Starship navigation usually assumes a ship is in orbit around an object at a certain radius, or some distance between leaving the orbit of one object and arriving in orbit around another one. Although this is normally true, there are other interesting places in a star system that might form destination points.
Orbits are favored because they are stable. But, as it turns out, for every two large objects, where one is much less massive than the second and is in orbit around it, there are five other points where a much smaller massed object is similarly stable. As this corresponds to the mass arrangement of a star, a planet and a spaceship, they work well for science fiction adventures.
These points are called the Lagrange Points after the mathematician who discovered them. The points themselves are imaginatively named L1, L2, L3, L4, and L5. This is easy to remember, but hard to tell apart. Referees are encouraged to come up with setting specific names for these.
The first three points, L1, L2, and L3 are known as “unstable points”, whereas L4 and L5 are “stable points”. If an unpowered object is placed in any of these points it will stay there indefinitely. If it is perturbed slightly from a stable point, it will tend to drift back to that point. If, however, it is perturbed from an unstable point, it will tend to drift away and out into a different orbit. Thus, objects in unstable points require more station keeping to remain in that position for long periods of time. Objects in stable points are likely to remain there for decades to millennia.
Another element in the mix is that an object does not have to just remain sitting in the exact point. It may orbit that point, much like it would a planet. This “halo orbit” allows for more objects to be in the position without too much crowding.
The L1 point is on the line between the planet and the sun, closer to the sun. Normally this would mean that objects at that point orbit faster than the planet, but if it is at just the right point, the planet’s mass slows that down enough to exactly balance out.
Objects in this point have a completely unobstructed view of the planet. It is relatively close, and always sees the planet in full sun. As such it is a good place for vanity projects. Some rich noble’s personal vacation spot, a resort hotel, or even a casino. Going in a different direction, it might be a notable place for notorious prisoners, with all eyes of the world watching.
Symbolically, being in full view, it is also a good point to conduct diplomatic relations. A possible location for embassies, a permanent station for discussions or just a meeting point for ships of conflicting fleets to rendezvous to negotiate.
It is an unstable point, and station keeping is required to keep objects in place. Although in reality, unmaintained objects are most likely to drift off into a stellar orbit, for dramatic purposes such abandoned facilities might threaten a planet if the plot required brave adventurers to reposition, repair or otherwise recover it.
This point is also on the line between the planet and the sun, but on the opposite side of the planet. In this case the object would tend to orbit slower than the planet, but at exactly the right point, the planet’s attraction speeds it up to the point where it exactly matches the planet’s orbital period.
Objects here equally have an unobstructed view of the planet, but in this case, it is the night side. Unless the object is in a wide halo orbit, it will be forever in darkness since the planet is exactly between the object and the sun.
This is not nearly as scenic as the L1 point, but only in visible frequencies. The whole planet is observable in other frequencies, and the fact that it is shielded from the sun, removes a rather noisy object that might otherwise interfere. Consequently, this is a great place to put a listening station.
In an oppressive police state or similar situation, this might be to regularly monitor the electromagnetic activities on this side of the planet. That might require underhanded things to be done only during the day. Or it might form a target for terrorist (or freedom fighter) activity to take out the listening station.
In a wider conflict, an opposing space faction might place spy satellites at this point. They might hire adventurers to sneak in and deploy them, or they may have put them there during a retreat, and require risk-embracing people to go and retrieve the data on them, or to refuel the station keeping engines.
Another use of such a point is by scouts before contact has been made. It’s a great place to observe a planet from and watch its development. It is harder for a primitive planet to spot such activities there.
Finally, looking the other direction, emerging planets wishing to study what is outside of their system, will find it convenient to place observation stations at this point. They are shielded from the noise of the sun and can get much better quality views of the rest of the universe.
This is the last point along the line between the planet and the sun, but this time on the opposite side of the sun. An object at this point is actually orbiting the average point of gravity (barycenter) between the planet and star, so it has the same orbital period as the planet.
This is often seen as the least popular Lagrange point. It is as far away as you can get from the planet while in the same orbit, you can’t even see the planet from there as the sun is in the way, and you don’t really get a better view of anything that you can get from any of several more accessible orbits.
However, when adventure comes into it, there are times where you may wish to be out of sight.
“No honest business is ever done at an L3 point”
—The Chief, The Raider’s Lament
The L3 point is easily 100 diameters away from the planet (and likely 100 diameters away from the star), so it is a point that can be jumped into and out of in the system. One that is not directly observable by the planet. Even if your universe has “jump flares” which alert sensors to interstellar transitions, those will likely be masked by the mass of the sun between any observers near the planet. So, if you want to enter or leave the system and have the best chance of not being observed, the L3 point is a good point for doing so.
Being in a place where high quality ground installations cannot observe or record your specific actions makes it a great place to exchange cargo unobserved. Since it is short term stable, the ships exchanging goods don’t have to be there at the same time.
L4 and L5: Trojans
These two points, the leading and trailing trojans, are along the orbit of the planet spaced sixty degrees ahead, and behind. As these are stable points, dust and debris can accumulate here naturally. Any system with both a planetoid belt and a gas giant will likely have a considerable number of asteroids in halo orbits around the two trojan points. Because of orbital mechanics there would be more in the leading point than the trailing point.
With the accumulation of natural objects in these positions, they are likely to be targets for asteroid miners. Because of distance they are a little more costly to exploit than main belt asteroids. An interesting background element would be to have a tiered society of belters, with three geographically distinct regions and cultures. The most favored would be in the main belt, those who are less so in the leading trojan, and the remainder trying to make a bare minimum margin in the trailing trojan.
Given the longevity of objects placed near these points, it is also an excellent place to look for artifacts from ancient civilizations. There could be an odd radar echo that leads players here, evidence of past resource exploitation, or crazy belter stories.
All in all, these points add an interesting difference to the normal scope of player interaction. They can be added in (or used by the players) to add some extra novelty to your game design and playing.