# Minimum energy required to remove the satellite from its orbit to infinity?

My book says that minimum energy required to remove the satellite from its orbit is equal to its total energy (K.E+P.E). But shouldn't it equal to only the potential energy difference of satellite in orbit and at infinity since Kinetic energy need not be zero.

$$\Delta E = (U_2 + K_2) - (U_1 + K_1)$$
Since $U_2=0$, the energy required by the body is
$$\Delta E = K_2 -U_1 -K_1$$
Since Gravitational potential energy is negative and Kinetic energy is positive, the $-K_1$ actually helps reduce the energy required to remove the satellite from its orbit. Also, it's obvious that $K_2$ needs to be zero if we want to minimize the energy required.
Hence, the minimum energy required will be $-(K_1 + U_1)$