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

In summary, in a binary system, one star with a non-zero quadrupole moment will experience an additional force from the quadrupole potential, while the other star will only experience the usual gravity force. This results in an imbalance between action and reaction on the two stars, but it is possible due to Newton's third law. Each star will feel an additional quadrupole term, one due to its own quadrupole moment and the other due to the other star's quadrupole mass distribution.
  • #1
andromeda123
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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?
 
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  • #3
phinds said:
??? 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
 
  • #4
andromeda123 said:
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.
 
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  • #5
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.
 

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

What is a quadrupole in the context of a star?

A quadrupole in the context of a star refers to a distribution of mass that creates a quadrupole moment, which is essentially a second-order term in the multipole expansion of the gravitational potential. It can occur due to the star's shape being distorted, for instance, by rotation or tidal forces from a companion star in a binary system.

How does a quadrupole moment affect a binary star system?

The presence of a quadrupole moment in one or both stars of a binary system can lead to more complex gravitational interactions. These interactions can cause deviations in the orbits of the stars, potentially leading to non-Keplerian motion and affecting the system's overall dynamics, including angular momentum transfer and orbital precession.

Why would a star with a quadrupole moment violate Newton's 3rd Law in a binary system?

Newton's 3rd Law states that for every action, there is an equal and opposite reaction. In a binary system with a star that has a significant quadrupole moment, the gravitational forces can become asymmetric due to the non-uniform mass distribution. This asymmetry can result in forces that do not strictly adhere to the equal and opposite reaction principle, leading to apparent violations of Newton's 3rd Law in specific contexts.

What are the implications of violating Newton's 3rd Law in such systems?

If Newton's 3rd Law appears to be violated in a binary system with a quadrupole star, it can have significant implications for our understanding of orbital dynamics and gravitational interactions. It suggests that additional factors or more complex models, possibly involving general relativity, need to be considered to fully describe the system's behavior. It may also impact the stability and evolution of the binary system.

How can these violations be detected or measured?

Violations of Newton's 3rd Law in a binary system with a quadrupole star can be detected through precise astronomical observations. Techniques such as astrometry, spectroscopy, and timing measurements of pulsars or eclipsing binaries can reveal anomalies in the orbital parameters and motion. These observations can then be analyzed to infer the presence of a quadrupole moment and the resulting deviations from expected Newtonian dynamics.

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