Originally Posted by
desiresjab
Absolutely Lagrange points exist around all massive objects. Here is the other point that Clarke first suggested. They are known as geostationary orbits. They are a different phenomenon from the Lagrange points because they stay with a single point on our equator as that point moves through night and day, while the Lagrange points are stationary (except for moving with us in orbit) and all points of our equator pass beneath them (assuming, that is, that they are aligned with our equator, which I do not know for sure).
As I think about it, I am starting to believe the Lagrange points would not be oriented above our equator at all, but about the Great Circle (a mapping term) which would be our equator without tilt. It is an interesting question which I have to find out though I am now pretty sure the Lagrange points would care nothing at all for our equator, any more than they would align themselves with some of the highly eccentric planetary orbits found in our solar system. Our home pair are a million miles away. No, they would not care about our little equator. Sometimes you answer your own questions.