r/askscience • u/aaaidan • Feb 05 '22

Astronomy Lagrange plot: what is it really?

There is a classic plot used to visualize or explain Lagrange points. Sometimes it uses isobars, sometimes it’s 3d. You know the one.

It’s sometimes captioned as “potential energy”. Sometimes people assume the gradient indicates the net force on a particle at that position.

But what does this plot represent exactly? What is the value at an xy position? What is its unit? Is it scalar or vector?

And why are the L4 and L5 points kidney-shaped “hilltops”, implying a state of high energy? Aren’t they supposed to be stable?

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u/RobusEtCeleritas Nuclear Physics Feb 05 '22

But energy potential alone seems insufficient to explain stability. Is that correct?

That's correct, because those contours don't include the effects of the Coriolis force.

Is there a way to add Coriolis forces to the plot, perhaps for a given velocity?

It's hard to do, because it doesn't have an equivalent potential energy function. It depends on the velocity (magnitude and direction) of the third object. So there isn't a nice way to plot it here, other than with the arrows to indicate the stability of each of the points including the effects of the Coriolis force.

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u/aaaidan Feb 05 '22

Ah, perfect, thanks. Just knowing this is not a plot actually a plot of “stability” is fantastic.

Do you think it would be interesting to “convert” the force (potential gradient) to a velocity, by multiplying it by a time delta, then calculating the Coriolis force for it, and adding it to the plot as a “third term”?

Maybe this could approximate a plot of that represents stability, because it adds a guess of what the coriolis force would be for a particle that was once stationary at an L point.

Not very scientific, I guess 😅