A satellite of mass \(m\) is in a circular orbit of radius \(r_0\) around a planet of mass \(M\), where its initial kinetic energy is \(K_0\). Thrusters are fired to transfer the satellite into a larger circular orbit of radius \(2r_0\). The gravitational potential energy of the satellite-planet system is defined to be zero at infinite separation.

Which row in the table correctly relates the change in kinetic energy \(\Delta K\), the change in gravitational potential energy \(\Delta U_g\), and the change in total mechanical energy \(\Delta E\) of the satellite-planet system between the two orbits in terms of \(K_0\)?

	Change in Kinetic Energy, \(\Delta K\)	Change in Potential Energy, \(\Delta U_g\)	Change in Mechanical Energy, \(\Delta E\)
(A)	\(+\dfrac{1}{2}K_0\)	\(-K_0\)	\(-\dfrac{1}{2}K_0\)
(B)	\(-\dfrac{1}{2}K_0\)	\(-K_0\)	\(-\dfrac{3}{2}K_0\)
(C)	\(-K_0\)	\(+2K_0\)	\(+K_0\)
(D)	\(-\dfrac{1}{2}K_0\)	\(+K_0\)	\(+\dfrac{1}{2}K_0\)