0.134 of Earth's, and an escape velocity of 2.025 kilometers per second, 0.181 of Earth's.

The moon Ganymede has a surface gravity of 1.428 meters per second per second, 0.146 of Earth's, and an escape velocity of 2.741 kilometers per second, 0.245 of Earth's.

The moon Callisto has a surface gravity of 1.235 meters per second per second, 0.126 of Earth's, and an escape velocity of 2.440 kilometers per second, 0.218 of Earth's.

Compare the ratio of each object's surface gravity compared to Earth's, and the ratio of each object's escape velocity compared to Earth's. Those two ratios are not the same for any of those five objects.

The surface gravity and the escape velocity are two different things and there are different formulas to calculate them.

https://en.wikipedia.org/wiki/Surface_gravity

https://en.wikipedia.org/wiki/Escape_velocity

So to form an atmosphere outside the spaceship, it needs an artificial escape velocity generator instead of an artificial gravity generatior.

Fortunately, it seems reasonable that an artificial gravity generator would vastly increease the otherwise insignifcent escape veloity of the spaceship as a side effect.

If you calculate the mass that a spherical object with the radius of your spaceship would have to have to have asurfucae gravity of 1 g at its surface, you can assume that your super scientific gravity generation somehow simulates the effect of having that much mass at the center of your spherical spacehip.

And that amount of simulated mass should presumably be used to calculate the escape velocity at various distances from the center of your presumably spherical spaceship. And thus you should be able to calculate the escape velocity at the surface of your spaceship, and at twice the radius of your spaceship, and at four times the radius of your spaceship, and so on.

And the strength of the escape velocity created as a side effect of your generated gravity shoud quickly fall off with multiples of the radius of your presumably spherical spaceship. Unles it is a supergiant spaceship like the Death Star or the Skylark of Valeron.

So whenever some of the atmosphere gets more than a few meters or kilometers from the surface of your spaceship - depending on the size of the spaceship - it should be travelling several times as fast as the escape velocity of at that distance and should escape very rapidly.

I also note that the solar wind includes fast moving particles which strike the upper atmospheres of astronomical bodies and knock atmospheric particles away from the planets, gradually eroding their atmospheres. Having strong planetary magnetic fields deflectes those charge particles away from the atmosphere and protects it from that process.

So if your spaceship retains atmosphere for a long time, it should generate a strong magnetic field for some reason which also protects the atmosphere around the spaceship. Possibly the magnetic field would be used to deflect charged particles and keep them from penetrating the ship's hull and harming the crew.

Or the spaceship could always operate far enough from the nearest star that the solar wind would deplete the spacehip's outer atmsophere much more slowly than particles escape from it anyway, and so is not a major factor in atmospheric loss.

So how would such an atmopshere be produced. If the ship's hull leaks, theleaking atmosheric gases might be trapped inside the outer atmosphere by the generated gravity. It would be a badly designed spaceship which leaked air fast enough to form a breathable atmosphere outside it.

And I doubt if a spaceship advanced enough to have generated gravity would use rockets, except for very advanced a powerful rockets.

A powerful rocket would work one of two ways. It would either::

A) Expel a lot of particles at rather slow speeds. But those rather slow speeds might be several times as fast as the escape velocity resulting from the genrated gravity. I think that they would have to expel matter faster than the escape velocity in order to move the spaceship while the geneated gravity was turned on. Thus such rockets couldn't produce an outside atmosphere for the spaceship.

Or:

B) Expel a small amount of particles at very fast speed, like ion engines. Those particles would certainly be travelling many times the secape velocity and would certainly all escape. And such small amounts of particles would certainly not accumulate to make a noticeable atmosphere around the spaceship.

In the Star Trek episode "Obsession",15 December 1967:

SCOTT: Captain, while we're waiting I've taken the liberty of cleaning the radioactive disposal vent on number two impulse engine, but we'll be ready to leave orbit in under half an hour.

And:

KIRK: Scotty, try flushing the radioactive waste into the ventilation system. See what effect that has.