m_em_s
F_gravity  = G ----------              F_gravity provides F_centripetal for satellites.
                        r² 

   
                        m_sv²                m_em_s                              m_e
F_centripetal = -----------  = G ----------------    =>  v = ( G------  ) ^1/2  
                          r                        r²                                 r

     
The satellite travels faster when you are closer to the Earth.

    
        2 pi r                        2 pi r
v = -----------   =>  T =  ---------------  With a faster v and a smaller r, T is smaller closer to Earth.
           T                              v

   
The Correct Answer is D.

However, this is not the complete answer.  When you accelerate a spacecraft, you are adding energy.  Since the total energy is greater, the space craft moves into a higher orbit to have a greater potential energy.  After the initial acceleration, the space slows down to a slower velocity as it does work to move away from Earth.

When you slow down a space craft in orbit around the Earth, the total energy is decreased as the space craft moves closer to Earth.  Because it is moving closer to Earth, it will change potential energy into kinetic energy.   This causes the space craft to speed up to a higher velocity than it had at the beginning.

The concept is this.

For space craft and satellites in orbit around Earth or any other object:

1.  You get a shorter period and a faster velocity by decelerating.

2.  You get a longer period and a slower velocity by accelerating.

If you want to catch up with a space craft in the same orbit, you initially decelerate to drop into a lower or bit and speed up.  You latter accelerate to move back to the original orbit.