Is an antigravity device possible? A resounding "No"? Then consider the following thought experiment. Two identical satellites A and B are placed in circular orbits of equal radius each having a centre coincident with that of the Earth. Although the satellites orbit in opposite directions, they are given the same speed V tangential to the earth's radius. The planes of the two orbits have a small constant angle between them so that their flight paths intersect at only two points located at opposite sides of the Earth (the straight line joining these points passes through the Earth's centre). This is equivalent to holding a circle between thumb and forefinger at the ends of its diameter and then slightly rotating it using the diameter as an axis. The initial and final circle positions represent the two orbits under discussion. The diagram (shown right) depicts the satellites at the two intersection points located at opposite ends of the orbital diameter.

A quarter of an orbit later, the satellites reach their points of closest approach on the far side of the Earth (shown left). At this moment, just as they pass each other in opposite directions, they link up with a hook and chain (shown in white) so that instead of continuing along their respective orbits, they now rotate around a radial axis (shown in red) upon which lies their centre of gravity. Their speed V tangential to the Earth's radius remains unaffected by this coupling. Also the process is reversible in that the chains can be uncoupled at any moment (an arbitrarily small time after the moment of coupling) so that each satellite resumes a circular orbit having the same radius as before. The question is as follows. Does the mere linking of the satellites by a chain (converting their kinetic energy to rotational energy) result in their descent to earth? If the answer to this is "No", then in theory, it is possible for a rotating body to stay suspended above the Earth's surface. However, what grounds are there for answering "Yes"?

	The following solution was provided by Daniel J. Scheeres, Assistant Professor of Aerospace Engineering, The University of Michigan.