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Author Topic: How much compacted mass is needed to simulate Earths gravity?  (Read 3922 times)

Offline McKay

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If I want my spaceship to have Earth-like gravity for its inhabitants and I figure I could make the floor (or something under the floor) out of very dense matter, perhaps I figure out how to make stable neutronium, - how much mass I would need to concentrate under the floor to have a gravitational attraction, similar to Earths, just meters or few dozen meters away from the spaceship mass center?
First I thought I need a mass the same as the mass of the Earth, but then I realized - everything could get much closer to the concentrated mass center and the required mass would be much less..
Perhaps it might actually be feasible, if we figure out how to get stable super compressed matter, to concentrate the mass of a asteroid in the floor of a spaceship. A large spaceship..
What do you think? How can I/ we calculate.. ?
« Last Edit: 04/06/2014 10:49:47 by Georgia »


 

Offline CliffordK

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Re: How much compacted mass to simulate Earths gravity
« Reply #1 on: 08/05/2014 18:46:33 »
One of the early criticisms of the supercolliders was that they would create mini-black holes, with a density great enough that the escape velocity was greater than the speed of light, but with an event horizon less than a fraction of an angstrom from the center. 

As the gravity is proportional to the square of the distance, you would have a very strange situation indeed if you could make your feet experience 9.8 m/s2 acceleration, but your head experiencing essentially no gravity.

So, I think you would first need to determine the desired acceleration at the surface, 1m, & 2m. 
 

Online syhprum

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Re: How much compacted mass to simulate Earths gravity
« Reply #2 on: 08/05/2014 20:09:41 »
I see a big problem any ball of Neutronium of sufficient mass to provide 1 g acceleration say 100 meters away (to avoid spaghettifying problem) would have a very large surface temperature due to Hawking's radiation and probably a short life.
 

Offline evan_au

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Re: How much compacted mass to simulate Earths gravity
« Reply #3 on: 09/05/2014 11:42:24 »
Take Newton's gravitational equation: F=GM1M2/r2
  • Rearrange a bit, and you have M=9.8*r2/G
  • Plug in G=6.70E-11 NĚ(m/kg)2
  • Pick a distance like r=10m (so the gravity on you feet is not so different from the gravity on your head)
  • You need M=15 billion tons (if I've done the math correctly).
  • To get an image of how massive this is, it is a cube of water 2.5km on each side.

Given the cost of fuel to power a spaceship, I am sure that there are solutions that are at least 14 billion tons lighter, like:
  • Keep your spacecraft always accelerating at 1g=9.8 m/s (automatically provides the same force on your head and feet)
  • Build a rotating section in your spacecraft (as in "2001 Space Odyssey"). The acceleration is a bit different between head and feet, but not very noticeable if the spinning section has a radius of 10m

Quote
a very large surface temperature due to Hawking's radiation
I understand that Hawking radiation is only a problem with black holes(?)
Neutronium/Neutron stars should not emit Hawking radiation - but you may need to wait an impractically long time for it to cool down from the supernova you would need to create it.

Quote
probably a short life
15 billion tons of neutrons may not be stable, as the surface gravity may not be enough to stop neutrons disintegrating to a proton + electron + neutrino, which might then exceed the escape velocity, causing the neutronium to evaporate over time: you would be sitting on a neutron bomb..
« Last Edit: 09/05/2014 11:52:34 by evan_au »
 

Online syhprum

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Re: How much compacted mass to simulate Earths gravity
« Reply #4 on: 09/05/2014 17:07:02 »
Would 10M be far enough away ?  being 1.83M tall I feel there would be quite a disturbing effect due to the difference in gravity between my head and my feet.
Not being very well informed as to the properties of Neutronium I assumed it was similar to a black hole for my next project I will specify a mini black hole  which will be compact but the radiation may well be a problem
 

Offline ScientificSorcerer

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Re: How much compacted mass to simulate Earths gravity
« Reply #5 on: 09/05/2014 23:09:10 »
wow that's a lot of tons. But the guy made a very interesting point, you could probably figure out how to make "artificial gravity" through rotating the ship (space odyssey) OR you could go with a different approach  which many people overlook.

For example, why not make a superconductor semi-perminant electro-magnet locked in persistent mode in-order to generate powerful a magnetic field, then wear a shiny jump suit made of mostly aluminum but with small "ferromagnetic" impurities.  This suit would be able to be attracted to the super-strong magnet (located under the floor) slightly. But considering that superconductors can circulate incredible current densities in persistent mode that can generate magnetic fields upward of 36 teslas of magnetic strength, you might want to be careful around something that powerful.

as an added bonus the superconductor magnets would be powerful enough to protect your space craft from solar radiation in outer space and act as ridiculously powerful batteries.

space ship with superconductor electromagnets would automatically get
~artificial gravity
~shields
~batteries

not a bad deal if you as me.

look at this link of one
http://www.ubergizmo.com/2011/07/worlds-strongest-magnet/
« Last Edit: 09/05/2014 23:45:24 by ScientificSorcerer »
 

Offline CliffordK

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Re: How much compacted mass to simulate Earths gravity
« Reply #6 on: 10/05/2014 01:47:10 »
  • You need M=15 billion tons (if I've done the math correctly).
  • To get an image of how massive this is, it is a cube of water 2.5km on each side.
Thanks, Evan,

Except, of course, the 2.5 km ball of water would have to squished into something where the center of mass was less than 10m away.  Would you make a small ball shaped mass, with a spherical space ship oriented around it?

As far as a magnetic field.  The human body is mostly water, and water is diamagnetic.  So, technically it would be repelled by a large electro magnet (which one could install on the ceiling).  Apparently experimenters on Earth have been able to 100% counteract gravity to levitate frogs with strong magnetic fields, ie applying 1G upward force on them.



However, it would take a much larger and stronger magnetic field to do so to humans. 

Nonetheless, a magnetic field suffers by the same square of the distance issue as gravity.  So, if you magnetized your deck plating, then had everyone wear a medieval set of armor, the feet would stick soundly to the deck, but you wouldn't feel it in your head. 

The gravity differential may not be a big issue, but there are notes that many aspects of the human body suffers in zero-g environments.  Gravity clothing may not be sufficient to get the benefits of a gravity environment.

Centrifugal force artificial gravity may suffer from issues such as dizziness or a gravity differential with a small ring, but it should be relatively comfortable and functional if the ring was large enough.
 

Offline dlorde

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Re: How much compacted mass to simulate Earths gravity
« Reply #7 on: 10/05/2014 12:02:46 »
Centrifugal force artificial gravity may suffer from issues such as dizziness or a gravity differential with a small ring, but it should be relatively comfortable and functional if the ring was large enough.
Yes, there is a problem with coriolis forces causing dizzyness and nausea at more than about 2 rpm. So to produce 1g, the radius of rotation would have to be 224 m (735 ft) or greater, which really means using a tether system rather than a ring.
 

Offline McKay

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Re: How much compacted mass to simulate Earths gravity
« Reply #8 on: 14/05/2014 16:40:35 »
Well, ok, neutronium might not be stable, but just for the sake of the discussion, we assume we have figured out something super dense (and stable, safe).
15 billion tons may not be well suited for a Tie-fighter or something, but, perhaps, for a generation ship or a cosmic outpost.. ?
Someone said 10 meters, someone said 100 meter distance would be required to avoid drastic effects of gravity differential - which one is it? What would be an optimal mass of the core/ floor distance from the core (a spherical spaceship enveloping the core would be logical)?
 

Offline CliffordK

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Re: How much compacted mass to simulate Earths gravity
« Reply #9 on: 14/05/2014 22:06:28 »
Say you decide to make a spherical mass.
For example in Evan's example, 10m radius, 20m diameter, & 15 billion tons.

The effect would be identical if you had a space filling sphere 20m in diameter which you stood directly on the surface vs a super dense 1cm sphere, inside of a hollow sphere 20m in diameter.

The sphere diameter depends on how large of a head/toe differential you find acceptable.  For a 10m sphere, your toes would be approx 10m from the center, and head at 12m, giving a differential of 100:144. 

For a 100m sphere, your toes at 100m, your head at 102m, for a differential of 10,000 : 10,404.  But you would have to carry around a mass 100x as heavy. 

A centrifugal accelerator of 100m or greater would likely be comfortable, and much lighter. 

Acceleration, deceleration, and a number of other issues would be a major problem when towing along such a heavy mass.

The only reason to carry such a heavy mass around would be if there was some secondary benefit, for example the ability to consume the mass for manufacturing, or energy production, which might leave one with less of a mass for generating the gravity over time.
 

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Re: How much compacted mass to simulate Earths gravity
« Reply #9 on: 14/05/2014 22:06:28 »

 

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