if you look at exercise number nine the satelite's acceleration is 8.89 m/s2, while the acceleration due to gravity is -9.8 m/s2. the two acceleration are canceling each other out making the astronauts weightless.

Astronauts orbiting the earth in the space shuttle feel weightless when the normal force is zero, because there is no force opposing gravity and thus one feels weightless.

This weightlessness is not caused because gravity is so much weaker, but because the shuttle is falling towards earth. The astronauts are experiencing "free fall." Gravity is causing the shuttle to fall toward the earth. Although the force of gravity acts on objects within the satellite, the objects experience a weightlessness feeling.

Astronauts experience "weightlessness" in the space shuttles not because the gravity is so much weaker, but because the shuttle is constantly falling towards the Earth due to gravity. Essentially, the floor is constantly "falling" out from under the astronauts and so they experience a weightless feeling.