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

Answer 1

The piece brought to rest falls straight down to Earth (and probably burns up along the way).
The ither part doubles its velocity in the same direction I(thus maintaining total momentum), making the orbit an ellipse with apogee much farther from Earth; and perigee where the exoplosion occurred.