A better estimation of the Universal Gravitational Constant

Abstract

The Universal Gravitational Constant (G) is the least- accurately known of all the fundamental physical constants. The reasons are several, but stem mainly from two sources: (i) gravity is a very weak force, and (ii) G always appears in product with masses and is therefore impossible to know better than we know the masses themselves. In the past, many researchers have sought to obtain high precision estimates of G, but have been limited by several practical problems. This research attempts to develop a spacebased experiment concept, designed to determine this constant to a better accuracy. Two small masses, each on the order of less than half a ton, are considered a gravitationally bound pair and their system dynamics is studied under two different cases - a three-body case, where the pair is in a high Earth-orbit, and a four- body case, where the pair is placed at the relatively stable Lagrangian point (L4 or L5) of the Earth-Moon system. The inverse-problem is solved to provide an 'optimal estimate' of G, i.e., given a large number of measurements of the system motion, that can be modelled as a function of several parameters including G, of which some may be poorly known, the aim is to produce more optimal estimates of all of these parameters. This is done using a conventional Gaussian least-squares differential correction algorithm and in the absence of model errors, making certain assumptions on how precisely we can manufacture the spherical masses, it is found that G can possibly be improved by three digits over its presently known value. This research being computational, the non-availability of real measurements is replaced by simulated measurements.