Question

STATEMENT-1 An astronaut in an orbiting space station above the Earth experiences weightlessness. and STATEMENT-2 An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free- fall'. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT- 1 is True, STATEMENT-2 is False (D) STATEMENT- 1 is False, STATEMENT-2 is True

Short answer

(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

Step-by-step solution

Understand Weightlessness

Weightlessness is a sensation experienced when there is no force of support acting on your body. In space, astronauts experience weightlessness not because gravity does not exist, but because they are in a continuous state of freefall towards Earth, while also moving tangentially at a velocity that keeps them in orbit.

Define Free-Fall

Free-fall is the condition of an object moving solely under the influence of gravity. Any object in free-fall experiences an acceleration due to gravity, but simultaneously, if it has a tangential velocity, it may orbit around the Earth instead of falling directly to it. This is because of the balance between the gravitational pull of the Earth and the object's inertia.

Evaluate Statements

Based on the definition of free-fall and weightlessness, STATEMENT-1 is true because astronauts in orbit experience weightlessness due to being in a continuous state of free-fall. STATEMENT-2 is also true because an object (like a space station) is indeed under the influence of Earth's gravitational force while in orbit.

Relate Both Statements

Now, the task is to determine if STATEMENT-2 is a correct explanation for STATEMENT-1. Since weightlessness experienced by astronauts is due to the orbiting space station being in free-fall, STATEMENT-2 does correctly explain why STATEMENT-1 occurs.

Key concepts

Weightlessness and Free-Fall

When we think of weightlessness, it's common to imagine astronauts floating effortlessly in a spacecraft. This phenomenon occurs not because gravity is absent in space, but rather because both the astronaut and the spacecraft are in a state of free-fall. Essentially, they are continually falling towards the Earth. However, they never actually fall to the surface because they have enough tangential velocity to keep it in orbit—meaning their fall around the Earth is what keeps them in motion.

In free-fall, objects do not experience a normal force, which we typically associate with the feeling of weight. On Earth, this force is the ground pushing up against us, but in orbit, there is no ground to exert such a force, and thus no sensation of weight is felt. This sense of weightlessness is a result of being in a state of continuous fall while also moving forward; an interplay between gravity pulling the object down and the object's motion creating a centrifugal force that 'pushes' it outward.

Understanding Orbital Motion

Orbital motion is a mesmerizing dance between an object's velocity and the gravitational pull of a larger body, like Earth. For an object to stay in orbit, it needs to have just the right horizontal velocity. If it's too slow, it will get pulled in and crash. Too fast, and it'll shoot off into space. The beauty of orbital motion lies in the balance—it's essentially free-fall but in a horizontal direction around a celestial body.

An object in orbit constantly 'falls' toward the Earth due to gravity but moves forward fast enough so that the curve of its fall matches the curvature of the Earth. It keeps falling around the Earth without ever hitting the ground. This continuous free-fall state explains the feeling of weightlessness experienced by astronauts as they orbit our planet. The entire system, including the astronauts, experiences the same gravitational pull, so relative to the spacecraft, the astronauts do not feel the force of gravity—the spacecraft and everything inside it are accelerating at the same rate.

The Role of Gravitational Force

Gravitational force is the invisible 'hand' that governs the motion of planets, stars, and galaxies. It's a fundamental force that pulls two objects with mass toward each other. On Earth, it's what gives us weight and keeps our feet firmly planted on the ground. The strength of the gravitational pull depends on the mass of the objects involved and the distance between them; it's why a spacecraft in low Earth orbit is still within the grips of our planet's gravity.

In the context of astronauts experiencing weightlessness, it's crucial to remember that gravity is still at play. The spacecraft orbiting the Earth is not outside the range of Earth's gravitational pull. In fact, it is the gravitational force that keeps the spacecraft in orbit, curving its path around the Earth. Without gravity, the spacecraft would move in a straight line off into space. Thus, the gravitational force is not just the reason we have orbits; it is also the reason that astronauts feel weightless. They are in a continual state of free-fall toward the Earth, but because the spacecraft is also moving tangentially, they don't collide with Earth but keep revolving around it.