https://blog.extraface.com/2024/08/07/pzyb3lsc 
The above drawing is a very simplified diagram showing the gravitational forces that are at work between the earth and the moon. As you notice it looks like a topographical map, and in one sense you can conceptually think of it like a topographical map of sorts. If you notice, there are five points, labelled L1 – L5 where the diagram changes. What are these points?
https://inteligencialimite.org/2024/08/07/yhoq49n31 Well, one way to help you think of these points is like eddies in a stream. Have you ever walked by a stream and seen a leaf caught in an eddy? If you notice, the water will flow past, but the leaf will spin around and around and go nowhere. It is caught in the eddy. In one sense, points L1 – L5 are gravitational eddies. An object of minimal mass, like a space station, that drops into one of those points at the right speed, will stay in those points without the space station needing to use any additional fuel to keep itself in place.
https://solomedicalsupply.com/2024/08/07/9au6ti5 Unlike the diagram above, the whole system is a moving system. The Moon rotates around the Earth, the Earth rotates around the Sun, etc. So you need to imagine the Moon rotating around the Earth. Now imagine those five points rotating around the Earth at the same speed, and you have a glimpse of how it functions.
https://aiohealthpro.com/3fcddwjlk These points used to feature much more prominently in science fiction. You see, if you place a space station at one of those points, you no longer have to worry about it “falling” out of the sky. It will stay there without additional fuel being needed. Nowadays you do not read about those points in science fiction. But, in all our discussions of possible future space stations, almost all science fiction writers would agree that those would be the points in which to place them for the sake of energy efficiency.
https://foster2forever.com/2024/08/j2q7krc.html NASA, the ESA (the European Space Agency), and the CNSA (Chinese National Space Agency) have sent probes and observatories to either the L1 or L2 points. Some of those missions are still operational. I do not believe that anyone has sent any probes to points L4 & L5, and definitely no one to L3. However, the CSA (Canadian Space Agency) has a planned 2018 launch of a telescope to the L2 point, in conjunction with NASA and the ESA.
https://www.psicologialaboral.net/2024/08/07/aw670gyiv4m It remains to be seen whether I will live long enough to see the science fiction dream fulfilled, a first step outside the Earth. That first step could be either a Moon or Mars colony, but could just as easily be the original science fiction idea of a Lagrangian space station.
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