Undergrad Force of gravity on JWST while orbiting L2

[Eugene]

TL;DR

Concerning the centrifugal force acting on James Webb telescope

When the Webb is at a point on its L2 orbit, (not at L2), what direction is the centrifugal force vector compared to the direction of the combined earth-sun gravity vector on the opposite side? Is the direction of this centrifugal vector ALWAYS parallel to the sun-earth plane? or is it always opposite (straght line connects the combined gravity and centrifugal)?

 

[Orodruin]

The Sun, Earth, and Lagrange points are all in the same plane, which is also the orbital plane. Therefore, the centrifugal force in the corotating frame also lies in this plane.

 

[Eugene]

but if the scope is 500,000 kilometers north of this point(on the L2 orbit) it is no longer in the plane. What is the relationship of the gravity force to the centrifugal force then?

 

[Orodruin]

The centrifugal force will always be in the plane of rotation. Regardless of whether or not you displace the satellite from the plane itself. Any displacement up or below the plane will therefore give a resultant force that attracts the satellite towards the plane. This is true everywhere, not only at the Lagrange points.

 

[Eugene]

Many thanks!