Planets A and B have masses MA and MB , respectively, where MA>MB , and radii RA and RB , respectively. The centers of the planets are separated by a distance D. A spaceship of mass m uses its engines to fly through the two-planet system a distance r from the center of Planet A along the dashed line shown. Point P is on the dotted line and on the line connecting the centers of the two planets. Express your answer in parts in terms of MA , MB , m, D, r, and physical constants, as appropriate. Derive an expression for the sum of the gravitational potential energy of the spaceship-planet A and spaceship-planet B systems when the spaceship reaches point P. Derive an expression for the magnitude of the net gravitational force on the spaceship when the spaceship reaches point P. Determine an expression for the work done by gravity as the spaceship moves from a very large distance away to point P

Planets A and B have masses MA and MB , respectively, where MA>MB , and radii RA and RB , respectively. The centers of the planets are separated by a distance D. A spaceship of mass m uses its engines to fly through the two-planet system a distance r from the center of Planet A along the dashed line shown. Point P is on the dotted line and on the line connecting the centers of the two planets. Express your answer in parts in terms of MA , MB , m, D, r, and physical constants, as appropriate. Derive an expression for the sum of the gravitational potential energy of the spaceship-planet A and spaceship-planet B systems when the spaceship reaches point P. Derive an expression for the magnitude of the net gravitational force on the spaceship when the spaceship reaches point P. Determine an expression for the work done by gravity as the spaceship moves from a very large distance away to point P