Your theoretical rocket would certainly leave the atmosphere eventually, yes–but what then? Things up in space are still affected by Earth’s gravity almost as much as at the surface (at the level where the ISS orbits the gravity is around 93% of ground level), so as soon as you turn your rocket motor off, you’ll start to fall back to the ground. In order to stay in space you need to go sideways really, really fast, which is why you’ll see rockets start to tilt over almost immediately they’ve been launched–just getting the 100km or so to space is the easy part, the hard part is getting to the 18,000mph needed to stay in orbit.
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