I don't know.
I always had a gut feel that calculations which relied on the speed of light or square of the distance worked fine while we were able only to apply them to terrestrial situations. Now that we're getting into bigger numbers, maybe we'll discover it's really only .99999999999 times the square of the distance.
The equivalence of inertial and gravitational mass--and the inverse square law--are constantly being tested. One such test is the "Eotovos" experiment. I don't have my references here, but I believe the latest versions of Eotovos have confirmed inertial=gravitational mass to one part in 10^13...one experiment is planned which will increase this to one part in 10^18 (or so I seem to recall).
http://www.physics.uci.edu/gravity/
"Research program
The UCI Gravity Lab uses torsion pendulums operating at cryogenic temperature to perform tests of Newtonian gravity (distance, composition, and spin dependence), the equivalence principle, and searches for new forces. The program includes:
"A measurement of the Newtonian gravitational constant G, currently in progress, with target accuracy of about 20 ppm.
"A test of the gravitational inverse square law, to be conducted in collaboration with the University of Washington group of Professor Paul Boynton. This inverse square law test will have maximum sensitivity at ranges of about 15 cm.
"A test of Einstein's Equivalence Principle also in collaboration with Professor Boynton's group. A search for composition dependence of the force at various ranges including a local laboratory source mass, a nearby mountain, the earth, and the sun.
In parallel with the above projects, tests have been conducted of the anelastic properties of various candidate torsion fiber materials and treatments, in terms of their pendulum quality factors."
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"Gravity accelerates all objects equally. This fact was known to Newton, and tested to an accuracy of 1 part in 100 million by Eotvos. Later work by Dicke and by Braginsky has improved the accuracy of the test to 1 part in a trillion. A space mission called STEP has been proposed which will test the equality of acceleration to 1 part per quintillion. In 2000 STEP was selected for further study in NASA's SMEX program.
"What is STEP?
"The Satellite Test of the Equivalence Principle (STEP) is a US-European joint program to test one of the most fundamental ideas in all of physics, the equivalence of gravitational and inertial mass. When two bodies fall in a uniform gravitational field free of other forces their measured accelerations are identical regardless of composition. This Universality of Free Fall, a consequence of the Equivalence Principle, discovered by Galileo and popularized in his famous Tower of Pisa experiment has had a continuously unfolding importance in physics, marking off gravity from all other forces in Nature. For other forces mass has only one function, as the measure of inertia. For gravity it also fulfills a second function, as a source of acceleration.. If magnetism had been the driving force in Galileo 's experiment, a glass or stone ball would certainly not have fallen with the same acceleration as an iron ball. Newton, who first made this crucial point, distinguished two quantities that prove to be 'equivalent' in gravitation, the 'weight' of a body and the 'quantity of matter' in it, or as we would say, its gravitational mass mg and inertial mass mi .
"The Equivalence Principle asserts that the ratio mg / mi is identical for all bodies. The Equivalence Principle is the founding assumption of Einstein 's theory of gravitation, General Relativity. There are good reasons from current models for a unified quantum theory of matter and fields for believing that at levels below the present limits of testing this invariant may break down.
"STEP will advance the testing of the Equivalence Principle from several parts in 10^13 to 1 part in 10^18. Whether it confirms Equivalence five to six orders of magnitude more precisely than known today or discovers a violation, it will be a landmark experiment in Fundamental Physics, with consequences extending from gravitation theory to cosmology to theories of the evolution of the Universe. It will probe a large and otherwise inaccessible domain in the parameter space of new interactions. A null result would remain for many years a severe constraint on new theories. A positive result would constitute the discovery of a new force of Nature.
"STEP will compare the accelerations of four pairs of test masses in orbit. The free-floating test masses will be isolated from disturbances inside a cryogenic dewar with superconducting shielding and ultra-high vacuum, and their accelerations will be measured by a superconducting circuit using a quantum interference device (SQUID) for the best sensitivity. The dewar is part of a "drag-free" satellite, i.e. a satellite compensated for drag by proportional thrusters, using the test masses as reference. This technique reduces low-frequency acceleration disturbances from air drag, magnetic field, and solar pressure to an acceptable level. Gravity gradient disturbances are eliminated by precise placement of the mass centers on each other. The mission will be flown in a near-circular sun-synchronous orbit, to minimize temperature variations, for a period of six months. The best altitude is approximately 550 km.
"Research on the STEP accelerometers began in 1971 at Stanford University, and has been supported since 1977 with NASA funding. STEP has been studied twice by ESA at the Phase-A level and has led two other space agencies (CNES and ASI) to study projects aimed at testing the Equivalence Principle in space. STEP is currently undergoing a Phase A study for NASA's office of Space Science Small Explorer program. Professor Francis Everitt and Dr. Paul Worden lead the STEP collaboration at Stanford with collaborating institutions including JPL, ESTEC Netherlands, University of Birmingham, UK, University of Strathclyde, UK, Imperial College, UK, Rutherford Appleton Laboratory, UK, ZARM University of Bremen, Germany, PTB Braunschweig, Germany, Friedrich Schiller University Jena, Germany, ONERA, France, and the University of Trento, Italy.
C.D. Hoyle/T. McGonagle/Univ. of Washington
"Close attraction. Extra spatial dimensions--beyond the three we know--could alter Newton's inverse-square law of gravity at short distances. But measurements using a suspended ring above a rotating disk show that Newton is correct down to at least 200 µm.
"You might think that Newton's law of gravity is about as solid as any principle in physics. But if some of the latest grand unification theories are correct, gravity may not operate exactly the way we expect. The 19 February PRL reports experiments that test Newton's inverse-square law down to 200 µm, with at least ten times the sensitivity of previous tests. Newtonian gravity remains intact so far, which eliminates some theories proposing extra spatial dimensions, beyond the three we know. But extra dimensions may still exist, "curled up" to smaller sizes.
"While string theories promise to unify the four known types of forces in one framework, they also require at least six extra spatial dimensions. These dimensions are said to be curled up in a way that makes them normally invisible--like the width of a distant telephone pole on the horizon, you can't see them until you come in close. Extra dimensions might solve other problems as well, says Jens Gundlach of the University of Washington in Seattle, such as the surprising feebleness of gravity compared with electromagnetism and the nuclear forces. According to this view, gravity's effects spread into other dimensions, whereas the other forces are limited to our three-dimensional world. "Gravity is so weak because it's diluted," he says.
"Theorists predicted that some of the extra dimensions might extend as far as a millimeter or so, making them accessible to tabletop experiments: With two "large" extra dimensions, the 1/r2 law of gravity would look more like 1/r4 at close range. Now a University of Washington team led by Eric Adelberger and Blayne Heckel, and including Gundlach, reports the first and most sensitive of a new generation of precision, short range gravity tests searching for extra dimensions.
"Inside a high vacuum chamber, the team suspended a small metal ring from a torsion (twisting) pendulum and placed a slowly rotating disk below it. The ring and disk were perforated by ten holes each, and gravity tended to align the holes ten times per revolution. A second disk rotating just below the first one also had ten holes, but at positions designed to partially cancel the attraction of the upper disk to the ring. A mirror affixed to the pendulum reflected a laser beam and allowed Adelberger and his colleagues to detect slight rotations of the ring. Gundlach explains that the experiment was difficult partly because electrostatic fields--static electricity--could easily overwhelm the tenuous gravitational force. The team carefully stretched a 20-micrometer-thick sheet of metal between the ring and disks to shield from such effects.
"The researchers recorded the rotation of the ring suspended at heights between 200 µm and 5 mm. At 2 mm--the height where cancellation was maximized--they saw the complete cessation of motion expected from Newtonian gravity, and their data at other heights were also completely consistent with the textbooks.
"The team came up with a 'brilliant design' and carried out a 'beautiful experiment,' says Aharon Kapitulnik of Stanford University in Palo Alto, CA. One important aspect, he explains, is that they measured a complete cancellation of the gravitational force at one height but could then move the ring above and below that height to check that their apparatus detected gravity cleanly, free of background interference. Kapitulnik is working on a much shorter range measurement of gravity and says he's never discouraged by so-called null results that do not disprove Newton. 'It's important to do it, and somebody has to do it,' he says."
Submillimeter Test of the Gravitational Inverse-Square Law: A Search for "Large" Extra Dimensions C. D. Hoyle, U. Schmidt, B. R. Heckel, E. G. Adelberger, J. H. Gundlach, D. J. Kapner, and H. E. Swanson Phys. Rev. Lett. 86, 1418 (19 February 2001)