Spacecraft are held in orbit by the gravity of the planet which they are orbiting. In Newtonian physics, the sensation of weightlessness experienced by astronauts is not the result of there being zero gravitational acceleration (as seen from the Earth), but of there being no g-force that an astronaut can feel because of the free-fall condition, and also there being zero difference between the acceleration of the spacecraft and the acceleration of the astronaut. Space journalist James Oberg explains the phenomenon this way:[1]

The myth that satellites remain in orbit because they have “escaped Earth’s gravity” is perpetuated further (and falsely) by almost universal misuse of the word “zero gravity” to describe the free-falling conditions aboard orbiting space vehicles. Of course, this isn’t true; gravity still exists in space. It keeps satellites from flying straight off into interstellar emptiness. What’s missing is “weight”, the resistance of gravitational attraction by an anchored structure or a counterforce. Satellites stay in space because of their tremendous horizontal speed, which allows them — while being unavoidably pulled toward Earth by gravity — to fall “over the horizon.” The ground’s curved withdrawal along the Earth’s round surface offsets the satellites’ fall toward the ground. Speed, not position or lack of gravity, keeps satellites in orbit around the earth.