A satellite of mass m travels in an elliptical orbit around Earth. At apoapsis (point A) its distance from Earth’s center is rA=1.5RE, and at periapsis (point P) its distance is rP=1.2RE, where RE is Earth’s radius. Neglect atmospheric drag and assume Earth’s mass is so large that its motion is negligible.
Answer the following about the satellite’s mechanical energies as it moves once around the orbit, beginning at point A and proceeding through point P back to point A.
(a) Describe qualitatively how the satellite’s speed changes as it moves from point A to point P. Identify the point at which the speed is greatest and the point at which it is least, and justify your reasoning without using explicit calculations.
(b) Rank the satellite’s kinetic energies at the following three locations, from greatest to least, and clearly justify each inequality:
• point A (apoapsis)
• a midpoint location where the radius is rm=1.3RE
• point P (periapsis)
(c) Rank the magnitudes of the satellite’s gravitational potential energies ∣U∣ at the same three locations, from greatest to least. Explain how your ranking is consistent with the form of the gravitational potential energy function.
(d) State whether the total mechanical energy E of the satellite–Earth system is positive, negative, or zero. Explain how you can determine this sign without performing a detailed numerical calculation.