[bizerl (OP)]

I was listening to the ask TNS podcast recently where Ben was discussing the tremendous pressure air puts on us at all times. It made me wonder:
a) would our weight change on a atmosphere-less Earth? and
b) would it be possible to simulate some sort of "gravity" on a space ship by somehow increasing the air pressure on top and decreasing it below.

Actually, just thinking about this as I type, that would just be a really big ceiling fan for a space ship. So now:
b)i) would a really big ceiling fan on a space ship put enough pressure on bones to reduce the osteoporosis (spelling?) suffered by astronauts?

[syhprum]

Although a blast of air sufficient to replace gravity would not be very useful on a space ship it might be a good idea to have a gentle breeze that would move airborne trash down to the "floor" something more subtle than a ceiling fan a system more like they have in a clean room.
As for our weight if there was no atmosphere to provide a degree of buoyancy we would weigh about 0.125% more.

[evan_au]

a) would our weight change on a atmosphere-less Earth?

Yes. If you weigh (say) 70kg on Earth, your volume will be about 70 liters.

• Air is about 80% N₂ (28g/mole) and 20% O₂ (32g/mole), an average of 29g/mole.
  
• A mole of air takes 24.8 liters at 25C.
  
• Your body displaces 2.8 moles of air, or about 82g of air.
  
• So if you weighed yourself in a vacuum, you would weigh about 70.082kg (until the moisture started boiling out of your lungs).

So, yes you would weigh more on an airless world, but only by 0.1% - not by enough to make a significant difference.

b) would it be possible to simulate some sort of "gravity" on a space ship by somehow increasing the air pressure on top and decreasing it below.

Astronauts often get puffy faces, because gravity is not pulling the fluids down to their feet. You could reduce this effect by putting their legs and lower torso in a reduced-pressure container.
On the other hand, pilots in high-G maneuvers often black out because all the blood rushes to their feet, starving the brain. This is counteracted by having an automatically-inflated pressure suit which squeezes the blood out of their legs.

However, the pressure from air blowing on you from a fan would not replicate the 70kg of weight your legs and spine would be supporting if you were on Earth. It would take hurricane-force winds which on Earth would blow you off your feet, or allow you to do indoor skydiving in a vertical orientation. Very noisy, and very power-hungry!

So, No, a fan is not really practical to prevent osteoporosis.

You would be better to use a pneumatic exercise machine which squeezes air from a cylinder through a valve, allowing you to lift with your legs and arms, allowing you to apply a force equivalent to your full body weight on Earth.

[evan_au]

PS: The force exerted by gravity is proportional to your mass, and independent of your orientation. This force is most spread out (lowest pressure) when you are lying down. So when you are ill, you can rest by lying down.

In contrast, the force exerted by wind from a fan is independent of your mass, but proportional to your area perpendicular to the airflow. So if you wound up the wind speed to provide 70kg of force when standing, the force would be perhaps 4 times higher when lying down. You would not be able to get up.

Even worse, if you started to fall, your area would increase, which makes you fall faster, resulting in a body-slam that would be worse than falling on Earth. Not good for an astronaut who spends most of the day in weightlessness!

A problem with most of these schemes for countering weightlessness is that they apply the same force to your whole body, placing excess strain on your back, and insufficient force on your legs. On Earth, your feet carry your whole weight. Your waist carries only about half your weight, your spine & shoulders carry even less. So the force should be graduated, and some applied from the waist down.

At this point in time, we are still not much better at preventing osteoporosis in space than the centrifugal force method envisaged by Arthur C Clarke in the book/film "2001: A Space Odyssey". Unfortunately, this requires building a space station and a spacecraft much larger than anything humanity has attempted to date.

[Pmb]

I was listening to the ask TNS podcast recently where Ben was discussing the tremendous pressure air puts on us at all times. It made me wonder:
a) would our weight change on a atmosphere-less Earth?

In principle, yes. The atmosphere presses on us from all sides with a force of 15 lbs/sq. in. However there isn't a vacuum under our feet so that there is a force pushing us uip too. If we stook out the air between our feet and floor we should weigh more ... I think. 

Note that when nobody is standing on the bathroom scale the atmospheric pressure is still pressing down on it.

and
b) would it be possible to simulate some sort of "gravity" on a space ship by somehow increasing the air pressure on top and decreasing it below.

If there is air in the cabin then it presses on us from all sides. Here there is no gravitational force pushing us down.

Actually, just thinking about this as I type, that would just be a really big ceiling fan for a space ship. So now:
b)i) would a really big ceiling fan on a space ship put enough pressure on bones to reduce the osteoporosis (spelling?) suffered by astronauts?

It wouldn't work. It'd have to be like a hurricane wind in force.