The important thing to remember is that satellites aren’t rockets; they don’t have thrusters, or if they do, they’re not nearly as powerful as the ones you’d see on a rocket. Rather, it’s those very rockets that determine a good bulk of a satellite’s travel speed. To actually get a satellite into orbit, it needs to be mounted onto a rocket, and they are shot into orbit at speeds of around 17,800 miles per hour. Once the rocket reaches orbit, it spits the satellite out, which carries the momentum of the initial launch along with it, give or take a few hundred miles per hour.
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A big factor that determines how much of that inertia the satellite maintains is which of the three primary orbital altitudes it’s launched to. For example, if it’s still relatively close to the Earth’s surface, around 200 to 1,200 miles above the surface, that’s known as a low-Earth orbit. It’ll travel around the same speed as the initial launch, approximately 17,500 miles per hour. According to the Japan Aerospace Exploration Agency, that’s about 90 times the average speed of a bullet train.
However, if a satellite is in geosynchronous orbit, it’s substantially further from Earth, about 22,000 miles above the surface. Satellites launched into this kind of orbit may have additional thrusters onboard, which are fired to subtly shift their arc. This is all with the intent of matching the speed of the Earth’s rotation, roughly 7,000 miles per hour. A slight variation of this is the geostationary orbit, where the satellite is parked directly over Earth’s equator.
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