An object in motion tends to stay in motion unless acted upon by an outside force. The only force acting on a satellite is gravity, but they were initially launched at a speed where, in the time it takes them to fall down to the earth, they’d pass it. In other words, they’re falling and failing to hit the ground.
In the absence of anything else, they’ll keep orbiting forever. In practice, satellites occasionally need to activate their thrust to gain additional speed as the trace gasses slow them down, otherwise they’ll slow down until their trajectory dives towards the Earth.
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