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Tidal Disruption

A comet grazes a planet at a distance R. Show that the planet's tidal force can disrupt the comet is the planet's mean density is greater than that of the comet.

P--------R-------C

F=-GMm/r2
Now my TA advises me to expand this function about r=R using a taylor series. But c'mon, this is an introductory astronomy class. We're not supposed to know Taylor series!
But even if I do, I get:
F_g=-GMm/R2+2GMm/R3(dr)
dr=dist from center of comet
m=mass of comet
M=mass of planet

/\
|____ Is this even right?

Then I show that F_t>F_sg
where F_t=?
F_sg=self gravity=?
I'm so utterly confused.
Please feel free to include a lecture on tidal forces and taylor series! Whatever help you can give would be great!
Thanks.
 

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