Lagrange points are not points. They are areas of space. This a typical "spherical chickens" problem. They are mathematical points when calculated from other mathematical points. The earth is not a point, nor is the moon or any other body. Add in the effects of distant bodies (jupiter et al) and the Lagrange "point" is best thought of as a Lagrange area.
A spacecraft will not gravitate to the center of the area, nor is a spacecraft guaranteed to stay in the area naturally. It will be nudged out eventually. So the normal approach is for spacecraft or orbit the area, pretending it is a point when it isn't. This is still an unstable orbit and requires station keeping.
Station keeping in deep space is hard. Without easy reference to earth locations (no gps) it is hard to remotely determine exactly where the satellite actually is. So you need local, on-orbit, sensors to track stars and the sun. But it is still going to take fuel.
If L points were points, If objects could be caught and stay there, the rocks would by now have bunched together into lagrange moons. Those moons would create new L points between them and other bodies, creating layers of new perturbations, until the system breaks down into chaos. These aren't "parking places in space".
At least in the idealized, restricted three-body problem — two large bodies in circular orbit plus a satellite of negligible mass — the Lagrange points are true points, but they represent not a destination for the satellite, but rather the center around which a near enough satellite will orbit harmonically, under essentially the same equations that govern a spring (a restorative force linear with displacement). It truly is a stable equilibrium in that sense. No station-keeping is required.
In practice there will be slight perturbations due to the presence of other bodies, but the ∆V requirements for station-keeping are minimal.
Unfortunately, it’s a 4 body problem. Sun, earth, moon, and artificial satellite which makes these points unstable even assuming point masses. At best L4 and L5 might possibly be stable over millions of years assuming ideal conditions.
I think the article make exactly that statement. Repeatedly. And thanks to many scifi stories (gundam) there is a common belief that spacecraft or colonies will sit nicely at these points when that simply is not true. Criticism of the article is deserved.
"The interaction of the forces creates a point of equilibrium where a spacecraft may be "parked" to make observations."
"Because of the stability of these points, dust and asteroids tend to accumulate in these regions."
"Points L4 and L5, however, are stable, "like a ball in a large bowl," according to the European Space Agency."
That last one is particularly deserving of ridicule because it narrates the false belief that there is only one "parking spot", that two unguided aircraft will collide like a pair of bowling balls "in a large bowl". The chances of that occurring are akin to throwing a basketball randomly out of a plane somewhere over north america and having it score the final points in the NCAA final.
L4 and L5 are like a large frictionless bowl. In a normal bowl with frictions the balls loose energy and eventually go to the bottom and colide. In a frictionless bowl they just keep spinning forever (until they colide by chance, if the bowl is large enough, the probability of collision is small).
Also it's not a circular bowl, so IIRC the orbits are not closed and are difficult to draw.
They should be compared to a reversed bowl where any slight deviation from the center makes the balls move away exceedingly fast. But, if anyone could place the balls exactly on top, they would stay.
> The earth is not a point, nor is the moon or any other body.
From a gravitational perspective, this doesn’t matter as long as you’re outside of the body: you can treat the object as a point mass located where the center was.
Yes, so long as its mass distribution is spherically symmetric.
The oblateness and other imperfections in the Earth do measurably affect satellite orbits, to the point where precision GPS navigation must incorporate corrections.
GPS satellites need to be absurdly precise to work: they need to account for both kinds of relativity and literally carry atomic clocks to make sure that they can provide consistent time. Most bodies are more or less spherical enough for the shell theorem to be a very good approximation.
They are equilibrium points between gravity of the two bodies and the fictitious centrifugal force. Three are on the line between the two bodies (one one each side and one in the middle) where these forces cancel.
The other two are also points where these cancel, on the sides, but the cancelation is component wise since the forces aren't all collinear at these point. Two because one on each side.
A spacecraft will not gravitate to the center of the area, nor is a spacecraft guaranteed to stay in the area naturally. It will be nudged out eventually. So the normal approach is for spacecraft or orbit the area, pretending it is a point when it isn't. This is still an unstable orbit and requires station keeping.
Station keeping in deep space is hard. Without easy reference to earth locations (no gps) it is hard to remotely determine exactly where the satellite actually is. So you need local, on-orbit, sensors to track stars and the sun. But it is still going to take fuel.
If L points were points, If objects could be caught and stay there, the rocks would by now have bunched together into lagrange moons. Those moons would create new L points between them and other bodies, creating layers of new perturbations, until the system breaks down into chaos. These aren't "parking places in space".