Consider a graph that plots the kinetic energy K of a satellite (vertical axis) versus its radial distance r from the center of a planet (horizontal axis) as the satellite travels once around a fixed elliptical orbit. On this graph, K decreases smoothly and monotonically from a maximum at r=rmin to a minimum at r=rmax.
Answer the following questions using only qualitative reasoning based on the described graph.
(a) Describe two distinct graphical features that indicate how the satellite’s speed depends on its radial position in the orbit.
(b) On the same set of axes, sketch qualitatively (no numerical scales required) curves representing the gravitational potential energy U and the total mechanical energy E of the satellite–planet system. Clearly label each curve and explain the key features you include.
(c) The slope of the K vs. r curve at a particular point represents drdK. Explain what the sign of this slope reveals about the direction of the net force acting on the satellite at that location.