Lagrange Points (1 Viewer)

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Estimate the distance of the L1 point from Earth.


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)
Solving for r gives a polynomial of 5th degree!!!
How do I go about this in an easier fashion???


Science Advisor
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.

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