Sheepscot

Assumptions:

Air at 29 atm and 230C has a density of only 0.02 g/cm2, which is essentially 0

Water is 1 g/cm2

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

= 1 - (0.98)^3 = 6%

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]

= [r{pebble}/r{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%

13%^(1/3) = 50%

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!!

like seriously I thought it was a silly little comic that won't get much attention so I decided to feel a little guilty and force myself to handwave the science for that cartoon cuteness sake. now that it got A LOT of attention I was seriously starting getting worried 😅

And from this I’ve always drawn two conclusions:

To always distrust Mr. Beast and his ilk who always want their acts of charity done on film, because the people who really want to do good and have no motives to do it besides the doing it never want recognition for it, and

This is a bigger deal than some of you might think, because Superman is one of the heroes in the DC Universe who keeps his secret identity pretty damn secret, because as probably the most powerful and influential person on earth, a lot of people do not wish him well - and would jump at the chance to hold people dear to him as leverage.

Yet, he trusts this poor, scared little kid. To comfort him, and entrust him with his biggest secret - just as Billy did for him.