"Daniel G. Emilio" <[Only registered users see links. ]> wrote in message
Three-space curvature is a vector field. When two components contributing
to the vector are exactly equal in magnitude AND exactly opposite in
direction, they will cancel each other. This creates what is called a
"saddle point" where the curvature along one axis is directed away from the
point, while the curvature in the plane perpendicular to that axis is
directed *towards* that same point.
It does, but only at EXACTLY the saddle points. For a mutually orbiting pair
of bodies there are 5 such points called the "Lagrange points" and
designated L1, L2, and L3 (points collinear with the bodies) and L$ and L5
(60° ahead and behind in the orbit). [Only registered users see links. ]
IOW, the space is "flat."
There is an old exercise in applied analytical geometry using calculus in
which the student demonstrates that the net gravitational attraction inside
a uniform hollow sphere is zero *at all points,* a proof often ignored by
the "hollow earthers". I encountered it in my text back in the 60's.
It is. Try playing catch on a carousel sometime.
At the right place, yes.
No it isn't. Two particles of different masses will "cancel" at a different
place. When you do the calculus for differential masses in a spherical
shell you will find that the inverse-square law of attraction leads to whole
sections "cancelling out" the attractions from other whole sections that are
of different sizes and at different distances.