Good thing you're here to use your high school geometry to wow us and show that it's impossible. Is there anything constructive you have to add?Lets figure out how much space is really up, and lets start with the volume of the Earth:
Here's the formula for volume of a sphere, I realize the Earth isn't a perfect sphere but its the best we can do:
Volume of a sphere calculator
So all we need then is the radius of the Earth which Wikipedia tells me is 3963 miles. So input that into the formula and we get "260,711,882,973 cubic miles."
Now low Earth orbit is 1243 miles(2000km) above the surface, but lets stick with a smaller number for the sake of not creating massive numbers. We'll go with 370 miles because below that is the most crowded space, based off this wikipedia source:
So lets add 370 miles to our formula and do it again, that gives us "340,764,760,245 cubic miles." Now that's the volume of the Earth plus 370 miles extra into space, but that's obviously not the number we are looking for because it counts the Earth and its atmosphere where obviously there is no space junk. So looking at the last source we see Sputnik flew at an altitude of 133 miles, I don't know if there's anything below that but lets go with that number. So what we need to find is the volume of space in a sphere that is 4333 miles in radius(3963+370) from its outward most point along the radius (4333) to 133 miles below that (4200).
Using the sphere volume formula again a sphere of 4200 miles in radius is "310,339,088,692 cubic miles," subtract that from our volume of a 4333 mile radius sphere and we get:
30,425,671,553 cubic miles of space That's 30 billion, 425 million, 671 thousand, 553 cubic miles of space to clean of space junk. And thats not even every altitude of all satellites around Earth, if we were to count everything we'd find an area of space larger than the entire Earth.