James Webb Telescope and L2 Orbit Question

[exchemist]

I see that it is said the telescope will not just sit at L2 but will be in orbit around it. I don't understand how this works, as I gather that L2 is at a  "peak", rather than a"hollow", in the gravitational field due to the Sun/Earth system, with the result that objects at L2 will drift away from it (rolling down the slope, as it were), unless artificially returned to it at intervals.  

If this is right, how can the telescope orbit L2? Can someone explain? 

[beecee]

 

https://webb.nasa.gov/content/about/orbit.html#:~:text=Webb at L2&text=The gravitational forces of the,spacecraft in orbit around L2.

 

 

[exchemist]

These videos do not answer my question. 

Later note: To explain myself a bit more: according to my understanding, there is no centripetal force acting towards L2, to keep an object in orbit around it. On the contrary, as soon as an object drifts away from L2 by even a minuscule amount, the net forces cause it to move even further away. There is thus a kind of net repulsion from L2, rather than an attraction towards it (if I understand the situation correctly). I do not understand how an object can orbit L2 on this basis.  If what they are doing is artificially keeping the telescope in a circular path around L2 by means of rocket thrust, that is not an orbit - and why are they doing it?  

Edited December 30, 2021 by exchemist

[beecee]

https://webb.nasa.gov/content/about/orbit.html

Some Technical Details: It is easy for an object (like a spacecraft) at one of these five points to stay in place relative to the other two bodies (e.g., the Sun and the Earth). In fact, L4 and L5 are stable in that objects there will orbit L4 and L5 with no assistance. Some small asteroids are known to be orbiting the Sun-Earth L4 and L5 points. However, L1, L2, and L3 are metastable so objects around these points slowly drift away into their own orbits around the Sun unless they maintain their positions, for example by using small periodic rocket thrust. This is why L1, L2, and L3 don't "collect" objects like L4 and L5 do.

Webb At L2

If Webb is orbiting the Sun further out than Earth, shouldn't it take more than a year to orbit the Sun? Normally yes, but the balance of the combined gravitational pull of the Sun and the Earth at the L2 point means that Webb will keep up with the Earth as it goes around the Sun. The gravitational forces of the Sun and the Earth can nearly hold a spacecraft at this point, so that it takes relatively little rocket thrust to keep the spacecraft in orbit around L2.

And Webb will orbit around L2, not sit stationary precisely at L2. Webb's orbit is represented in this screenshot from our deployment video (below), roughly to scale; it is actually similar in size to the Moon's orbit around the Earth! This orbit (which takes Webb about 6 months to complete once) keeps the telescope out of the shadows of both the Earth and Moon. Unlike Hubble, which goes in and out of Earth shadow every 90 minutes, Webb will have an unimpeded view that will allow science operations 24/7.

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In summing, L2 is actually only semi stable and still needs some rocket thrust to keep it in orbit around L2.

https://solarsystem.nasa.gov/resources/754/what-is-a-lagrange-point/

"L4 and L5 correspond to hilltops and L1, L2 and L3 correspond to saddles (i.e. points where the potential is curving up in one direction and down in the other). This suggests that satellites placed at the Lagrange points will have a tendency to wander off (try sitting a marble on top of a watermelon or on top of a real saddle and you get the idea). But when a satellite parked at L4 or L5 starts to roll off the hill it picks up speed. At this point the Coriolis force comes into play - the same force that causes hurricanes to spin up on the earth - and sends the satellite into a stable orbit around the Lagrange point".

[TheVat]

I had an interesting time explaining to a relative why an object at L2 couldn't "just use the Earth's shadow to keep cool."  I sent along your first link, which clarifies the issues much better than I did.  I did point out that at the distance of L2, the apparent disk of Earth would be too small to cover the sun adequately (even if it were possible to hold such a position).  

L5 is ideal for a colony, hence the name of the famous L5 Society.  

[joigus]

6 hours ago, exchemist said:

[...] as I gather that L2 is at a  "peak", rather than a"hollow", in the gravitational field due to the Sun/Earth system, [...]

Maybe not a peak, but a saddle point. A saddle point would be unstable too. I studied this ages ago, and I don't remember.

Wikipedia:

Quote

The points L₁, L₂, and L₃ are positions of unstable equilibrium. Any object orbiting at L₁, L₂, or L₃ will tend to fall out of orbit; it is therefore rare to find natural objects there, and spacecraft inhabiting these areas must employ station keeping in order to maintain their position.

It's as @beecee says. Apparently you need some thrust now and then to keep it in orbit.

[Sensei]

BTW, if anyone is interested in where JW Telescope is, there is an online tracker available:

https://www.jwst.nasa.gov/content/webbLaunch/whereIsWebb.html

 

[geordief]

5 minutes ago, Sensei said:

BTW, if anyone is interested in where JW Telescope is, there is an online tracker available:

https://www.jwst.nasa.gov/content/webbLaunch/whereIsWebb.html

 

So the Sunshield has been deployed?

Thst sounds good

 

[iNow]

From the JWST FB page 7 hours ago:

 

Here's everything that has taken place since our sunshield pallets successfully opened up on Dec. 28:

1. Yesterday, our team confirmed that we successfully extended our Deployable Tower Assembly (DTA), which creates space between Webb's upper and lower halves. This helps keep the telescope cold and makes room for our upcoming sunshield deployments.

2. This morning, we completed the deployment of our aft (back) momentum flap, which helps balance pressure from solar radiation on Webb's sunshield, much like a trim tab helps stabilize a boat or plane!

3. Our sunshield covers protected the sunshield while it was folded for launch. Today those covers were removed to prep for unfolding the sunshield.

Keep up to date through our blog: blogs.nasa.gov/webb
Or track Webb's journey here: webb.nasa.gov/whereiswebb

[exchemist]

7 hours ago, joigus said:

Maybe not a peak, but a saddle point. A saddle point would be unstable too. I studied this ages ago, and I don't remember.

Wikipedia:

It's as @beecee says. Apparently you need some thrust now and then to keep it in orbit.

Now and then? If it's a saddle, there is no orbit at all, surely? 

Any object not perfectly at L2 will tend to oscillate between the "upward" slopes to either side of the saddle, while at the same time "falling down" one or other flank, never to return. That's never an "orbit" with occasional tweaks.  It seems to me that making the telescope describe a closed loop around L2 has to be a totally artificial exercise, requiring continual interventions to force it into such a path.

Why do that, considering the expenditure of rocket fuel when, if it just sat at L2 itself, it would require only tiny corrections as it started very slowly to drift off-station?

I realise I must be missing something here but the responses to date don't seem to be addressing my difficulty.   

[StringJunky]

@Janus might know.

[joigus]

4 minutes ago, StringJunky said:

@Janus might know.

Good call.

1 hour ago, exchemist said:

Now and then? If it's a saddle, there is no orbit at all, surely? 

I'm not sure. In the reference that @beecee provided, they say it requires relatively little thrust to keep it in orbit. If it's a very gentle saddle... What the technical reasons are, I don't know. Based on this, I'm assuming little fuel needs to be spent in order to keep it in orbit. The only thing I'm sure about at this point is that it's not going to be there forever.

[StringJunky]

8 minutes ago, joigus said:

Good call.

I'm not sure. In the reference that @beecee provided, they say it requires relatively little thrust to keep it in orbit. If it's a very gentle saddle... What the technical reasons are, I don't know. Based on this, I'm assuming little fuel needs to be spent in order to keep it in orbit. The only thing I'm sure about at this point is that it's not going to be there forever.

I found this but way over my head. 

https://space.stackexchange.com/questions/284/why-should-the-james-webb-space-telescope-stay-in-the-unstable-l2

The maths seems to be here, as mentioned at the end of the first link:

https://physics.stackexchange.com/questions/286642/why-are-the-lagrangian-points-l-1-l-2-l-3-unstable

[joigus]

9 minutes ago, StringJunky said:

I found this but way over my head. 

https://space.stackexchange.com/questions/284/why-should-the-james-webb-space-telescope-stay-in-the-unstable-l2

The maths seems to be here, as mentioned at the end of the first link:

https://physics.stackexchange.com/questions/286642/why-are-the-lagrangian-points-l-1-l-2-l-3-unstable

Yeah it seems that L₁, L₂, L₃ are all saddle points:

Quote

The 𝐿1, 𝐿2, 𝐿3, are all saddle shaped whereas the 𝐿4 and 𝐿5 points occur at local maxima. They are like hilltops but quite flat hilltops.

Very interesting. There's a part of it I can follow; other parts, like the stability conditions on the Hessian, which make sense to me but go over my head too. This is quite advanced Newtonian mechanics, and I don't think all of it can be safely done without computers.

 

 

[exchemist]

17 minutes ago, StringJunky said:

I found this but way over my head. 

https://space.stackexchange.com/questions/284/why-should-the-james-webb-space-telescope-stay-in-the-unstable-l2

The maths seems to be here, as mentioned at the end of the first link:

https://physics.stackexchange.com/questions/286642/why-are-the-lagrangian-points-l-1-l-2-l-3-unstable

Well done, you've found it! 

The stack exchange correspondence explains it. What I was missing is that this is of course a 3D problem. In the plane of the Earth's orbit around the sun, it is a saddle, with the flanks of the saddle extending radially towards and away from Earth. So an object that is not exactly at L2 will tend to slide in or out along the radius of the Earth's orbit around the sun.

BUT, perpendicular to that radius, it is a gravity well, so an object can indeed orbit L2 if it does so in a plane perpendicular to the radius. The only correction needed is to stop its tendency , driven by the saddle effect described earlier, to drift in or out along the radius, i.e. to stop movement out of its orbital plane around L2. 

I think that must be it. But let's see if @Januscan be tempted away from his mince pies and port to confirm. 

[joigus]

Just a couple of comments to add (and without getting into Hessian traces and eigenvalues .) The centrifugal term scales like v², and the Coriolis term scales like vr(v). So it's, in principle, within our control to set that value (a low-enough orbiting speed) such that the line of instability can be controled by means of appropriately-gentle thrusts. At least that's what my physical intuition tells me.

1 hour ago, exchemist said:

What I was missing is that this is of course a 3D problem.

We must all learn to think in 3D!!!  I spend hours on end on 1D.

Happy New Year.

Edited December 31, 2021 by joigus
correction

[exchemist]

19 minutes ago, joigus said:

Just a couple of comments to add (and without getting into Hessian traces and eigenvalues .) The centrifugal term scales like v², and the Coriolis term scales like vr(v). So it's, in principle, within our control to set that value (a low-enough orbiting speed) such that the line of instability can be controled by means of appropriately-gentle thrusts. At least that's what my physical intuition tells me.

We must all learn to think in 3D!!!  I spend hours on end on 1D.

Happy New Year.

And Happy New Year to you as well.

Yes my error was to consider everything as happening in the plane of the ecliptic.  In that plane you see a saddle, but that is because it is a cross-section through a doughnut.   

[Prometheus]

5 hours ago, joigus said:

Based on this, I'm assuming little fuel needs to be spent in order to keep it in orbit. The only thing I'm sure about at this point is that it's not going to be there forever.

I heard that its lifespan, if all goes well, will be determined by the amount of fuel it has to keep it in its L2 orbit - because the Ariane 5 rocket did such a good job on its infection burn that is anticipated to be 10 years.

[iNow]

14 minutes ago, Prometheus said:

I heard that its lifespan, if all goes well, will be determined by the amount of fuel it has to keep it in its L2 orbit - because the Ariane 5 rocket did such a good job on its infection burn that is anticipated to be 10 years.

Time of life estimates have actually been revised significantly upward because it was so successful/efficient during the stage they just completed, so bravo to the team!

This was posted to their social media pages 2 days ago:

Quote

Due to the precision of our launch and our first two mid-course corrections, our team has determined that #NASAWebb should have enough fuel to allow support of science operations for significantly more than a 10-year science lifetime! 

 

[beecee]

20 hours ago, joigus said:

It's as @beecee says. Apparently you need some thrust now and then to keep it in orbit.

And of course, as to the lifetime of it at L2.

Some info on that here.......

https://blogs.nasa.gov/webb/2021/12/29/nasa-says-webbs-excess-fuel-likely-to-extend-its-lifetime-expectations/

NASA Says Webb’s Excess Fuel Likely to Extend its Lifetime Expectations

After a successful launch of NASA’s James Webb Space Telescope Dec. 25, and completion of two mid-course correction maneuvers, the Webb team has analyzed its initial trajectory and determined the observatory should have enough propellant to allow support of science operations in orbit for significantly more than a 10-year science lifetime.  (The minimum baseline for the mission is five years.)

The analysis shows that less propellant than originally planned for is needed to correct Webb’s  trajectory toward its final orbit around the second Lagrange point known as L2, a point of gravitational balance on the far side of Earth away from the Sun. Consequently, Webb will have much more than the baseline estimate of propellant – though many factors could ultimately affect Webb’s duration of operation.

Webb has rocket propellant onboard not only for midcourse correction and insertion into orbit around L2, but also for necessary functions during the life of the mission, including “station keeping” maneuvers – small thruster burns to adjust Webb’s orbit — as well as what’s known as momentum management, which maintains Webb’s orientation in space.

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It seems iNow has already supplied this in previous post. I'm blaming the drink after New Year!

[beecee]

Another incredible aspect of the James Webb....

The temperature difference between the hot and cold sides of the telescope is huge - you could almost boil water on the hot side, and freeze nitrogen on the cold side!

from previous link.....

[zapatos]

How fast will Webb be traveling when it reaches L2?

How will Webb begin to achieve an orbit that is perpendicular to the orbit of the planets about the sun? Is its motion away from the sun essentially halted as it begins its orbiting maneuvers?

Are orbits around Lagrange points necessary to maintain position? Meaning, is it possible for a satellite like Webb to just 'sit' in the position around which it will orbit, instead of orbiting?

[swansont]

9 hours ago, zapatos said:

Are orbits around Lagrange points necessary to maintain position? Meaning, is it possible for a satellite like Webb to just 'sit' in the position around which it will orbit, instead of orbiting?

Some of them them are points of stable equilibrium, but the others are not.

https://en.wikipedia.org/wiki/Lagrange_point

L1, L2, and L3 are on the line through the centres of the two large bodies, while L4 and L5 each act as the third vertex of an equilateral triangle formed with the centres of the two large bodies. L4 and L5 are stable, which implies that objects can orbit around them in a rotating coordinate system tied to the two large bodies.

The L4 and L5 points are stable points and have a tendency to pull objects into them. Several planets have trojan asteroids near their L4 and L5 points with respect to the Sun; Jupiter has more than one million of these trojans.

[exchemist]

17 hours ago, zapatos said:

How fast will Webb be traveling when it reaches L2?

How will Webb begin to achieve an orbit that is perpendicular to the orbit of the planets about the sun? Is its motion away from the sun essentially halted as it begins its orbiting maneuvers?

Are orbits around Lagrange points necessary to maintain position? Meaning, is it possible for a satellite like Webb to just 'sit' in the position around which it will orbit, instead of orbiting?

I don't see why a satellite can't just sit at L2, albeit with occasional nudges to keep it there and stop it starting to slide either in towards, or out away from, earth, which is what would otherwise happen, given that L1, 2 and 3 are only metastable locations.

There was some information posted earlier in the thread explaining that the the telescope will be put into an orbit so as to keep it out of the shadows of the earth and the moon. I'm not sure why this is necessary, but evidently it is.  

[beecee]

"And Webb will orbit around L2, not sit stationary precisely at L2. Webb's orbit is represented in this screenshot from our deployment video (below), roughly to scale; it is actually similar in size to the Moon's orbit around the Earth! This orbit (which takes Webb about 6 months to complete once) keeps the telescope out of the shadows of both the Earth and Moon. Unlike Hubble, which goes in and out of Earth shadow every 90 minutes, Webb will have an unimpeded view that will allow science operations 24/7".

https://webb.nasa.gov/content/about/orbit.html