What I find impossible to believe is that a random spec of paint just happened to be floating in space, yet it somehow eludes space debris.

The speck of paint could be from another satellite which has (say) been hit by a micrometeorite.

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Fitting satellites into the available space, assuming they and the ISS are actually "up there" ...

Low earth orbit starts at 160km or so, so let's take that as the lowest possible orbit for a satellite.

THe geostationary orbits are at around 36000km, so let's take that as the highest.

To find the available volume of space for satellites, we need to work out the volume of a sphere enclosed by each of these orbital heights, and subtract the smaller from the larger.

Radius of Earth = 3671km

Radius of lower orbit = 3671+161 = 3832km

Radius of higher orbit = 3671+36000 = 39671km

Calculate volumes of spheres = 4/3 * pi * Radius cubed

Using an online calculator

Volume of lower orbit sphere = 2.36 x 10 to 11th power, or 236,000,000,000 cubic km

Volume of higher orbit sphere = 2.62 x 10 to 14th power, or 262,000,000,000,000 cubic km

The available space for satellites is the difference between these numbers, or 261,764,000,000,000 cubic km

If we take the number of operational satellites (2300 or so), and put them in this space, each would have,

on average, 113,810,434,783 cubic km all to itself.

There are more than 8700 objects larger than 10 cm in Earth orbits, so if we take that figure, each

would have 30,087,816,092 cubic km all to itself.

Assume 100,000 objects, and each has 2,617,640,000 cubic km all to itself, on average.

Convert that volume back into a sphere around each object, and each has a sphere of space, on average, of 1,710km diameter around it, so on average, each other object is that distance away from it (each one being, on average, 2 radii away).

Space is big. Really big.