Assuming S-T distortion is the cause of the acceleration, what type of factor would the distortion be in the orbital mechanics of Saturn's Ring System or that of others? If a ring particle's orbit deviates by latitude, the distortion of Space-Time would exhibit a force gradient that would return the particle back to the equatorial plane. There would effectively be a latitudinal potential well. Perhaps this is a significant factor in stabilizing planetary rings. One might wonder why the distortion would not accelerate a ring particle eventually out of orbit. This may be due to the orbiting particle being in a nearly inertial frame relative to the rotation rate that consequently reduces the acceleration force such that it is insignificant compared to gravity or collisional forces in the ring system. On the other hand, for a vehicle flying by, there is a net energy transfer from the S-T distortion via the acceleration, as seen from a sun-centered inertial reference frame (just the same as with gravitational assists). I am not absolutely certain of my interpretation but I'll throw this out for consideration and feedback and continue to evaluate the mechanics. Alternatively, it may be that the longitudinal acceleration, if it does exist, would not allow planetary rings to persist for long periods but rather disband them.

I think Dark energy is really too much time in one area. It may be time can move mountains and space too. Maybe expanding time has the ability to distort space like gravity.Time is a force to reckon with.

What about time? Why do we expect to view things in real time from our vantage point? We look at a distant galaxy and wonder why it behaves funny and come up with an explanation for "missing mass" and we call it something nebulous called "dark matter" We are viewing that galaxy as it was millions of light years in the past. And the light reaching us from one side of that galaxy is reaching us hundreds of thousands of years before the light from the other end of that galaxy and we think we can make calculations as if we are viewing it as if the view to us of that galaxy is all happening at the same time. not to mention the slowing of time as we look toward the center of that galaxy where the super massive black hole exists. Is it just me, or are a lot of people missing the basics here?

Does the gain reverse into a loss of speed if the flyby is opposite to rotation and the associated frame dragging

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