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Homework Statement
For a satellite of mass ##m_s## in a circular orbit of radius ##r_s## around the Earth, determine its kinetic energy K.
Homework Equations
## K = \frac {1}{2}mv^2 ##
Gravitational potential energy ## U(r) = - \frac {GmM_E}{r}##
The Attempt at a Solution
My answer is ## K = \frac {1}{2}m_sv^2 ## My textbook indicates that this is wrong and avoids using ## K = \frac {1}{2}mv^2 ## without saying why. Perhaps I can't use that equation in this question, but if that's the case, what's the reason? However my textbook states that the total energy for objects far from Earth's surface is the combination of both kinetic energy and gravitational potential energy
##\frac {1}{2}mv_1^2 - G \frac {mM_E}{r_1} = \frac {1}{2}mv_2^2 - G \frac {mM_E}{r_2} ##
Clearly, ## K = \frac {1}{2}mv^2 ## can be used in the same situation as gravitational potential energy. So why can't ## K = \frac {1}{2}mv^2 ## be used to solve the question, but it can be used for the total energy?