In an accidental explosion, a satellite breaks in half while in circular orbit about Earth. One half is brought momentarily to rest. What is the fate of the half brought to rest? What happens to the other half?

the one half that stops will just fall while the other will continue around the earth

The fate of the half brought to rest depends on the specific conditions of the accident, but in general, it would likely begin to experience a change in its orbit. When an object in orbit comes to rest, it means that its velocity has been significantly reduced or reduced to zero. Without sufficient velocity to maintain a stable orbit, the half of the satellite brought to rest would start to fall towards Earth due to the force of gravity. This would result in the half eventually reentering the Earth's atmosphere and burning up, unless it is somehow reboosted to regain enough velocity for a stable orbit.

As for the other half of the satellite, it would continue along its original orbit path, unaffected by the event. In space, objects in orbit will remain in motion at a constant velocity unless acted upon by an external force. Therefore, the other half of the satellite would continue to circle the Earth as it did before the explosion, unless another force, such as atmospheric drag or gravitational influences from other celestial bodies, alters its orbit.