Some people have proposed building a giant elevator from Earth's surface to geosynchronous orbit. The top of the elevator would then have the same orbital distance and period as any satellite in geosynchronous orbit. Suppose you were to let go of an object at the top of the elevator. Would the object fall? Would it orbit Earth? Explain.

In the tower, the object would already be rotating around the earth once per day. Once released, it would have the correct speed of a geosynchronpus satellite. It would orbit the Earth and not "fall". The gravity force upon it would provide the centripetal force needed to keep it in a circular orbit.

If you were to let go of an object at the top of the giant elevator connected to geosynchronous orbit, the object would not fall towards Earth, nor would it orbit the Earth.

This is because geosynchronous orbit is a specific orbit where an object orbits the Earth at the same rotational speed as the Earth's rotation. This means that objects in geosynchronous orbit remain stationary relative to a point on the Earth's surface. Instead of falling or orbiting, the object would effectively stay in place relative to Earth.

Gravity at this altitude is still pulling the object towards Earth, but the centrifugal force caused by the orbital speed is counteracting this gravitational force. This balance of forces allows the object to remain stationary despite the gravitational pull.

Therefore, if you were to release an object at the top of the giant elevator, it would simply stay in place relative to Earth without falling or entering into an orbit.

If you were to let go of an object at the top of the proposed giant elevator to geosynchronous orbit, the object would neither fall nor orbit the Earth. This is because the concept of gravity changes significantly as we move away from Earth's surface.

To understand why, let's first consider how gravity works on Earth. Gravity is an attractive force that pulls objects towards the center of the Earth. When an object is close to the surface, this force of gravity is what causes the object to fall (or if given the right initial velocity, orbit).

As we move away from Earth's surface, the force of gravity weakens due to the decreasing mass of Earth beneath us. However, since Earth's gravity extends infinitely into space, there is always some gravitational force acting on an object.

In the case of the proposed giant elevator to geosynchronous orbit, the object at the top would experience a weaker gravitational force compared to an object on the surface, but it would still experience some gravitational force. However, the centripetal force required for an object to orbit Earth is much higher than the force it would experience at the top of the elevator. As a result, the object would not be able to achieve a stable orbit.

So, when you let go of an object at the top of the elevator, it would basically be in a state of freefall but without any significant gravitational force causing it to fall towards Earth or orbit around it. It would essentially float in space, accelerating away from Earth due to the absence of other forces to counteract its initial velocity.