Flattening spacetime near the Earth

Experimental regions where all forces are minimized are desired for many types of space experiments such as those involving gravity measurements and materials processing. In a free-fall orbit, the gravity acceleration force of the Earth is canceled to first order by the orbital motion. The cancellation, however, is perfect only at the center of mass of the freely falling object. At the other points in the object there will be accelerations induced by the gravity gradient tides of the Earth. These can cause acceleration forces of 10^-7 m/sec² (10 nanogravities) at a distance of only 3 cm from the center of mass and proportionately larger accelerations at greater distances. We show that if we place six 100-kg spheres in a ring whose plane is orthogonal to the local vertical and whose center is at the center of mass of the experiment, the gravity attraction of the spheres will produce a counter-tide that can reduce the Earth tide accelerations by factors of 100 or more in significant experiment volumes. We give an example where we produced calculated acceleration levels below 10^-11 m/sec² (1 picogravity) over a disk-shaped experiment volume 30 cm in diameter and 20 cm thick in a geostationary orbit space laboratory. In materials-processing experiments, the acceleration levels attainable will be limited by the self-gravity of the material being processed. Typical self-gravity acceleration levels are 1-100 nanogravities near the outer surface of batches of moderately dense materials a number of centimeters in size. The self-gravity of a disk-shaped sample can be reduced by first using "guard rings" and "guard caps" to smooth out edge effects. Then a combination of gravity gradients from two massive spheres and rotation of the sample can be used to null the self-gravity everywhere inside the sample disk. We give an example where the maximum surface acceleration in a disk of water 30 cm in diameter and 10 cm thick in geostationary orbit is reduced by a factor of 2000 from 3×10^-8 m/sec² (3 nanogravities) to 1.3×10^-11 m/sec² (1.3 picogravities). Since the gravity gradient forces in a region are manifestations of the Riemann curvature of spacetime caused by the mass of the Earth and the self-mass of the experiment, these techniques for reducing the gravity forces in a region can be thought of as a method for "flattening" a region of spacetime-even a region that has mass in it.