The surface area of the sphere at 1400km is far greater than the earth's surface area. And satellites at that altitude are traveling much slower. Put together, the probabilities would akin to a handful of birds flying on earth, at random altitudes/places/directions, and two of them colliding.

> The surface area of the sphere at 1400km is far greater than the earth's surface area

It's only about 50% larger (1+1400/6371)^2 = 1.49

This! How likely would collisions be on a sphere the size of the earth? How do the probabilities change from low earth orbit to higher orbits?

"much slower" is still >7000 m/s

Yes but at that altitude their orbital period is about 1/2 that of low orbits, meaning that even if two orbits do cross paths, there would be fewer potential collisions in a given time. They are 'slower' in relation to size of the sphere they occupy.

90 mins at 400km vs 110 mins at 1400km

I guess that makes sense since the Earth’s radius is around 6400km so from 400 to 1400km is really a change from 6800 to 7800km which is proportionally similar to a change from 90 to 110 minutes.

Edit: I just looked up the formula for orbital period and it turns out period is proportional to radius^(3/2) (See: https://en.m.wikipedia.org/wiki/Orbital_period)

Yeah, that statement makes a lot of assumptions about the next 99,950 years.

That's true, but the chances of quite a lot of things happening over 100,000 years are fairly big.

Almost everything we do carries a small but non-zero risk of something which, if you stretched it over a hundred thousand years, would almost certainly be realized.

On the other hand, the average damage from a collision in space within 100,000 years is also pretty small.