Sorry, I’ve been away for a few days…
What you’re saying makes sense, but your fingers and shoulders are designed to take this sort of load. What if you were hanging by your head?
quote:“Two equal and opposite forces yield no net force. Thus there is no net acceleration, and you would be motionless (or continue on your previous trajectory). However, you would be subject to internal stress. Think of it like two people pulling on a rope. As long as they are pulling with equal force, the rope stays still. The tension in the rope, however, is not zero. If they pull hard enough, the rope would break.”
Not exactly, as I understand the equations (Physics/Astronomy grad).
The two opposing gravitational forces would oppose each other, but with no internal stress (such as the rope-pull scenario).
The forces of a field (be it magnetic, electric, gravitational,) act as a superposition of forces when added together. They act equally to cancel each other out. you are confusing, I think, the internal strain on an object under tension, with a force.
In the case of a rope tug, internal strain and tension results from the opposing forces. In a field effect, however, there is no internal strain resulting from the sumation of forces. So at your Lagrange points, superposition both cancels out the forces while also resulting in zero internal strain. This is a necessary result of General Relativity and equivalency. Otherwise, it would be potentially possible to set up an experiment that could detect whether your zero G point was “naturally” zero G or a net result of +1000 and -1000. Relativity says that such a difference shouldn’t exist.
Now, there could be potential differential forces as you drift off center, depending upon how strong the gradient between the two 1000g forces is.
GargoyleWB, what you say is correct, but only if you either have uniform gravitational fields or you’re only making your measurements at a single point. It’s tempting to say that the Equivalence Principle is inconsistent with tidal forces, and I suspect that every student of relativity has made that mistake at some point. But in fact, it is possible for your head and your feet to feel different gravitational forces, and this means that it’s also possible for your head and feet to be experiencing differing gravitational accelerations. It’s a bit less straightforward to explain how it can be that your head and feet can experience different accelerations without you being pulled apart; this is where the curvature of space (and all the complicated math that goes along with it) comes in.