I've studied the basics of this in a physics textbook, and have searched on this forum, but one thing about this escapes me. My understanding is that a satellite is elevated somewhere above the Earth's atmosphere where air resistance is negligible. The satellite is then accelerated to a very high speed where it is moving laterally as fast as it is falling toward the center of the Earth so it continues to orbit around the Earth. What I don't understand is if the acceleration of gravity, being 9.8m/s^2 (or slightly less since it's farther from the center of the Earth) is causing it to fall toward Earth faster and faster, how does a constant lateral speed keep it in orbit? In other words, if it falls 5 meters in the first second, it'll fall exponentially faster each additional second as it picks up acceleration with no terminal velocity (due to the lack of air resistance) until it is falling faster toward Earth than it is moving laterally in order to 'escape' Earth, so how do satellites stay in orbit without falling back down toward us? Of course my reasoning is incorrect somewhere, so please help me understand!