(II) For a satellite of mass in a circular orbit of radius r_S around the Earth, determine
(a) its kinetic energy K
Verified step by step guidance
1
Identify the mass of the satellite (m) and the radius of its orbit (r_S).
Recall that the gravitational force provides the necessary centripetal force for the satellite's circular motion. Use the formula for gravitational force, F = \frac{G \cdot M \cdot m}{r_S^2}, where G is the gravitational constant and M is the mass of the Earth.
Set the gravitational force equal to the centripetal force required to keep the satellite in orbit, which is given by F_c = \frac{m \cdot v^2}{r_S}, where v is the orbital speed of the satellite.
Solve the equation \frac{G \cdot M \cdot m}{r_S^2} = \frac{m \cdot v^2}{r_S} for v^2, and simplify to find v^2 = \frac{G \cdot M}{r_S}.
Calculate the kinetic energy (K) of the satellite using the formula K = \frac{1}{2} m v^2. Substitute v^2 from the previous step to find K = \frac{1}{2} m \frac{G \cdot M}{r_S}.