L1: between the Sun and the Earth. The Sun reflecting off the Earth would interfere with instruments.
L3: This is suitable for positioning but impractical because of distance from a communication and perspective.
L4 & L5: these are unsuitable because they're stable. Distance is an issue too. Why are stable Lagrange points unsuitable? Because things tend to collect there. Over the eons a whole bunch of crap has built up there and will continue to do so. That's not what you want when dealing with sensitive instuments.
Now you could say that you could orbit L4 or L5 like JWST orbits L2 and that's true but you still expend energy for stationkeeping. At L2 you spend energy to stay around the L2 point. At L4 and L5 you spend energy to avoid falling into the Lagrange point.
According to [1][2] it's more expensive (in delta-V terms) to get to L4/L5 than L2 but not hugely so.
[1]: https://space.stackexchange.com/questions/27010/how-does-the...
[2]: https://space.stackexchange.com/questions/57463/what-is-the-...
That still leaves the L2s of Venus, Mars, Jupiter etc.
And you can probably fit a few more into Earth L2.
It has an orbit around L2 of roughly 0.8 million km. L2 is about 1.5 million km from Earth. The moon is only 0.36 million km from Earth.
* L1 is between the Earth and Sun, so orienting the sun-shield toward the sun would result in the cold-side being heated by reflected light from the earth. It would also have access to the same patch of sky as at L2 for any given time of year, so there wouldn't be an advantage to having it at L1 as opposed to having a second telescope at L2.
* For L4 and L5, there's a ± 60 degree orbital offset relative to Earth. That gives access to a different part of the sky at any given time, but over the course of 6 months, both locations could access any part of the sky. There's a potential for time-correlation studies, where an observation at L2 and L4 are made at the same time, with the ~150 million km between them serving either as the base of a triangle for parallax measurements or as a known distance for measuring speed of travel between the
That said, I'm not sure how useful those would be. The parallax measurements could be done by ground-based telescopes simply by waiting a few months between measurements, and the speed of travel measurements would primarily provide a measurement of the index of refraction inside the heliosphere.
Overall, I'd guess the biggest scientific bang for the buck would be to load up more telescopes at L2. The proposals for the first 12 months of observations totaled about 48 months of observation time [0], so most of the proposals were rejected. The biggest advancement I can see would be to simply have more telescope time overall.
[0] https://www.stsci.edu/contents/news/jwst/2020/jwst-cycle-1-g...
[1]: https://www.esa.int/Science_Exploration/Space_Science/Hersch...
That's what I supposed.
Even L2 is big. I'm sure you could 10s or 100s of kilometres either side of "L2" and still have the same benefits as Webb has. In fact it you have enough objects there, and cooperate, they could effectively orbit each other.
Not a concern.
First: The Sun/Earth L2 is a big place. JWST's orbit around L2 is substantially larger than the Moon's orbit around Earth, and its orbit moves around in multiple dimensions -- it isn't constrained to a single dimension, like a geosynchronous orbit around Earth is. Even if there were debris in the vicinity, the odds of hitting it would be negligible.
Second: Orbits around L2 are inherently unstable -- it's a "saddle point", not an attractor. JWST has to maneuver a bit to keep itself in orbit, so any debris that ended up around L2 would naturally drift away.