Measurement of the gravitational constant $G$ in space (Project SEE): sensitivity to orbital parameters and space charge effect

Abstract

We describe some new estimates concerning the recently proposed SEE (Satellite Energy Exchange) experiment for measuring the gravitational interaction parameters in space. The experiment entails precision tracking of the relative motion of two test bodies (a heavy "Shepherd", and a light "Particle") on board a drag-free space capsule. The new estimates include (i) the sensitivity of Particle trajectories and G measurement to the Shepherd quadrupole moment uncertainties; (ii) the measurement errors of G and the strength of a putative Yukawa-type force whose range parameter λmay be either of the order of a few meters or close to the Earth radius; (iii) a possible effect of the Van Allen radiation belts on the SEE experiment due to test body electric charging. The main conclusions are that (i) the SEE concept may allow one to measure G with an uncertainty smaller than 10^{-7} and a progress up to 2 orders of magnitude is possible in the assessment of the hypothetic Yukawa forces and (ii) van Allen charging of test bodies is a problem of importance but it may be solved by the existing methods.