A rocket blasts off from the surface of the asteroid system Didymos with a speed of vi $=1\mathrm{.}0$e$+02$ m$/$s$.$ Assume the launch happens quickly and then the rocket coasts away from the asteroid.

Two spheres A and B of mass $8\mathrm{.}5$ kg and $8\mathrm{.}3$ kg respectively are separated by a distance of $0\mathrm{.}56$ m$.$

$($a$)$ Calculate the magnitude of the gravitational force A exerts on B and B exerts on A$.$

force A exerts on B$$ N force B exerts on A$$ N

$($b$)$ If the force between the spheres is now $4\mathrm{.}1010-9$ N$,$ how far apart are their centers?

m