Constraints on a Yukawa gravitational potential from laser data of LAGEOS satellites

In this Letter we investigate the possibility of constraining the hypothesis of a fifth force at the length scale of two Earth's radii by investigating the effects of a Yukawa gravitational potential on the orbits of the laser-ranged LAGEOS and LAGEOS II satellites. The existing constraints on the Yukawa coupling a, obtained by fitting the LAGEOS orbit, are of the order of \alpha\ < 10(-5)-10(-8) for distances of the order of 10(9) cm. Here we show that with a suitable combination of LAGEOS and LAGEOS It data it should be possible to constrain alpha at a level of 4 x 10(-12) or less. Various sources of systematic errors are accounted for, as well. Their total impact amounts to 1 x 10(-11) during an observational time span of 5 years. In the near future, when the new data on the terrestrial gravitational field will be available from the CHAMP and GRACE missions, these limits will be further improved. The use of the proposed LARES laser-ranged satellite would yield an experimental accuracy in constraining a of the order of 1 x 10(-12). (C) 2002 Elsevier Science B.V. All rights reserved.