LEGA L NOT ICE lo(Governmen t sponsored work. Neither the UnJted This repart was prepared as an accoun Ung n behalf of the CommJeeto n: States, nor tbe Commissio n, nor any person ac o ed o implied with respect to the accu-A. Makes any warranty or re~r:~~: ::~=~::s con~ed tn th.ts rePort, or that the use racy, completene ss, or useful nee, dJ 1 ed tn this report may not tnCrtnge of any tnformaUon , apparatus, method, or process sc oe privately owned rights; or t to th use of or for damages resulting from the B. Assumes any UablUUes with r=c or prO:ess di~closed in thJs report. use of any tnformaUon , apparatus, me ' behalf f the CommtSsio n" includes any em-As used in the above, "perso:ea~: :u~::m('lln yP.: of lll\lCh contractor , to the extent that ployee or contractor of the Cu@mi 1 • t t or employee of eucb contractor prepares, sucb ewiJ\uyee or contract"'" nf the Comm ee on, uant to biB empluywcl1 t or oontrlM:t dtesem.lne. tee, or provides e.ccees to, any tnformatto~ pure wt th the Comm!eeto n, or bis employmen t with such contractor .

LEGA L NOT ICE lo(Governmen t sponsored work. Neither the UnJted This repart was prepared as an accoun Ung n behalf of the CommJeeto n: States, nor tbe Commissio n, nor any person ac o ed o implied with respect to the accu-A. Makes any warranty or re~r:~~: ::~=~::s con~ed tn th.ts rePort, or that the use racy, completene ss, or useful nee, dJ 1 ed tn this report may not tnCrtnge of any tnformaUon , apparatus, method, or process sc oe privately owned rights; or t to th use of or for damages resulting from the B. Assumes any UablUUes with r=c or prO:ess di~closed in thJs report. use of any tnformaUon , apparatus, me ' behalf f the CommtSsio n" includes any em-As used in the above, "perso:ea~: :u~::m('lln yP.: of lll\lCh contractor , to the extent that ployee or contractor of the Cu@mi 1 • t t or employee of eucb contractor prepares, sucb ewiJ\uyee or contract"'" nf the Comm ee on, uant to biB empluywcl1 t or oontrlM:t dtesem.lne. tee, or provides e.ccees to, any tnformatto~ pure wt th the Comm!eeto n, or bis employmen t with such contractor .

The first "constant of nature" to be identified, Newton's constant of universal gravitation G, is presently the least accurately known. The currently accepted value (6.672 59k0.000 85 ) X lo-" m3 kg-' sC2 has an uncertainty of 128 parts per million (ppm), whereas most other fundamental constants are known to less than 1 ppm. Moreover, the inverse-square law and the equivalence principle are not well validated at distances of the order of meters. We propose measurements within an orbiting satellite which would improve the accuracy of G by two orders of magnitude and also place new upper limits on the field-strength parameter a of any Yukawa-type force, assuming a null result. Preliminary analysis indicates that a test of the time variation of G may also be possible. Our proposed tests would place new limits on a = a s ( q , / p ) , ( q s / p ) z for characteristic lengths A between 30 cm and 30 m and for A > 1000 km. In terms of the mass mb of a vector boson presumed to mediate such a Yukawa-type force, the proposed experiment would place new limits on a for 7X lop9 e V < m b c 2 < 7 X 1 0 -' eV and for m b c 2 < 2 X 1 0 1 3 eV. Two distinct tests of the inverse-square law, one employing interactions at intermediate distances and having a peak sensitivity if A is a few meters (i.e., mbc2-l o p 7 eV), and the other employing interactions at longer distances and having a peak sensitivity for A-RE,,,, (mbcZ-3X 10-l4 eV), would both place limits of lo-' to on a. These interactions also provide tests of the equivalence principle (Eotvos' experiment). The intermediate-distance interaction would test the equivalence principle to 5 parts in 10' for A > 5 m ( m b c 2 < 4 X lo-' eV), while the longer-distance interaction would test the equivalence principle to 4 parts in lOI3 for A > REarth ( m b c Z < 3 X eV). Specifically, we propose to observe the motion of a small mass during the encounter phase of a "horseshoe" orbit-that is, in the vicinity of its closest approach to a large mass in a nearly identical orbit. The essential aspect of the interaction of the two bodies during the encounter is an exchange of energy, and we call the proposed method the "satellite energy exchange" (SEE) method. Successful application of the SEE method to gravity measurements will depend on the particular experimental design, including the configurations of the test bodies, the characteristics of the systems for maneuvering the test bodies and the satellite, and the choice of orbital parameters, which are described below. We are not aware of any existing or proposed method which approaches the accuracy of the SEE method. PACS numberk): 04.80. +z,

The vector potential has been obtained for a coil coaxial with an arbitrary number of cylindrical conductors. The derivation is quite general and employs an iterative process that has been adapted to computer programs. After the vector potential has been obtained, it is used to calculate the mutual and self-impedance of multiple and single coils, the effect of defects in the conductors on the mutual and self-impedances, and the induction heating density in the conductors.

No abstract