I Star with quadrupole in a binary system violates Newton's 3rd Law?

[andromeda123]

TL;DR Summary

If in binary system, one of the two stars has a non-zero quadrupole moment, then the other star feels an additional force. On the other hand, the second star feel only the usual gravity.

Assume that, in a binary system, one (and only one) of the two stars has a non-zero quadrupole moment. Then the other star feels the usual gravity force $F_g$ plus an additional force $F_q$ coming from the quadrupole potential. On the other hand, the first star feels only the usual gravity force $-F_g$. Applying Newton's third principle, however, results in an imbalance between action and reaction on the two stars, since only one of them feels a quadrupole force. How is it possible?

 

[phinds]

Reference: https://www.physicsforums.com/forums/astronomy-and-astrophysics.71/post-thread

??? Your "reference" is a link to where you can post a new thread. It has nothing in it.

 

[andromeda123]

??? Your "reference" is a link to where you can post a new thread. It has nothing in it.

Sorry, there is no reference, I have just deleted the link

 

[Vanadium 50]

there is no reference

As far as I can tell, you are asking us to explain why something is true, but that something isn't true to begin with.

 

[Ken G]

Yeah, you can be sure Newton's third law supercedes your intuition. If you go to calculate the gravitational forces, you will take every point in one star and apply its force to every point in the other star. Since you do that for both the total forces, they always obey Newton's third law. So both stars will feel an additional quadrupole term, one because of what you have, its quadrupole moment produces additional gravity on the other star, and the other because its own quadrupole mass distribution receives an additional force from the other star.