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Satellites stay in orbit by balancing gravitational pull with inertia from "summary" of Rocket Science: A Beginner's Guide to the Fundamentals of Spaceflight by Andrew Rader

A key concept in understanding how satellites remain in orbit is the delicate balance between two fundamental forces: gravity and inertia. Gravity is the force that pulls objects toward each other, while inertia is the tendency of objects to continue moving in a straight line at a constant speed. When a satellite is launched into space, it is initially moving very fast to overcome the gravitational pull of the Earth. However, gravity is still at play, trying to pull the satellite back down to Earth. In order to stay in orbit, the satellite must maintain a delicate balance between these two forces. If the satellite were to slow down too much, gravity would overpower its inertia and it would fall back to Earth. Conversely, if the satellite were to speed up too much, it would escape the Earth's gravitational pull and drift off into space. Therefore, satellites in orbit are constantly moving at just the right speed to counteract the gravitational pull of the Earth. This allows them to continue orbiting the planet without falling back to the surface or drifting off into space. By understanding this concept of balancing gravitational pull with inertia, scientists and engineers are able to design and launch satellites that can effectively perform their intended functions in orbit around the Earth.
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    Rocket Science: A Beginner's Guide to the Fundamentals of Spaceflight

    Andrew Rader

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