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Can’t help but want to build that. Apparently all the mined gold in the world would fit inside a 5 m diameter sphere. Spheres are suspicious in hiding weight.
Wouldn't a cube be a better choice for visualizing volume? A more complete version would do it alongside with minerals, biomass, etc
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The sphere for all liquid water seems to be close in size to the asteroid Ceres. https://lightsinthedark.com/wp-content/uploads/2013/06/ceres...
But would this sphere of water have enough mass to hold itself together as a sphere in space? Put aside it freezing into a ball of ice as a thought exercise.
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Humans are notoriously terrible about estimating volumes when things are curved and volume functions are exponential. A great example of this done in 8th grade science classes across the US is to put 100ml of water in a 100ml graduated cylinder, 150ml in a 1L beaker, and ask the class which has more. Humans are awful at estimating how much volume the increased radius adds, and usually will say the 100ml. The problem…
Volume functions are not exponential. They are polynomial. (Fair point that people are lousy at estimating even polynomial functions, though...)
I don't think this word means what you think it does. Or I don't. Exponents are just the number the value is raised. Squaring a value just uses an exponent of 2 where cubing uses an exponent of 3. Polynomials are x^2 + x + 1 type of equations. But admittedly, it has been 30+ years since I've thought about them at that level, so maybe I'm the one with fuzzy groking
Just a few quick calculations to make it more relatable... They say the smallest sphere of freshwater lakes and rivers amounts to 93,113 cu km. There are 1 bil cu m per cu km. With a global population of 8.2 bil people, that comes to 11,355 cu m per person. That's a 22.5 meter wide/deep/tall cube (or about 7 or 8 stories tall building). If we use the sphere that includes groundwater, 10,633,450 cu km. Then we end up…
Also.. the largest sphere has a radius of about 92 miles. It reaches to the edge of the atmosphere, and about 1/3 of the way to low earth orbit.
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But would this sphere of water have enough mass to hold itself together as a sphere in space? Put aside it freezing into a ball of ice as a thought exercise.
Freezing? Wouldn't it boil instead due to the low pressure?
Can’t help but want to build that. Apparently all the mined gold in the world would fit inside a 5 m diameter sphere. Spheres are suspicious in hiding weight.
The World Gold Council says: > If every single ounce of this gold were placed next to each other, the resulting cube of pure gold would only measure around 22 metres on each side So that can't possibly be right, you must be off by a factor of 10 or so at least—Wolfram Alpha says a 30m diameter sphere.
It's still a mind bogglingly small amount considering that humans have spared no toil, sweat and blood on industrial scale gold mining ever since the dawn of written history - and since gold is so valuable and hard to destroy, most of it should still exist to this day in form or another.
Yet, if you smelted it all to a single object it would fit on a typical single family housing plot.
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The sphere for all liquid water seems to be close in size to the asteroid Ceres. https://lightsinthedark.com/wp-content/uploads/2013/06/ceres...
But would this sphere of water have enough mass to hold itself together as a sphere in space? Put aside it freezing into a ball of ice as a thought exercise.
A cold enough body, though, has a low enough vapor pressure that this isn't relevant even over cosmological timescales. That's why Europa can can have a stable icy surface. It's far enough from the Sun (and has a low enough albedo) that it's very very cold (about 100K), and at that temperature ice doesn't sublimate very much.
TLDR: a Ceres-sized ball of water could hold itself together, but only as long as it stayed water. But it wouldn't be able to. Either it'd be cold enough to freeze over at the surface, or hot enough to evaporate into vapor that would escape.
[1] https://en.wikipedia.org/wiki/Atmosphere#/media/File:Solar_s...
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But would this sphere of water have enough mass to hold itself together as a sphere in space? Put aside it freezing into a ball of ice as a thought exercise.
Freezing? Wouldn't it boil instead due to the low pressure?
