Question for astronomers: Based on the linked article from that blog post about the five LaGrange points relative to the Earth and Sun (https://webb.nasa.gov/content/about/orbit.html) are there similar points associated with the other planets? If so, how does the heavier gravity of the Sun (for a planet like Mercury) or the gas giants and their large moons impact the points?
- The ratio of masses between the two bodies is sufficiently large.
- The mass of objects orbiting at or near the Lagrange points is sufficiently small.
There are Lagrange points in the Earth-Sun system (JWST will orbit near L2), the Earth-Moon system (the "L4 Society" is named for one of these, proposed as the location for permanent habitable space colonies), and the other planets of the solar system and the Sun.
For bodies of sufficiently similar masses, the Lagrange points aren't well defined, as with Pluto and its comparatively giant moon / sister-dwarf-planet Charon.
And there are limits to the mass of an object which can be orbited at a Lagrange point. It's not possible, for example for there to be a "twin Earth" orbiting opposite the Sun from Earth, at the L3 point, as the mass of that object would destabilise the entire Earth-Sun-Twin system.
Lower mass of the secondary system would move Lagrange points closer to that body, higher masses would place Lagrange points at a greater distance from the secondary (lower-mass) body in an orbital pair.
I'm not sure what the situation is for highly complex orbital systems as with Jupiter and Saturn in which there are many moons which might peturb orbits near other planet-moon Lagrange points, though I suspect that these would still be reasonably well-defined for some of the larger moons of Jupiter and Saturn.
For a good visual explainer, see: https://yewtu.be/watch?v=Gu4vA2ztgGM
I am curious about Mercury's Lagrange points. Per the video, they should theoretically exist ... but have astronomers observed natural satellites at those locations, like the corresponding points for Earth or the Jupiter trojans?
I don't think I understand your question about the sun. The Lagrange point used for JWST is an Earth-Sun one.