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S-------------r------------L1--(a-r)--E

The centripetal force on this object at L1 is equal to the net force on the object. At L1, (to the left of L1 is negative)

F_net=F_sun+F_earth

-(mv

^{2})/r=-GM

_{s}m/r

^{2}+GM

_{e}m/(a-r)

^{2}

Solving for r gives a polynomial of 5th degree!!!

How do I go about this in an easier fashion???