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=-GM_sm/r²+GM_em/(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.

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StephenPrivitera	Lagrange Points Tweet 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=-GM_sm/r²+GM_em/(a-r)² Solving for r gives a polynomial of 5th degree!!! How do I go about this in an easier fashion???

krab Recognitions: 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.