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Suppose two bodies S and L are in proximity (asteroids say). L is substantially larger than S. For simplicity, let them initially have negligible angular and linear velocity.

S will begin to fall towards L. Since S is in free fall it feels no inertial effects.

Now, S is instrumented with a laser range finder which may be used to measure it's acceleration a. When a reaches some set value thrusters on L activate causing it to accelerate away from S also at a.

Prima facie, it would appear that we have a stable system wherein S is accelerated at a but feels no inertial effects. This seems problematic (e.g. the distinction in the twins paradox is said to be that the moving twin feels accelerated).

Where is the flaw? Perhaps S feels inertial forces on account of some kind of tidal effects?

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  • $\begingroup$ Are you sure the system is stable at that point? Maybe I'm misusing "stable" here, but any system with rockets involved suggests a great deal of energy being imparted into the particles being thrust away from L. $\endgroup$ – Cort Ammon Jul 15 '17 at 23:38
  • $\begingroup$ Why do you say S doesn't feel acceleration? It should still feel the pull from L - the only force on S. The entire system LS is also accelerating. Both L and S feel acceleration a. $\endgroup$ – Floris Jul 15 '17 at 23:52
  • $\begingroup$ Presumably you meant that L is instrumented rather than S. Otherwise, without a communication device, how does the instrumentation on S make the control system on L activate its thrusters? $\endgroup$ – David Hammen Jul 16 '17 at 5:28
  • $\begingroup$ 1) The system wouldn't be 'stable' in static sense but the instrumentation would ensure that L and S remained at an unvarying distance. 2) S doesn't feel force. It is falling under gravity. This is the definition of free-fall. 3) I must admit I skipped over the details of the instrumentation. Certainly L would need something. S could simply have a mirror to reflect the laser ranging pulse. I described S as instrumented out of a preconceived notion that S would contain payload and control structures. $\endgroup$ – user3473715 Jul 16 '17 at 9:56
  • $\begingroup$ The usual relativistic twin thought experiment does not involve gravity. If you would like to modify the scenario by having the accelerating twin accelerate purely because of gravity, this is possible, but then the gravity changes the age difference. Both fast travel and spending time in lower gravitational potential slows down aging. Feeling acceleration plays no role. In fact from the point of view of an observer on Pluto we on Earth are in the role of the accelerating twin who ages slower while he feels no inertial effect. $\endgroup$ – Ján Lalinský Jul 16 '17 at 21:13

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