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A common picture of someone floating on the Dead Sea or Great Salt Lake, shows how high you float.

lMan Floating

If you had that water in a bath tub, I don't think you would sink to the bottom, you would just awkwardly float in the tub. Bathing in small tub where your body does not rest on the bottom would be impractical/impossible. Imagine bobbing around in the tub trying to wash without tipping over and banging your head against the side of the tub.

With the gravity on Mars being much less than Earth, would you float in the bath water?

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Short answer, No different from Earth in floating.

Buoyancy in water or any fluid is based on the weight of water displaced. Floating is based on the weight of the item displacing water. This is ultimately ends up in comparing densities. If the density of the displacing object is greater than the density of the fluid it will weigh more and sink, if it's density is less it will weigh less than the water displaced and float. On Earth people float higher on very salty water because the water is denser than fresh water, so less fluid must be displaced to support the weight of the person.

In a lower gravity field like on mars, your body and the water would both weigh less by the same amount (local gravity), but your densities would compare the same way, so floating or sinking would be unchanged.

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    $\begingroup$ There is something missing here though. It is true that while at rest your buoyancy will remain unchanged, but as pointed out in the linked question regarding swimming, it is easier to push yourself to the surface because of lower gravity. This may be relatively unnoticeable in a bathtub--I'm not sure--but it is possible that moving around in a full tub might feel a little different. $\endgroup$ – called2voyage Aug 17 '16 at 14:49
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    $\begingroup$ @called2voyage So what you're saying is.. Humans swimming on Mars may be able to frolic around like dolphins, leaping from the water? Sounds fun. $\endgroup$ – Saiboogu Aug 17 '16 at 17:02
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    $\begingroup$ @Saiboogu Well, Mars gravity isn't quite as low as the moon, but something like that, yes. $\endgroup$ – called2voyage Aug 17 '16 at 17:03
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    $\begingroup$ If your pool on Mars was an outdoor pool, you'd sink straight to the bottom (because the water evaporated away) $\endgroup$ – Cody Aug 17 '16 at 17:27
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    $\begingroup$ @Saiboogu what-if.xkcd.com/124 $\endgroup$ – kasperd Aug 17 '16 at 20:53

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