🚀 go-pugleaf

In article <1992Dec15.013620.24161@galois.mit.edu> jbaez@riesz.mit.edu (John C.
Baez) poses a question about a rigid body in Earth's gravitational field. He
claims that the object can be distorted by that field by an amount which will
produce an elastic potential energy gradient opposite to and stronger than the
gravitational potential energy gradient at the surface. That this can be done
is, of course, not in question; it can't. What I can't see is why it would
appear that it can be. GR aside, the distortion of a rigid body in a
gravitational force field is not proportional to the strength of the field; it
is, rather, proportional to the gradient of the (force) field. The tidal force
produces the distortion which makes manifest the elastic energy. 

Aha! I think I see the puzzle now: implicitly the distortion is proportional to
the force (Hookes' law intuition) and the elastic potential energy is
proportional to the square of the distortion, and hence to the square of the
force! Is that it, John? If so, I think I have solved it above. The distortion
will only be proportional to the force if a constraint force acts in addition
to gravity. Any "antigravity" action would not serve to levitate the object
sufficiently to lift it from the constraining floor on which it rests.

Leigh

Nah, I've got to find a better sig!