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The reason astronauts feel weightless in space is actually because they are falling towards Earth! The reason it doesn't look like they're falling is because they're moving forward so fast that they never actually hit the Earth. Imagine when you throw a ball - notice how the ball makes an arc before it hits the ground? Well if you could throw that ball hard enough that the arc was bigger than the Earth, then that ball would be orbiting the Earth! We call this a "microgravity environment". So it's not really how high you have to go to feel weightless, but how fast do you have to go! To give you an idea, the International Space Station is orbiting the Earth at about 17,500 miles per hour!