Astronaut Weightlessness in Orbiting Space Station and Free Fall

To determine the correctness of the statements and their relationship, we analyze the physics of an orbiting body:

1. Analysis of STATEMENT-2:
   By definition, an object is said to be in a state of free-fall if the only force acting upon it is gravity.
   An orbiting satellite or space station moves in a circular or elliptical path around the Earth solely under the influence of the Earth's gravitational force.
   The gravitational force provides the necessary centripetal force:
   $F_g = \frac{G M_E m}{r^2} = m a_c$
   Therefore, the acceleration of the object is strictly equal to the local acceleration due to gravity:
   $a = g(r) = \frac{G M_E}{r^2}$
   Since no other non-gravitational force (like thrust or aerodynamic drag) acts on the object, it is continuously falling towards the Earth while moving forward, which means it is in a perpetual state of free-fall.
   Thus, STATEMENT-2 is True.

2. Analysis of STATEMENT-1:
   Consider an astronaut of mass $m$ standing on the floor of the orbiting space station. Both the astronaut and the space station are subject to the same gravitational field at distance $r$ from the Earth's center:
   $a_{\text{station}} = g(r) \quad \text{and} \quad a_{\text{astronaut}} = g(r)$
   Applying Newton's second law to the astronaut in the radial direction:
   $m g(r) - N = m a_{\text{astronaut}}$
   Since the astronaut accelerates along with the space station at $a_{\text{astronaut}} = g(r)$, we have:
   $m g(r) - N = m g(r) \implies N = 0$
   Here, $N$ is the normal contact reaction exerted by the floor of the space station on the astronaut.
   Apparent weight is defined as the magnitude of the contact/support force acting on a body. Since $N = 0$, the astronaut experiences an apparent weight of zero, which is the state of weightlessness.
   Thus, STATEMENT-1 is True.

3. Relationship between the statements:
   The reason the normal force $N$ is zero (causing the sensation of weightlessness) is precisely because both the astronaut and the station are falling together purely under the influence of gravity—that is, they are both in a state of free-fall.
   Therefore, STATEMENT-2 is the correct scientific explanation for STATEMENT-1.

Hence, the correct option is (A).