Would a rope fall down back to Earth if it is strecthing all the way to Earth’s geostationary orbit in space?

 In a hypothetical scenario where a rope extends all the way to Earth's geostationary orbit in space, a peculiar balance of gravitational forces comes into play. The gravitational pull from Earth diminishes with distance, following the inverse square law. Consequently, as the rope extends further into space, the force of gravity weakens. At the same time, tension within the rope increases as it strives to resist the gravitational pull and maintain its structural integrity.

As the rope reaches the geostationary orbit, a point where the orbital period matches Earth's rotation, a unique equilibrium is achieved. The gravitational force from Earth is countered by the tension force in the rope, resulting in a state where the rope remains suspended in space without falling back to Earth. This delicate balance exemplifies the intricate interplay between gravitational forces and tension in such an extended system.

This hypothetical scenario underscores the fascinating physics at play beyond our planet's atmosphere. While the concept of a rope stretching to the geostationary orbit is theoretical, it serves as a captivating illustration of the complex dynamics governed by gravity and tension in space.