Lagrange points are fascinating to me and I feel they are underrepresented in science fiction, compared to how the space age ahead of us may play out.
The events of human history on earth have revolved in great part around settling at or controlling strategically advantaged locations, for example any coastline, or a geographic bottleneck for trade and travel (think of Singapore and the Strait of Malacca).
A Lagrange point is the simplest space-based analog to this that I know of, if you want to put something in a fixed location relative to other bodies, the Lagrange points are places where you can do it with the highest fuel economy. Then when operating from that position you will have more energy available to do other things, granting you advantage over competitors who are not at the Lagrange point.
So whether it's science, research, trade, defense etc. there is a compelling reason to locate things at a Lagrange point, and it seems this is already happening as we have science satellites at L1 and L2 and I believe L3 has been talked about. The Lagrange points are not all created equal in terms of distance to their respective bodies, size, energy required to maintain a position etc. All two body systems have them, so for example the Earth and Moon have a set of Lagrange points that are significant to us.
The LPs are what a lot of our space politics and problems may eventually revolve around (quite literally!).
> events of human history on earth have revolved in great part around settling at or controlling strategically advantaged locations, for example any coastline, or a geographic bottleneck for trade and travel
Not only that, it's easier to send mass between Lagrange points than it is to send it to them from either of the orbital bodies.
Getting from Earth to L1 or L2, each 1.5mm km away, takes 15 km/s, escape + 12 km/s. (You have to fight both the Sun and the Earth's gravity.) Getting from L1 to L2 takes less than 100 m/s. (L1 to L3, L4 or L5 about 1 to 2 km/s.)
This confers strong defensive first-mover advantages; it's energy-wise easier to hold five than take one from the Earth. (Obviously, it's mass-wise easier from the Earth.)
Relays at L4 and L5 (also described in the linked Wikipedia) would be useful. If both are built it's reasonable for relay stations or satellites stay in contact continuously, if over different paths at different times of the day. The second relay station would also be useful if other objects naturally collected within the regions of stability disrupt communication.
Lagrange points are a key plot device in Iain M. Banks’s The Algebraist. I did figure out the location of the Dweller wormhole pretty quickly, thanks to thinking about how Lagrange points worked, but it is a great work of science fiction.
Regarding sci-fi; Joshua "Lagrange" Calvert did a fancy maneuver in Peter F. Hamilton's Reality Dysfunction involving a lagrange point that gave him that nickname.
I always wondered what kind of fun treasure might be hiding in the L4 and L5 points. And what kind of secret missions were already sent there by various countries to look for stuff. There could be whole precious metal asteroids sitting around!
The events of human history on earth have revolved in great part around settling at or controlling strategically advantaged locations, for example any coastline, or a geographic bottleneck for trade and travel (think of Singapore and the Strait of Malacca).
A Lagrange point is the simplest space-based analog to this that I know of, if you want to put something in a fixed location relative to other bodies, the Lagrange points are places where you can do it with the highest fuel economy. Then when operating from that position you will have more energy available to do other things, granting you advantage over competitors who are not at the Lagrange point.
So whether it's science, research, trade, defense etc. there is a compelling reason to locate things at a Lagrange point, and it seems this is already happening as we have science satellites at L1 and L2 and I believe L3 has been talked about. The Lagrange points are not all created equal in terms of distance to their respective bodies, size, energy required to maintain a position etc. All two body systems have them, so for example the Earth and Moon have a set of Lagrange points that are significant to us.
The LPs are what a lot of our space politics and problems may eventually revolve around (quite literally!).