Disequilibrium of the solar system

[petrushkagoogol]

As the Sun's supply of hydrogen gradually gets exhausted gravity takes over and predominates over fusion energy. As this happens does the equilibrium of the solar system gets distorted, and if so is there a cut-off point for the same ?

 

[Grinkle]

http://cseligman.com/text/stars/masslosseffects.htmDeriving the Effect of the Sun's Loss of Mass
With the above as background we are now ready to see how the loss of mass the Sun is bound to suffer when it gets very old affects the size of planetary orbits. In doing so we will assume that the orbits are sufficiently circular that we can use the simplifications applicable to that case, and that any friction due to gases lost by the Sun passing the various planetary orbits produces negligible effects on their motion. In that case, the only thing we need worry about is that as the Sun loses mass it exerts less gravitational force, and cannot hold the planets in the orbits that their current velocities require. As a result the planets would gradually move away from the Sun, attaining higher orbits and in the process, reducing their speeds to values which the Sun's reduced gravity could maintain in such orbits.

 

[Chronos]

The only way gravitational equilibrium can change is if the mass of the sun changes in a way that alters the center of gravity of the solar system - i.e., ejecta. The sun is the only body in our solar system with enough mass to induce any such effect of any real significance. It appears safe to say this is unlikely to occur for at least a few billion years.

 

[Ken G]

And note that the linked analysis by Seligman is only correct in the limit of infinitesmal changes in the Sun's mass, which they fail to mention in their analysis. The analysis is incorrect if the Sun's mass changes by a significant amount, one cannot analyze that situation by saying that the planet then has the mechanical energy it had before, minus the change in potential energy, that's pretty much make believe physics. You can tell the analysis is wrong in general if you simply add a lot of mass instead of removing a little, and note the answer makes no sense. The correct way to do the analysis in general is to take their requirement that the potential energy must be -2 times the kinetic energy, which is correct, and couple it to the requirement of conservation of angular momentum of the Earth's orbit. Then you can include any mass change you like, the angular momentum is much harder to change than the mechanical energy of the Earth's orbit.