I think I see the misconception at work here; it is a common one.
The Earth's gravity does not stop just 100 km up. It goes out forever,
growing weaker with distance. It declines as one divided by the square of
the distance from the center of the Earth. We call the gravity 1 g at the
surface (6400 km from center) so at 100 km altitude (6500 km from center),
it is still .97 g (this is (6400/6500)^2). You could probably not even
notice the difference in gravity if you stood on a 100 km high platform.
What keeps satellites in orbit is not that they are beyond the reach of
gravity, but that they are going sideways very fast. Like anything thrown
sideways, their path bends downwards as they begin to fall. However, they
are going so fast that after they have fallen 1 km, the earth below them
has receded more than 1 km becuse of its curvature. So they keep falling
toward the Earth, but missing.
What I said in my original post is that it is much harder to get enough
sideways speed to get to orbit than merely to get to 100 km of height.
--Carl Feynman