$13.(14$ points$)$ The Nittany Lion has been thrust into an alternate universe, where the force of gravity is radial, attractive, and has the magnitude

F $=$ F$0$ m $+$ G$0$m$1$m$2$sinr r $$ r$0$ and F $=0$ when r $>$ r$0$ m$0$ r$0$

where F$0=4\mathrm{.}32106$ dynes, r$0=12,402$ AU$,$ m$0=4\mathrm{.}72104$ g$,$ and G$0=8\mathrm{.}521018$ dynes g$2.$ The spacecraft is falling radially towards a $5\mathrm{.}67$ M$$ star with a radius of $1\mathrm{.}76$ R$.$ The Nittany Lion is a sphere of radius $440\mathrm{.}0$ m; its structure can withstand a differential acceleration between the center and the hull of $75$ g$.$ Can the spacecraft survive the tidal forces during the plunge to the star? Can you?