Final answer:
The assertion that an object would not have any inertia in a gravity-free environment is false; inertia is due to mass, not gravity. Furthermore, an external force is necessary to initiate motion in a gravity-free space, confirming Newton's First Law of motion.
Step-by-step explanation:
An object would not have any inertia in a gravity-free environment; this statement is false. Inertia is a property of mass, independent of the presence or absence of gravity. It is an object's inherent resistance to changes in its state of motion, as defined by Newton's First Law of motion. Meaning, even in the vacuum of space, where gravitational influences are negligible, an object retains its inertia.
An external force is indeed required to set a stationary object in motion in outer space, away from all gravitational influences and atmospheric friction; this statement is true. According to Newton's First Law, without an external force, an object will remain at rest or continue to move at a constant velocity in a straight line.
The concept of astronauts living in a condition similar to a freely falling box aboard the International Space Station illustrates the non-reliance on gravity for the manifestation of inertia. Even in this microgravity environment, objects have mass and hence inertia, and will only change their state of motion due to the application of a force.