Lagrange Points

[StephenPrivitera]

Estimate the distance of the L1 point from Earth.

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
-(mv2)/r=-GMsm/r2+GMem/(a-r)2
Solving for r gives a polynomial of 5th degree!!!
How do I go about this in an easier fashion???

[krab]

The key word is your first one: Estimate. Make use of the fact that the sun's mass is far larger than the earth's. This will mean for example that a-r<<a. Rewrite the equation in terms of say a and delta = a-r. Then you will find terms like (a-delta)^3, which can be approximated as a^3-3a^2*(delta). After that, it's easy.