## 2017-04-05

### Gravity plating

In sci-fi there is artificial gravity.

But it occurred to me gravity is more complex that just saying the "gravity plating" on your Starship Enterprise is set to 1g.

1g, or 9.80665ms2 is the nominal average on Earth. It is a result of being 6371km (ish) from a centre of gravity of a mass of 5.972 × 1024 kg.

Basically the force is based on a constant times the mass of each object divided by the distance squared. So the force per mass of the object on the surface (i.e. you) is based on this constant times the mass of the earth divided by the radius squared.

But you get the same end result if the mass of the planet on which you are standing is much higher and the radius much lower. If you stood on a super dence object only 1km wide you could experience 1g.

There is a difference though, now your (near) 2m height means that the radius is noticeably different when considering the gravitational force at your feet and your head. You would feel the difference I expect! If you jumped in the air you would quickly have much lower gravitational force - reaching escape velocity would be way easier, surely?

Take it to the extreme, a 1m radius object with enough mass to be 1g at your feet, what is that at 3m from centre of gravity, 1/9th g? Light headed or what - jump and you are gone!

So the gravity plating on starships is not just a matter of being 1g, it is also about the apparent distance involved, surely. But the gravity is not exerted much beyond the ship, if at all. Lots of episodes show this, so it must be the like 1m radius Earth... Emulating a super dense but small structure.

Do all star trek people get used to being so light headed?

If we lived in such a world, would we evolve to be midgets?

These are questions we need to ask, people...

P.S. As per one of the comments, creating gravity by spinning part of the ship has the same issue. You can have a small radius spinning fast or a large radius spinning more slowly. The effect will be 1g at your feet but the change in gravity at your head would depend on the radius. I really had not though that gravity at a point in space has both a force and a rate of change like that, but it is obvious when you think about it! It also means that gravity because you are simply in a box that is accelerating is different yet again, indeed, you should be able to detect that this is not the same as gravity on earth, from inside a sealed box, even if you measure 1g, because it is not different at different heights in the box.

1. There's another possibility: the inertial dampers show that they have a way to imitate the effects of acceleration (so as to cancel it out). Acceleration is indistinguishable from gravity. They just need to fake acceleration at 1g towards your head, and oh look gravity, no tides.

(See also the McAndrew stories by Charles Sheffield, which feature a 'balanced drive' which produces exactly this effect, cancelling out acceleration using no super-physics, only ordinary gravity and the ability to create plates of matter a few thousand tons per mm^3 -- if you ignore the super-physics required to get something weighing several trillion tons to move at all.

2. The new generation of space ships in movies with a spinning bit around the main body, is actually quite plausible. A 50m disk would only need to revolve at 2rmp to simulate gravity

3. The other classic story for this sort of thing is Larry Niven's Neutron Star.

matbed: I fear your calculation is incorrect. a=rω² so for 1 gravity at 2rpm (about 0.2 radian/second) you need a radius of 223m. The faster you spin (in order to get a smaller habitat) the more gravity gradient you get between head and feet, the more the spin will be perceived as spin rather than gravity, and the more coriolis forces will confuse the occupants.

1. Yeah quite probably i misremembered and it's 20rmp for the 50m diameter, rather than 2rpm

4. I have a few physics textbooks you could borrow if you like :)

A 1 m sphere with a surface acceleration due to gravity of 9.81 m/s^2 would have a mass smaller than the Earth's, so yes, escape velocity would be lower and it would be easier to escape. Since escape velocity is the velocity an object at a given radius from an object needs to escape that object, the higher you start the lower the escape velocity. So by saying "If you jumped in the air you would quickly have much lower gravitational force - reaching escape velocity would be way easier" you're just saying that once you've jumped half way you don't have as far yet to go.

For gravity plating the actual result is interesting, and exactly the opposite of your conclusion. All of what you've discussed is related to the gravitational field around a spherical massive object. If you have an infinite massive plane the gravitational field is uniform, so the force due to gravity is constant anywhere above or below the plane, at any distance (http://www.mathpages.com/home/kmath530/kmath530.htm). For a finite plane the same would be true to a reasonable approximation while near to the plane. With dense matter as gravity plating your spaceship would be fairly heavy, so its acceleration would be awful :).

I think my favourite result in physics is that the gravitational field at any point inside a massive uniform sphere at distance r from the center is the same as it would be on the surface of a sphere of the same density with radius r. Or in other words, as you descend in a tunnel towards the centre of the Earth, the gravity of all of the matter in the shell above you balances out, so you're only feeling gravity due to the sphere beneath your feet.

5. What Simon Key said.

6. You missed the minus sign on the 2 or the division operator after the m.

7. Plenty of artificial gravity stuff in the book series The Expanse by James SA Correy. Dismissing the one "extraterrestrial technology so advanced it's like magic to dumb mammals" case, there are two realistic situations in the books:
- downward pull on objects in a ship created by acceleration of said ship (so not just moving fast, but moving faster. Cruising at constant speed leaves you free floating)
- a spinning object, like part of a big ship, a space station or a small celestial object sent spinning. That gets you a pull down, but it has a couple of drawbacks depending of how close you are from the center of spin (i.e. depth within the object, usually). The pull will be stronger or weaker depending of your proximity to that of course, but there's also the Coriolis that applies, with some levels in the object where things get a disconcerting sideway pull (think water from tap falling diagonally).

I warmly recommend the books, but the TV series is nice too :)

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