# Possible deltaV savings by usage of Lagrange points in intra-solar transit

The question here is actually pretty straightforward (not),

So I'm going to expound upon it. Lagrange points are areas within a gravitational system which experience near null gravity. At least, that's an adequate description for how L1, L2, and L3 behave on a casual level which, I admit, I'm not that far above.

However, with regards to L4 and L5, due to centrifugal forces, the areas within said "areas" allows for a not so circular orbit around a central point, and so allows for a stable placement of objects. However, it crossed my mind that this (and this is true for orbits that circle around all LaGrange points) could potentially allow for enormous(?) assists when it comes to gravitational slingshots. This is because you would not just be draining the rotation of the earth but the suns rotational energy as well, and in turn allowing for exceptionally high velocities to be attained, maybe, I'm not sure.

Though I could be misunderstanding something and not taking into account that no energy is being lost or added within a reference frame of the sun. While this is true for classical orbital slingshots in the reference frame of the planet being subject to the drain of rotational energy, as it is a LaGrange point (and especially a l4 and l5 point) I would have no clue as to if it would behave in the same way when it comes to potential orbital slingshots. I'm not even entirely sure I know what I'm asking. But what I think I'm asking is

Is it possible to use LaGrange points around earth, particularly L4 and L5, as a medium to accomplish something akin to an orbital slingshot? And, if so, how effective would it be compared to a plain orbital slingshot around earth, if comparable?

The most educated I am on this topic is a partially finished first year collage/ap physics class so I genuinely have very little clue as to the outcome of this. I have no idea how my reputation got so high.

• Lagrange points don't really have "mass" to slingshot around, see here. They likely change the trajectories of things passing by, but I don't know enough to speculate. This question might be better asked on the Space Exploration stack exchange.
– BMF
Commented Jul 20, 2022 at 3:46

Absolutely.

Your idea sounds very similar to the Interplanetary Transport Network.

The general idea is that orbits around L1, L2, and L3 are unstable. Any trajectory leading into those points will eventually lead back out. And there are quite a lot of different orbits that lead into (and out of) the Lagrange points.

(I'm not sure how L4 and L5 factor into this, as their orbits are stable. But trajectories that take a spacecraft through these points but don't quite result in it getting captured in a halo orbit there can probably be used the same way.)

Switching from one of those trajectories to another while at the Lagrange point requires very little delta-V.

So a spacecraft could make its way to a Lagrange point, burn a little bit of propellent, and by doing so put itself on an entirely different trajectory.

And that trajectory could be chosen to send the spacecraft off to an intercept with another Lagrange point, where it could repeat the process. In principle, a spacecraft could get anywhere in the solar system by this process, while using very little fuel.

The downside to all this is that these types of maneuvers are very slow. Hohmann transfers orbits get you from one orbit to another in half the orbital period of the transfer orbit. Getting anywhere useful on the Interplanetary Transport Network can take many times longer.

Orbital slingshots work because one of the bodies involved "steal" momentum from the other, similarly to what happens when ice skating and you push your friend, with you coming to an alt while your friend goes much faster.

With orbital slingshots one of the two bodies is so massive that practically doesn't notice any change in velocity.

A Lagrange point however is just a point with no mass nor momentum, thus it cannot participate in any exchange due to its pointy nature.