Two lonely soccer balls in outer space feel nothing but their mutual attraction. In the

beginning they have a distance of $20$ km and a mass of $440$ g with a diameter of $22$ cm$.$ What

is each ball$$s momentum just before they collide as potential energy is converted into kinetic

energy?

How large are the accelerations of the balls when they start moving and just before they

collide? Find the acceleration as a function of distance a$($r$).$ Compute the times they would

travel before they collide according to the initial and final accelerations. How large are the

balls$$ velocities just after the collision if the collision was elastic and if the collision was

$($fully$)$ inelastic?

$\backslash$Gamma $=6\mathrm{.}671011$ m$3$

kg $$ s

$2$