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

[DaveC426913]

What is that a plot of.

It's just an oblique angle of the same diagram, showing potential a little better. Doesn't really address your concerns

Please see my comments and questions in post 26.

 

[Integral]

Perhaps it is I misinterpreting the graph but...

L2 is deeper in Earth's g-well than L5, yes?

Which scenario makes more sense:
1. A satellite at L5 getting destabilized and "falling" to L2, or
2. A satellite at L2 getting destabilized and "rising" to L5?

It's not that the ridges are "huge", its that they're very flat - meaning very little change in potential over a very large distance. L4 and L5 are relatively flat space, and far from Earths steep sided well.

neither of those make any sense. L2 is the throne and crown of the L points. The Earth sun L4 and L5 are tiny dimples at 97 million miles from earth. L2 is a mountain in the back yard.

 

[DaveC426913]

neither of those make any sense. L2 is the throne and crown of the L points. The Earth sun L4 and L5 are tiny dimples at 97 million miles from earth. L2 is a mountain in the back yard.

AFAIK, nothing in the diagram contradicts what you say.

It sounds like you are mixing extent with gradient of potential

L5 is almost flat - very little change in potential over distance - which necessarily means its very large in extent.

Or look at it another way, L5 is so weak, you'd have to travel millions of miles from it to even notice a change.

L2 OTOH is so strong but also so compact that a small deviation will be a huge climb uphill. Thats what makes it so stable. A satellite is confined to a very small space that also has a strong restorative force. Ideal conditions for an L point

 

[Integral]

It's just an oblique angle of the same diagram, showing potential a little better. Doesn't really address your concerns

Please see my comments and questions in post 26.

Ok, just a rendition.
It would be nice if one could just add the potential of Earth to the potential of sun. Unfortunately the common expression of potential is the result of the integral of force, a constant of integration is dropped. I see the Earth and sun forces acting in parallel along the Earth sun axis. Thus there has to be a potential cone emanating from Earth to L2 and beyond.

 

[Integral]

AFAIK, nothing in the diagram contradicts what you say.

It sounds like you are mixing extent with gradient of potential

L5 is almost flat - very little change in potential over distance - which necessarily means its very large in extent.

Or look at it another way, L5 is so weak, you'd have to travel millions of miles from it to even notice a change.

L2 OTOH is so strong bit also so compact that a small deviation will be a huge climb uphill.

excep that way I see it L2 is the lowest potential on the map are these not potential maps?

 

[DaveC426913]

excep that way I see it L2 is the lowest potential on the map

It would seem the literature has it that L1 is the lowest, just as these diagrams indicate.

Surely that makes sense; L1 is deeper in the Sun's gravity well than L2. You'd have to get a boost of energy to lift a satellite from the sunward side of Earth to the spaceward side.

 

[Integral]

It would seem the literature has it that L1 is the lowest, just as these diagrams indicate.

Surely that makes sense; L1 is deeper in the Sun's gravity well than L2. You'd have to get a boost of energy to lift a satellite from the sunward side of Earth to the spaceward side.

I'll give you that. However L2 should be ignorantly higher then all. That is not what I see on that plot. It is barely higher then L1. And is lost in the shadows of L4 and 5.

 

[DaveC426913]

I'll give you that. However L2 should be ignorantly higher then all. That is not what I see on that plot. It is barely higher then L1. And is lost in the shadows of L4 and 5.

The wiki page has a much higher rez diagram. I tried to post it here but its too large and I can't do much about that on my phone.

https://www.google.com/url?sa=t&sou...AQFnoECAQQAQ&usg=AOvVaw1C1JEYhcHCMAW2NJrGjZQh

 

[A.T.]

IF you look at the caption for that it claims that it is a plot of potential and centrifugal force. How do you do that?

You add the gravitational and centrifugal potential.

I am not sure what this is a plot of but it is not a potential plot of the L points.

It is the total effective potential in the rotating reference frame, where both massive bodies and the L-points are at rest. That is the reference frame where you have a time independent effective potential, so you can visualize the initial acceleration of bodies released at rest in that frame based on the slope of that potential. But as soon they start moving the Coriolis force kicks in, so the objects will circle around on plateaus, instead of directly sliding off them.

 

[Integral]

Ok so it is not a gravitation potential plot. That needs to be made very clear. Now the existence and location of the L points do not depend in any way on this centrifugal potential. They are completely determined by the 2 body sun Earth system. Seeing the raw gravitational potential plot would make the L points more understandable. The main thing this plot does is erase L2. The function of the centrifugal force is not explained well. Why do I say that? There are to many people thinking that if you drop the central force the body will then fly off in the centrifugal direction. This is a misconception that this model fosters. This plot is nearly misinformation since it it just not clear what it is. Why not just analyze it as a central force problem. We know the central force, sum of Earth sun. We know the period, 1 yr. now algebra you way to a radius.

 

[A.T.]

Now the existence and location of the L points do not depend in any way on this centrifugal potential.

L points are the stationary points of the effective potential (gravitational + centrifugal) in the rotating frame

Seeing the raw gravitational potential plot would make the L points more understandable.

The gravitational potential alone is only relevant in the inertial (non-rotating) frame, where the two massive bodies are moving. In this frame you don't have a static potential, but one that is rotating all the time, and the L points are not the stationary points of that potential, because they are moving in circles, so they must lie on slopes of the rotating gravitational potential to provide centripetal acceleration.

I don't think this is simpler, but an animation for comparison with the rotating frame potential would be interesting.

The main thing this plot does is erase L2.

No it doesn't. L2 is clearly a stationary point (saddle).

There are to many people thinking that if you drop the central force the body will then fly off in the centrifugal direction.

In the rotating frame that is what happens.

 

[hutchphd]

I'm a bit confused, but I'm used to it. First this rendering, to my eye, is upside down

Did this oblique view a few years ago. View attachment 297124

The correct pseudo potential has Earth and sun on "mountain tops" because of the centrifugal barrier. The blue arrows point uphill the red downhill vis

Seeing the raw gravitational potential plot would make the L points more understandable.

Perhaps for you,certainly not for me !

In the rotating frame that is what happens.

And this all seems pretty straightforward to me once you get the signs right. Am I missing something?Fromthe Wikipedia ar

 

[A.T.]

The correct pseudo potential has Earth and sun on "mountain tops" because of the centrifugal barrier.

You are confusing two types of "effective potential":

1) Test body orbiting a single massive body - rotating frame with the same angular velocity as the test body

2) Test body in a system of two massive bodies- rotating frame with the same angular velocity as the two massive body system, but independent of the test body.

Centrifugal barrier relates to 1) but L-points are stationary points in 2), which is what the diagrams show.

 

[hutchphd]

Yes thank you I misspoke. The Wikipedia diagram is fine (but I think @DaveC426913 diagram is misleading at least to my eye). I agree with you and was trying (badly it turns out) to illuminate seeming areas of confusion.
So why the out-of-ecliptic oscillation? Does this serve to "average out" the perturbations?

 

[DaveC426913]

The Wikipedia diagram is fine (but I think @DaveC426913 diagram is misleading at least to my eye).

As in: you think it's inverted?

I think it's a valid visualization as a model of objects tending to roll downhill. No?

 

[A.T.]

The Wikipedia diagram is fine (but I think @DaveC426913 diagram is misleading at least to my eye).

They are equivalent. You are misinterpreting the Wikipedia diagram:

The correct pseudo potential has Earth and sun on "mountain tops" because of the centrifugal barrier. The blue arrows point uphill the red downhill vis

View attachment 297155

All arrows (blue & red) point downhill. I think the different colors are just used to emphasize the difference between maxima and saddle points.

 

[hutchphd]

With particular apologies to @DaveC426913 I will stop (for now) while I'm behind. I am still confused by the effective potential as I turn down the Earth's mass to zero.

 

[A.T.]

I am still confused by the effective potential as I turn down the Earth's mass to zero.

Which effective potential are you referring to?

1) Test body orbiting a single massive body - rotating frame with the same angular velocity as the test body

2) Test body in a system of two massive bodies- rotating frame with the same angular velocity as the two massive body system, but independent of the test body.

Note that turning the Earth's mass to zero doesn't make them the same.
1) frame rotates with the test body at varying angular velocity for non-circular test body orbits
2) frame rotates with the Earth at (approx.) constant angular velocity, independent of the test body.

 

[Integral]

Thanks all for your input, I am digesting it. still think a detailed gravitational potential diagram of L2 would help al lot while explaining the l2 halo orbit.

 

[hutchphd]

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

 

[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.