Finding Lagrange Point L2: Gravity and Harmonics

The distance from the earth to the L2 Lagrange point is approximately 1.5 * 10^9 meters. This can be verified through a Google search or by checking out information on the JWST. It is recommended to double check your work if it seems incorrect.
  • #1
jackal123
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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?
 
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  • #2
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. :wink:

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. :smile:
 
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  • #3
Your equation is correct.
 
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FAQ: Finding Lagrange Point L2: Gravity and Harmonics

What is a Lagrange Point L2?

A Lagrange Point L2 is a location in space where the gravitational forces of two larger bodies, such as a planet and its moon, balance out. This point is located on the line connecting the two bodies, but further away from the smaller body.

How is the Lagrange Point L2 useful for space exploration?

The Lagrange Point L2 is useful for space exploration because objects placed at this point can maintain a stable orbit without using much fuel. This allows for long-term observations and measurements of distant objects, such as planets or galaxies.

What factors affect the position of the Lagrange Point L2?

The position of the Lagrange Point L2 is affected by the masses and distances of the two larger bodies, as well as the gravitational constant. It can also be influenced by other nearby objects, such as asteroids or other planets.

How is the Lagrange Point L2 related to gravity and harmonics?

The Lagrange Point L2 is related to gravity and harmonics because it is a point where the gravitational forces of the two larger bodies are in perfect balance. This balance is achieved through the interaction of gravitational forces and the harmonics of the orbiting bodies.

Can the Lagrange Point L2 be used for more than just space exploration?

Yes, the Lagrange Point L2 can also be used for telecommunications and satellite placement. Objects placed at this point can maintain a fixed position relative to the Earth, making it an ideal location for communication satellites.

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