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I'm assuming that to hold onto more atmosphere, the planet would have to have more gravity, or the atmosphere itself would have to be comprised of denser gasses.
So, assuming that the planet has a mass similar to earth's and that the percentage of oxygen was close to that of earth's atmosphere (or higher), could a planet have an atmosphere dense enough for humans to swim through?
Your assumptions aren't quite correct.
The gravity at the surface depends on the mass of the planet AND the radius. A larger radius and lower density planet can still have a 1g surface gravity.
But when you increase the radius, you also increase the distance that it takes to get down to a given lower value of g.
E.g. For earth with a radius of 6000 km (rounding here) for 1g, you have to move to 12000 km from the centre to get down to 1/4 g.
For a lower density planet (less iron in the core...) suppose that the radius was 7500 km. For this planet you would have to be 15,000 km from the centre to get to 1/4 g.
http://hyperphysics.phy-astr.gsu.edu/hbase/vesc.html
If you give a planet 2 times the mass of earth, but 1.414 times its radius you still get a surface gravitation of 9.8 m/sec. But escape velocity has increased from 11 and change km/s to 13 and change. This drastically increases the energy needed by a gas molecule at the top of the atmosphere to escape. So the planet doesn't lose gas nearly as fast.
This planet will have a thicker atmosphere all other conditions being equal. How much thicker? Probably lots. Venus isn't much different from earth in either mass or diameter but it has a lot more atmosphere. On Earth most of the CO2 is in the form of carbonate rocks. Earth has a moon that creates tides in the atmosphere. When the tide is high, it's easier for gas molecules to escape. Larry Niven in one of his stories/articles wonders if a big moon is an essential ingredient to clearing enough of the atmosphere for sunlight to reach the surface. Alas we don't have enough examples.
I am skeptical about getting a thick enough atmosphere to swim in with your present scenario. But normal pressures and lighter gravity could do the trick. See Heinlein's "Menace from Earth" which features flying in the air storage caverns of Luna City.
M = 1.25 M_earth R = 3 M_earth gives you an escape velocity of 7 km/second, and a surface gravity similar to that of the moon. This much of a radius increase means 27 times the volume, but only 1.25 times the mass, so the overall planet has a density about 1/5 that of earth. Not a lot denser than water.
Play around with the calculator. I suspect that even a 1/3g human powered flight isn't unreasonable, especially if you run at an air pressure of 3 atm or so.
It is NOT clear to me what a 3 atm surface pressure does to weather.
could a planet have an atmosphere dense enough for humans to swim through?
Obligatory xkcd What if: Jupiter Submarine.
Summary: no, no, no and very much no.
The problem is not that we cannot get such a dense atmosphere. The problem is that we will not be doing any swimming (because we will be very dead), and we cannot get such a dense atmosphere under a gravity of 1 g.
For purposes of example, and with some simplification, let us pick Xenon as a gas and assume that the atmosphere is mostly Xenon. Xenon has a specific gravity of 4.53 kg/m3, which is a lot when it comes to gasses. In order to achieve buoyancy for the human body you need a fluid with a specific gravity of about 1000 kg/m3 in order to float in it.
You can get Xenon (and any other gas) to that specific gravity by compressing it. And if we assume the ideal gas law (*) this means the pressure needs to be least 200 times of NTP — that is to say what we consider normal atmospheric pressure and temperature — in order to achieve 1000 kg/m3.
Soft fragile, fleshy Hominidae do not fare well in 200 atmospheres of pressure. Already at 33 atm we need very special gas mixtures just to be able to breathe. Humans surviving in 200 atm? No. Just... no. And this is not even considering we would be squished and made much more dense, which would mean we need even more pressure to make the gas dense enough to float in.
(*) This is probably very wrong if we take it up to 200 atm, but let us do it anyway
You could have such a world but the normal gases would kill a normal human; carbon dioxide, nitrogen, oxygen, and even hydrogen are lethal toxins above certain pressures and concentrations. If you stretch your definition of human to include something heavily altered to deal with the atmosphere's inherent toxicity and corrosive effects at those pressures then yeah maybe you could have swimmers in the sky. Such pressures aren't likely to be stable over geological time on a 1g world but they could occur. Wil McCarthy suggests a mechanism for such an atmosphere in Lost in Transmission, something to do with late formation phase out-gassing I can't remember the exact details, it's not nearly thick enough for your purposes but from memory Sorrow has less than 0.7g too.
Human body has an average density of 1.062 g/cm^3.
In order to be able to swim through a fluid with a human body, the fluid needs to have a density equal or higher. Water is around 1 g/cm^3, that's why we swim in it (and breathing influences our immersion depth). Oil has a lower density, that's why if you dip into a pool full of oil, you sink.
Typical density for gases is about 3 order of magnitude lower than liquids, so there is no way a (static) gas can support a human body.
I will answer this question in two parts:
A) By swimming you mean lift with minimum thrust/flying - This is possible. I won't go into much details as this is an aerodynamics topic. We could build wearable suits to assist in this also. Also understand that a higher gravity might also make this imposssible.
B) High atmospheric pressure - atm pressure depends mostly on the height of the gas column above a surface. If we go by earthly factors we can say the height also greatly depends on the distance from host's star and also it's magnetic field strength. So gravity doesn't affect this alone by itself.
Fine-tune those two above and what you imagine is possible. We could also throw the argument that humans in such an atmosphere have ways built into them by the creator to survive in such an atmosphere.
Consider also if this question had been posted by a fish. Other fish would give answers believing water is 'their atmosphere' and would agree their could be an atmosphere where they could sink rather than swim.
High atmospheric pressure is definitely possible in a 1g environment for example Venus. But as with other cases described (and even more so in the case of Venus due to temperature and chemical composition of the atmosphere) unprotected humans would die nearly instantly. However if you are willing to allow a very contrived atmosphere and take a very liberal attitude to what constitutes “swimming” it might just be possible, although the reason why anyone would want to is beyond me.
The first thing you will need is one of these or similar:
The ADS can dive to depths of 700m roughly equivalent to 70 atmospheres or 7 MPa pressure. pressure converter
Modifications would be needed to provide flippers and something better than the pincers on the arms (and much else).
You then need a planet with a dense Xenon atmosphere. At a temperature of 30 degrees C and a pressure of 7.3 MPa the density of Xenon gas is 1.01 g/cc
https://www.nist.gov/document-1757 (downloads as a pdf) page 82 Michels et al density reference
And off you go. Would such an atmosphere be likely to exist naturally? No. Is that swimming? Maybe depending on how you define swimming. Would it be dangerous? Yes hugely dangerous. The suit would be operating at the limit of its pressure capability and beyond at a very uncomfortable 30 degrees C. Any significant leaks of Xeon would be fatal. As well as being an asphyxiant Xeon is also an aesthetic.
The suit would need to be Xeon gas proof instead of water proof, although this should not be beyond the wit of man. Given sufficient funding I would imagine greater pressures could be withstood and a slightly more swimmer friendly orientation could be arranged (Slightly).
Not strictly relevant but might be of interest NASA have considered floating craft in the Venusian atmosphere. Venus blimp
