I Why does Webb orbit L2, is it because of the Moon?

[A.T.]

2) frame rotates with the Earth at (approx.) constant angular velocity, independent of the test body.

This one. Isn't this the one depicted in the Wiki diagram?

Yes.

Won't you get the nice pseudopotential with a trough at the orbital radius and the sun behind the centrifugal barrier?

No. As already explained, the "centrifugal barrier" occurs only for type 1) effective potential, where the angular velocity of the reference frame increases with decreasing distance of the test body to the massive body. So the centrifugal potential field in that frame changes.

For type 2) the angular velocity of the reference frame is constant, and so is the centrifugal potential field. And close to the massive body the gravitational force dominates because the centrifugal force doesn't "blow up" as in type 1).

 

[A.T.]

still think a detailed gravitational potential diagram of L2 would help al lot while explaining the l2 halo orbit.

The halo orbit cannot be easily/directly explained in terms of 2D potentials alone, as it goes out of the orbital plane of the Earth. Additionally you have the Coriolis force (in the rotating frame), and orbital dynamics (in the inertial frame).

The video below goes through all that:

 

[hutchphd]

For type 2) the angular velocity of the reference frame is constant, and so is the centrifugal potential field. And close to the massive body the gravitational force dominates because the centrifugal force doesn't "blow up" as in type 1).

I am still woefully confused here. The potential I wish to examine is in a frame fixed by the rotational speed of Earth about the sun which is roughly fixed at 1 rev per year. The "test" mass is the JWST and we look for "very slow" motion wrt that rotating frame. So in this frame I am looking at static equilibria. The frame I want has constant angular velocity with origin ~at the sun. The Earth is stationary and the Langrange points also.

 

[A.T.]

The potential I wish to examine is in a frame fixed by the rotational speed of Earth about the sun which is roughly fixed at 1 rev per year.

Yes, and in this potential there is no "centrifugal barrier". Look at the video I linked above. The centrifugal potential slope decreases when you get closer to the frame rotation center (within the Sun), while the gravitational potential slope increases when you get closer to the Sun's surface. Combined you still have an increasing slope towards the Sun, when you get closer to it.

Don't confuse the potential above (for constant frame omega) with the one described here (variable frame omega):
https://en.wikipedia.org/wiki/Effective_potential

 

[A.T.]

still think a detailed gravitational potential diagram of L2 would help al lot while explaining the l2 halo orbit.

Here is a more detailed explanation of the halo orbit based on vectors.

 

[hutchphd]

Yes, and in this potential there is no "centrifugal barrier".

Yes. Thank you, it finally sank in...don't know why that was so hard. And at my age I can always blame a small cerebral event. Thanks again !

 

[sophiecentaur]

still think a detailed gravitational potential diagram of L2 would help al lot while explaining the l2 halo orbit.

I have seen them. They don't show the real situation, though. What counts is the Net Orbital Energy, including the Kinetic Energy because, with all orbits, the position and velocity of the object is a function of both. There is no 'explanation' for L2's existence if you don't include the velocity. Without the appropriate velocity, the gravitational forces are all towards the Sun.
The only L point that makes sense without motion being included is (near) L1 where, with no orbital motion at all, there is a potential maximum. The 'idea' of L1 can be grasped almost by anybody without introducing motion; it was talked about in terms of "where the gravity of the Moon takes over" and that worked for me long before any formal Physics lessons.

I guess L1 would be the point for 'those aliens' to hang at. A small ship would be pretty well undetectable against the Sun's radiation. Hidden in plain sight and watching our every (daytime) move.

 

[A.T.]

The only L point that makes sense without motion being included is (near) L1 where, with no orbital motion at all, there is a potential maximum.

It's a maximum along the radial line, but a saddle in general. And the "near" part is important. The actual L1 with orbital motion is on the sunward slope near the saddle of the purely gravitational potential, to provide centripetal acceleration towards the Sun. Only the combined potential (gravitational + centrifugal) has the saddle at L1.

 

[sophiecentaur]

It's a maximum along the radial line, but a saddle in general. And the "near" part is important. The actual L1 with orbital motion is on the sunward slope near the saddle of the purely gravitational potential, to provide centripetal acceleration towards the Sun. Only the combined potential (gravitational + centrifugal) has the saddle at L1.

That is totally correct but does it really add anything to my statement about how the situation is perceived, first time through, by the uninitiated? I find it interesting how the process of learning Science takes place and the concepts in that post come in well after the initial appreciation of a trip to the Moon.

I am aware of just how much many PF know about Science; I am also aware of just how little we know at the start of our learning.