Answer
No, the hammer will not fall to the earth.
Work Step by Step
No, the hammer will not fall to the earth.
When an object is in orbit around a planet, the gravitational force of the planet on the object is equal to the centripetal force required to keep the object moving in a circle.
Initially, the hammer is in orbit around the earth because of the gravitational force of the earth on the hammer. Therefore, even if the astronaut drops the hammer, the hammer will continue orbiting around the earth because the gravitational force of the earth on the hammer does not change.
