The rocket was 9000 miles away from the Antarctica -- How far exactly do you expect to see?

Well, as the pressure is about 800 - 900 times less than it is at Denver, and you can see 20 miles from there, I would guess you could see about 800 - 900 times as far. So, about 16,000 - 18,000 miles?

It's 9000 miles away, but also several miles up.

Let's say, 20 miles (random approximation based on the fact that space starts at 30 miles).

That means a hypotenuse of about 9001 miles. Not a big difference, but still significant.

The average atmospheric pressure in Denver is 84 kPa (.82 atm). The average atmospheric pressure at 20 miles up is 6 kPa. That's 14 times more, not 900.

So, that's 240 miles.

Or, we can make the height 30 miles (beginning of space). That's about 1 kPa, or 82 times more. That's 1680 miles. I'm being generous and using the maximum instead of the minimum, BTW.