Finding Lagrange Point L2: Gravity and Harmonics

[jackal123]

Homework Statement

If an object is placed at a Lagrange point in outer space it will orbit the Sun ‘in concert’ with the Earth. Basically, the combined gravity of the Earth and Sun create the proper force to keep the object “fixed” in the Earth-Sun system. There are five Lagrange points. I’d like you to find the second Lagrange point labeled L2 above. By find I mean determine its distance, d, from the Earth. You may use the mass of the Earth and Sun, as well as the distance between the Earth and Sun.

Relevant Equations

(GMsun m)/(r+d)^2 + (GMearth m )/(d^2) = m * GMsun / r^3 * (r+d)

So we are finding the L2 Lagrange point, specifically the distance from the earth, or d in this instance. I have used the equation above and I have come out with 1.5 * 10^9 meters as d, or L2's distance from the earth. Can anyone verify this, is the equation correct and is my final distance accurate?

 

[berkeman]

With L2 being so much in the news lately, you should be able to find the distance to check your answer either with a Google search or checking out the JWST info sites.

Let us know what you find please. If it ends up seeming wrong versus the things you find, we can check your work if you post it in detail.

 

[haruspex]

Your equation is correct.