Force of gravity on JWST while orbiting L2

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SUMMARY

The discussion focuses on the dynamics of the James Webb Space Telescope (JWST) while in orbit around the second Lagrange point (L2). It establishes that the centrifugal force vector remains in the plane of the Sun-Earth system, even when the JWST is displaced from this plane. The relationship between gravitational force and centrifugal force indicates that any displacement from the orbital plane results in a net force that pulls the telescope back towards the plane. This principle applies universally, not just at Lagrange points.

PREREQUISITES
  • Understanding of orbital mechanics
  • Familiarity with Lagrange points
  • Knowledge of centrifugal force in a rotating frame
  • Basic concepts of gravitational forces
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  • Study the principles of centrifugal force in non-inertial reference frames
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Astronomers, astrophysicists, aerospace engineers, and students studying orbital mechanics and satellite dynamics will benefit from this discussion.

Eugene
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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)?
 
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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.
 
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?
 
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.
 
Many thanks!
 

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