Stand on a mountain and throw a ball. It moves horizontally to the surface of the Earth, but gravity pulls out down so it eventually his the ground.
Now imagine a really tall mountain and you throw the ball really fast. It moves away from the Earth because you are on the high mountain, but gravity pulls it back towards the Earth as well.
There is a specific velocity where these forces balance out and the ball “falls” all the way around the Earth and just keeps falling. That’s a satellite.
It’s not just the horizontal motion. The horizontal motion is a result of the upward motion and the pull of gravity.
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