Gaia Space Telescope and Lagrangian Point 2

[Johnnyallen]

I'm confused (what else is new) about L2.
While watching a video from PBS Digital Spacetime about the latest data drop from Gaia Space Telescope, Matt O'Dowd showed a CGI animation of the telescope leaving Earth then circling/orbiting L2 perpendicular to the Earth/sun plane.
I thought that the craft would remain stationary at L2. That didn't seem to be the case in the animation.
Why is this?
BTW I'm just an old retired guy who is fascinated by this stuff and never studied Physics in college. This PBS Spacetime series is awesome and very accessible (usually)

 

[darth boozer]

There are already several satellites in the L2 orbit, including the Wilkinson Microwave Anisotropy Probe,the Gaia Space Telescope and the Herschel and Planck space observatories. But there's plenty of room for another neighbor, and the Webb telescope will be heading out to L2 in the near future (2021).

 

[A.T.]

I thought that the craft would remain stationary at L2.

If you placed it exactly there, and there were no disturbances:
https://en.wikipedia.org/wiki/Lagrangian_point#Stability

Below is the effective potential in the rotating rest frame of Sun and Earth. If you place something approximately at a Lagrangian point it can go "downhill" in various directions. But the Coriolis acceleration tries to make it go in circles, so it stays in the vicinity of the Lagrangian point. And some probes can make small corrections with their thrusters.

 

[Johnnyallen]

If you placed it exactly there, and there were no disturbances:
https://en.wikipedia.org/wiki/Lagrangian_point#Stability

Below is the effective potential in the rotating rest frame of Sun and Earth. If you place something approximately at a Lagrangian point it can go "downhill" in various directions. But the Coriolis acceleration tries to make it go in circles, so it stays in the vicinity of the Lagrangian point. And some probes can make small corrections with their thrusters.

View attachment 236765

This is very helpful. Thanks.
Next question: Does the Moon have any effect?

 

[A.T.]

Does the Moon have any effect?

That's one of the disturbances. There are also the other planets, the eccentricity of the Earth's orbit, etc.

 

[Johnnyallen]

If you placed it exactly there, and there were no disturbances:
https://en.wikipedia.org/wiki/Lagrangian_point#Stability

Below is the effective potential in the rotating rest frame of Sun and Earth. If you place something approximately at a Lagrangian point it can go "downhill" in various directions. But the Coriolis acceleration tries to make it go in circles, so it stays in the vicinity of the Lagrangian point. And some probes can make small corrections with their thrusters.

View attachment 236765

This attachment was very helpful. It's a good representation of Spacetime in 3 dimensions. Given this, this would explain why the CGI of the Gaia orbit (in the PBS series) is or can be perpendicular to the Earth/sun plane.
Am I correct in this assessment?

 

[A.T.]

This attachment was very helpful. It's a good representation of Spacetime in 3 dimensions.

That isn't spacetime. It is the effective potential in 2 space dimensions.

Given this, this would explain why the CGI of the Gaia orbit (in the PBS series) is or can be perpendicular to the Earth/sun plane.

The diagram doesn't show the spatial dimension perpendicular to the Earth's orbital plane. And it shows only the potential, not the Coriolis effect.

 

[Bill McKeeman]

I find this discussion very helpful. But, still, in the neighborhood of L2, there must be a net potential well to hold an object. Is there a similar illustration of just L2 and its force field? It seems to me that it must be similar to the force field that would surround a real satellite at that position? How big would such a satellite be?

 

[A.T.]

But, still, in the neighborhood of L2, there must be a net potential well to hold an object.

The net potential doesn't have a local minimum there, and the Coriolis force cannot be expressed as a potential, because it is velocity dependent, not position dependent.