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Problem : The free fall acceleration of any object near the surface of the earth is 9.8 m/s. How much force does a 50 kg man exert on the earth?

The acceleration of the man is due to the gravitational force exerted by the earth, and has a magnitude given by F = ma = (50)(9.8) = 490 N. We now have the force on the man, but we need to find the force exerted on the earth. To do so, we simply invoke Newton's third law. If the earth exerts a force on the man directed toward the center of earth, the man exerts a force on the earth equal in magnitude, but opposite direction. Thus the earth experiences a force of 490 N directed away from its center. This force, like all other forces, causes the earth to accelerate. This seems counterintuitive, as the earth seems to be a stable object. The acceleration caused, though, is quite small due to the large mass of the earth, and is negligible.

Problem :

Imagine an astronaut floating in deep space, with only his spacesuit. Is there any way for him to move himself back to earth?

No. Since he is in deep space, there is no surrounding matter on which he can exert a force. In addition, by Newton's third law, any force he exerts on his own body in an effort to propel himself causes an equal and opposite force. The two forces exactly cancel, and the astronaut cannot move.

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