I was curious about the math on this because... they're made from rocks and their atmosphere is way higher pressure than ours. But I think the math works out!!
Air at 29 atm and 230C has a density of only 0.02 g/cm2, which is essentially 0
Eridians are 5 g/cm2 (rocks are 2-3 and metals are 5-12 so I'm going with a funky average with nice numbers)
xenonite is the same density as Eridians
xenonite barrier is 2% of the radius of the ball (1cm for a 1m ball)
I can do all my calculations assuming Earth gravity because bouyancy/weight would both be affected equally by the double gravity, thus cancelling out
We can estimate the radius of a pebble by picturing them loafing cutely into their carapace
In order to float, the ball has to be less dense than water; however, water displacement is directly related to density, so
to be comic-accurate, we're looking for the balls (with pebbles inside them) to be roughly 20-50% as dense as water.
Let's start with the xenonite shell:
% of ball that is xenonite = (volume of outer shell - volume of inner shell)/(volume of outer shell)
= [(4/3)πr{outer}^3 - (4/3)πr{inner}^3]/[(4/3)πr{outer}^3]
= 1 - (r{inner}/r{outer})^3
So the density of the ball alone is roughly:
6% x 5g/cm3 + 94% x 0g/cm3 = 0.29 g/cm3
We're already pretty much there without adding a pebble!
Now let's see what radius pebble we'd need to get to 0.5 g/cm3:
[% of volume taken up by pebble] x [density of pebble] + [% xenonite x density xenonite] + [% air x density air] = 0.5g/cm3
% of volume taken up by pebble = (0.5 - 0.29)/5
= 4% of the total ball volume
What a cute little pebble!!
but remember volume scales by radius cubed.
% of ball is pebble = volume of pebble/volume of ball
= [(4/3)πr{pebble}^3]/[(4/3)πr{outer}^3]
0.04^(1/3) = r{pebble}/r{outer}
...so the radius of the pebble is about 35% the radius of the ball!
To find the maximum size of a pebble that can float, let's say the density of the entire ball has to be 0.95 instead of 0.5:
% of volume taken up by pebble = (0.95 - 0.29)/5 = 13%
However, this would mean they'd be mostly underwater (like an iceberg)
So the pebble has to use a ball that is at least 3 (for safety) times taller than its loaf height in order to float!!
(2-3 for safety if they have a low density like a rock, 5-6 for safety if they have a high density like a metal)
romaincrisis
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