Do the L4 and L5 points travel in a geodesic?

[kmarinas86]

Given a two body system like the sun and the earth:

Do the L4 and L5 points travel in a geodesic, or is it just the sun and the Earth which do so?

 

[Garth]

The two body problem in GR is fiendishly complicated and can only be solved numerically.

However, having said that, test-particles co-orbiting in the L₄ or L₅ points are in free fall, and in GR they would travel along geodesics.

Garth

 

[sir-pinski]

The L4 and L5 points in a two body system, such as the sun and the earth, do not travel in a geodesic. Only the two main bodies, in this case the sun and the earth, follow geodesic paths due to their mutual gravitational attraction. The L4 and L5 points are not physical objects, but rather points where the gravitational forces of the two bodies balance out, creating stable orbital positions for smaller objects like asteroids or spacecraft.

Since the L4 and L5 points are not physical bodies, they do not have the ability to travel in a geodesic path like the sun and the earth. Their motion is determined by the gravitational forces of the two main bodies, rather than following a geodesic trajectory.

It is important to note that while the L4 and L5 points do not travel in a geodesic, they do follow stable orbits around the sun and the earth, maintaining their relative positions to these two bodies. This is due to the fact that these points are in a state of equilibrium, where the gravitational forces of the two main bodies cancel each other out.

In summary, while the sun and the earth travel in a geodesic path due to their mutual gravitational attraction, the L4 and L5 points do not have the ability to do so. They follow stable orbits determined by the gravitational forces of the two main bodies, but do not travel in a geodesic trajectory.