Final answer:
To determine the energy of the satellite-Earth system in a new stable circular orbit at an altitude of 12RE, we need to consider the conservation of total mechanical energy. The energy of the satellite-Earth system in the new orbit is equal to the kinetic energy in the current orbit plus the change in gravitational potential energy.
Step-by-step explanation:
To determine the energy of the satellite-Earth system in a new stable circular orbit at an altitude of 12RE, we need to consider the conservation of total mechanical energy. The total energy of the satellite-Earth system is the sum of kinetic and gravitational potential energy. Since the satellite is in a stable circular orbit in its current position, its total energy is E.
When the satellite moves to a new orbit at an altitude of 12RE, the distance from the center of the Earth changes, and therefore the gravitational potential energy changes. However, the kinetic energy remains the same because the satellite is in a circular orbit. Therefore, the energy of the satellite-Earth system in the new orbit is equal to the kinetic energy in the current orbit plus the change in gravitational potential energy. So the energy of the satellite-Earth system in the new orbit is E plus the change in gravitational potential energy, which depends on the difference in distances between the two orbits.