Satellites, like any object that is thrown into the air, are still affected by the force of gravity. They do fall towards the earth, in a sense. The harder you throw an object, the farther it will go before it lands. If you were able to throw it hard enough, and if air resistance didn’t slow it down, it could theoretically fall at the same rate that the earth curved away from it. In a sense, it’s always falling, but the earth is always curving away from it. Satellites don’t experience sufficient resistance from the atmosphere to slow them down enough to fall out of orbit. They can keep flying at a very high horizontal speed and keep “falling” back to earth. Since the earth is round, the earth “falls away” at the same rate, so they stay at the same altitude.
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