Say you’ve got an object floating in water, like a wooden boat. The waterline is marked (Plimsoll marks, or just paint it at the waterline.)
Now take the bucket of water and the boat and everything to the Moon. Will the boat float higher, lower, or at the same level?
If you were in a swimming pool on the Moon, would you float higher, lower, or about the same? Would it be more difficult to dive down to the bottom of the pool? Would you natural buoyancy be enhanced, or reduced, or about the same?
(Research for a sci fi novel. But also naturally curious! Thank you, all!)
(My instinct is that the boat floats at the same level, and that swimming is really pretty similar to swimming on earth. The water weighs less…but so do I…so it still takes about the same amount of exertion to swim down to the bottom of the pool. Amirite?)
First of all - any water taken to the moon will boil off almost instantly !! due to the low pressure.
So assuming - you create an artificial atmosphere around a swimming pool or your container. The buoyant force on you (and the boat) is (rho1 - rho2)gv . Since there is the g term - your buoyancy will be significantly less on the moon and you’ll sink more (so will the boat).
The OP is correct. Archimedes principle works just as well on the Moon. Yes the buoyant force of the water is less, but so is the force of gravity on you and the boat. You and the boat will float at the same level as on Earth.
On second thought, I stand corrected. Although I note that this will be the case for static equilibrium - a small force on the boat will sink it downwards and it will take a longer time to come to equilibrium or even topple over more easily.
So it is, in fact, easier to swim to the bottom of the pool?
Are you sure about the toppling effect? Why would the critical “heeling angle” of a boat change, if the weight of the boat and of the water change in the same proportion?
But it seems that my main question has been answered: the boat (or a person floating) floats at about the same level, not “higher in the water.”
If, though, it is easier to swim downwards…or easier to be pushed downwards, then swimming would feel slightly less secure, wouldn’t it? As if a careless swimming stroke might put you deeper below than you thought?
Thank you for any and all advice, science, and scientific opinions! (Now we just gotta build a resort hotel on the Moon, with a really big swimming pool!)
Put it this way: An object with half the density of water will float half submerged. Or for any density, really: The portion submerged is equal to the ratio of densities.
And all of the out-of-equilibrium motions will also be the same, aside from a sqrt(g) scaling on the time. Take a video of the boat rocking on the Earth, slow it down, and it’ll be indistinguishable from the boat rocking on the Moon (so long as there aren’t any other time cues, like moving animals).
The maximum force an animal can exert, meanwhile, does not scale with gravity, so a human on the Moon can jump higher and dive deeper than on the Earth.
I am not sure that is true. First of all - water or waves breaking off the sides of the boat will go 6 times higher than on earth. Also - theEötvös_number will change significantly since the surface tension to gravity ratio changes and water drops splashing will be bigger from waves etc.
The density of the water will decrease ever so slightly, though, due to the fact that the water would be under slightly less pressure because of the lower gravity. It would be a minuscule, minuscule effect, and easily swamped by variations in the air pressure at the surface, but all other things being equal it would cause the boat to float ever so slightly lower.
Yeah, I was thinking after I posted that that I ought to clarify that that was assuming an ideal fluid, with zero viscosity, surface tension, etc. Wave height, though, wouldn’t be a giveaway, since you can have big or small waves on Earth, too.
Not only that, but you don’t have to equalize your ear pressure as quickly either.
Here on Earth, I have to equalize my ears by 6’ depth or earlier, to avoid an unpleasant but minor sharp pain when they pop. At about 30 feet, the pressure is doubled.
On the moon, the gravity is IIRC 1/6 that of Earth. So, if I’m guessing the math correctly, I wouldn’t need to equalize my ears until about 36 feet. Yay, since it’s such a nuisance to remember to equalize in the very beginning of a nice jackknife dive.
On the other hand, it seems to me that a jackknife dive will be a lot slower on the moon, too. Oh darn. Now I’m suspecting that a jackknife dive won’t take me as deep as it would here on Earth.
Not so fast. Here are some other things to think about relevant to swimming in low gravity :
1> Fluids : The behavior of fluids in low gravity is contrary to our expectations. For example - if you light a match in low gravity (assuming the same atmosphere and pressure as earth), the flame will be very spherical and it will quickly extinguish itself because the buoyancy of the combustion products is not the same as on earth. Surface tension of water will make it “feel” more elastic at the surface; it will rise up onto the sides (capillary effect) and get into places it did not on earth - like your ears and nose. Water will not splash the same way on earth when you drop it either.
2> The Human body : Our bodies have evolved under 1g and are not point masses. Our center of gravity and muscles have evolved us to keep us stable under 1g situations. The Vestibular system in our body relies on fluids for us to maintain balance. It takes upto a few days for astronauts to get acclimatized to changes in g. If you live on the moon - your whole body will have to evolve over time to optimize for the changes in g - your muscles will get weaker - since it does not have to work so hard to maintain balance while moving.
Swimming may be completely different than on earth - for one thing - as you are coming out of water to breathe - you may have to blow out a lot more water that will rise in your nose from the capillary effect. Also - it will be hard for your brain to tell which is down and which is up when you are in the water. It will be even harder for you as you come out of the water to come head up and not feet up since you do that on earth using buoyancy difference between your upper body and lower body.
Yes - I am sure that the human body will adapt over time - but it will not be same experience as on earth.
Low gravity basically means that everything in the environment governed by gravity happens slower. While that might take some getting used to, it’s a lot easier than getting used to everything happening faster.
On the jackknife dive, if you just jump from some distance above the water and don’t propel yourself beyond that, then how deep you end up will scale with how high you jump from, just like on Earth. If we neglect the fluid drag from the water, then jumping from a particular height on the Earth or Moon will get you to the same depth in either case. If we do include fluid drag, then you’d go deeper on the Moon, because fluid drag increases with velocity, and you’d be going slower. Also, if you propel yourself in any way once you’re in the water, you’ll also go deeper on the Moon, since the force you’re exerting doesn’t depend on gravity.
All my comments below assume the person is neutrally buoyant. Once a person is totally submerged, they are now weightless, and gravity will have no effect on the person as a whole. We can now move the person up, down, or sideways at infinitesimally slow speeds without using any energy as long as the person remains totally submerged.
I don’t understand what you are trying to say here. If there is no fluid drag, someone diving into the water will hit the bottom of the pool every time if they are neutrally buoyant.
This I don’t understand. Fluid drag is the same on Earth and Moon, agreed? Are you saying if you are gliding through the water faster, you will stop faster? So someone totally submerged and initially gliding at 2 m/s will stop faster than someone initially gliding at 1 m/s? Won’t the person gliding at 2 m/s slow to 1 m/s at some point? How can they not glide further?
I don’t agree with this either. Water is essentially incompressible at the depths we are talking about, so the fluid drag will be the same on Earth and Moon. If you are submerged and push off from the side of the pool at 1 m/s on Earth and Moon, it will require the same level of exertion, and you should glide the same distance.
It should be a little easier to swim along the surface. Raising you arms, head, and chest out of the water will take noticeably less energy on the Moon.
My point is that the main propulsion from the dive is from the weight of one’s legs above the surface of the water. That weight would be much lower, producing less force, and the momentum of the body is the same, as is the fluid resistance of the water. So, slower dive (just as falling is slower).
Another disadvantage occurs to me. When swimming with lungs full of air, one is quite buoyant (even me, with scary low body fat, until I turned 40.) A surface dive pretty quickly moves one deep enough to where buoyancy is much closer to neutral or even a little negative, making it easier to swim deeper using muscle power alone. You’d have to go deeper on the moon to reduce the buoyancy. Hmm, but then, the buoyant force would also be lower, so that’s not as big an issue. In either case (Earth or Moon), a surface dive should take you deep enough below to where you can use your limbs effectively. It’d just be in slow motion, on the Moon.
I agree with newme here. You’ll go deeper on Earth, because you hit the water faster. By the time you’ve slowed down to the speed you’d get on the moon, you’ve already gone some distance. The rest of the trajectory is the same, ignoring buoyancy (which I would predict to have marginal impact here, and newme is assuming neutral and constant buoyancy.)
The force you’re exerting doesn’t depend on gravity on Earth either, ignoring buoyancy. If we factor in buoyancy, for the vertical component, then you go down slower on the moon, because your buoyancy drops (due to the air in your lungs compressing) more slowly.
So, you go deeper on Earth, and it does depend on gravity (as the differences in buoyancy depend on gravity.)
But I might not have all the factors correct about buoyancy gradient for a body with a compressible air-filled cavity. I’m relying on knowing that about 33 feet on Earth adds one atmosphere of pressure, doubling the pressure.
On the moon, how many feet down do you need to go to double the pressure? I assume that’s due to the weight of the water column. If so, at 1/6 gravity, you’d have to go 6 times as deep (200 feet). Is this reasoning correct?