An antenna loosens and becomes detached from a satellite in circular orbit around the earth. Describe the antenna's subsequent motion. If it will land on earth, describe where: if not, describe hw it would be made to land on earth.
Isn't the antenna in the same orbit as the satellite?
They were orbiting together at one point, but the antenna becomes detached.
Which direction will it instantaneously head?
move toward the earth
When an antenna becomes detached from a satellite in circular orbit around the Earth, it will continue to move in its own trajectory. Initially, it will continue to orbit the Earth along a path that is slightly different from the satellite's orbit.
This happens because the antenna has lost the force that keeps the satellite in orbit: the centripetal force provided by the satellite's velocity and the gravitational force from the Earth. Without this force, the antenna will start to drift away from the original orbit.
The motion of the detached antenna will depend on its speed and direction at the moment of detachment. If the velocity of the antenna is greater than the satellite's orbital velocity, it will move into a higher orbit. On the other hand, if the velocity is less than the satellite's orbital velocity, it will move into a lower orbit.
In either case, due to atmospheric drag, the antenna will gradually lose speed over time. This drag is caused by the Earth's atmosphere, which creates resistance against the antenna's motion. As the antenna loses energy, its orbit will decay further, and it will gradually descend towards the Earth's surface.
Eventually, the antenna will re-enter the Earth's atmosphere and burn up due to the intense friction caused by the high speeds. This is known as atmospheric re-entry, and it is designed to prevent space debris from posing a risk to human activities on Earth or other satellites in orbit.
So, in answer to your question, the detached antenna will not land intact on the Earth's surface. Instead, it will burn up during re-entry.