No, you won't orbit just by going high enough. To orbit you need to going fast enough horizontally that as you fall you never hit the body you're orbiting. If

No, you won't orbit just by going high enough. To orbit you need to going fast enough horizontally that as you fall you never hit the body you're orbiting. If you just keep going straight up you'll eventually fall back to Earth, or be on your own independent orbit around the Sun.