An interstellar spacecraft from an advanced civilization

is hovering above Earth, as

shown in Fig. $12\mathrm{.}35.$ The ship

consists of two pods of mass

m separated by a rigid shaft of

negligible mass and one Earth

radius $($R$\_($E$))$ long. Find $($a$)$ the

magnitude and direction of

the net gravitational force on

the ship and $($b$)$ the net torque

about the center of mass. $($c$)$

Show that the ship's center of

gravity is displaced approxi$-$

FIGURE $12\mathrm{.}35$ Problem $65$

mately $0\mathrm{.}083$R$\_($E$)$ from its cen$-$

ter of mass.