Condition for Free Fall around Earth

For a body to stay in orbit around Earth, it must travel tangentially (magenta arrow) with a velocity that lets the body fall a radial distance due to the force of gravity (black arrow) in such a way that it follows the curvature of Earth (yellow arrow). The resultant displacement can be represented as the sum of both motions (blue arrow). As an example, astronauts inside a space shuttle appear to be floating in zero gravity with an absence of gravity, but actually they are continuously falling around Earth.
It is easy to calculate that near Earth's surface a body must travel tangentially at about 7.9 kilometers per second to stay in orbit.

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