STATEMENT - 1 : An astronaut in an orbiting space station above the earth experiences weightlessness. because STATEMENT - 2 : An object moving around the earth under the influence of Earth's gravitational force is in a state of "free-fall".

Step 1: Analyze Statement 2 regarding free-fall.

An object orbiting the Earth under the sole influence of gravity is in a state of free-fall because there is no contact or support force acting on it, where gravity provides the necessary centripetal force.

$$\frac{GMm}{r^2} = \frac{mv^2}{r}$$

Thus, Statement 2 is true.

Step 2: Analyze Statement 1 regarding weightlessness.

Both the space station and the astronaut accelerate towards the center of the Earth at the same rate.

$$a = g = \frac{GM}{r^2}$$

Because they share the same acceleration, the normal contact force between the astronaut and the station is zero.

$$N = 0$$

The apparent weight of the astronaut is determined by this normal force.

$$W_{\text{apparent}} = N = 0$$

Thus, the astronaut experiences weightlessness, making Statement 1 true.

Step 3: Determine the relationship between the statements.

The weightlessness in Statement 1 is a direct consequence of the free-fall condition described in Statement 2.

Answer: Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation of Statement 1.