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This is the first of five connected papers detailing progress on the Gravity Probe B (GP-B) Relativity Mission. GP-B, launched 20 April 2004, is a landmark physics experiment in space to test two fundamental predictions of Einstein’s general relativity theory, the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection began 28 August 2004 and science operations were completed 29 September 2005. The data analysis has proven deeper than expected as a result of two mutually reinforcing complications in gyroscope performance: (1) a changing polhode path affecting the calibration of the gyroscope scale factor C g against the aberration of starlight and (2) two larger than expected manifestations of a Newtonian gyro torque due to patch potentials on the rotor and housing. In earlier papers, we reported two methods, ‘geometric’ and ‘algebraic’, for identifying and removing the first Newtonian effect (‘misalignment torque’), and also a preliminary method of treating the second (‘roll-polhode resonance torque’). Central to the progress in both torque modeling and C g determination has been an extended effort on “Trapped Flux Mapping” commenced in November 2006. A turning point came in August 2008 when it became possible to include a detailed history of the resonance torques into the computation. The East-West (frame-dragging) effect is now plainly visible in the processed data. The current statistical uncertainty from an analysis of 155 days of data is 5.4 marc-s/yr (∼14% of the predicted effect), though it must be emphasized that this is a preliminary result requiring rigorous investigation of systematics by methods discussed in the accompanying paper by Muhlfelder et al. A covariance analysis incorporating models of the patch effect torques indicates that a 3–5% determination of frame-dragging is possible with more complete, computationally intensive data analysis.

The contribution of the Mattis-Bardeen theory to the understanding of the surface impedance of superconductors and normal conductors is reviewed. The early theoretical and experimental studies of the surface impedance of conductors are sketched to provide the context in which the Mattis-Bardeen theory and, independently, the Abrikosov-Gor'kov-Khalatnikov theory were developed. The Mattis-Bardeen theory is described along with the methods for numerical calculation of the surface impedance from their expression for the current density. Extensions to include the effects of anisotropy and strong coupling are briefly discussed. Theory is compared with representative measurements of the surface impedance, demonstrating excellent agreement in absolute magnitude and in the dependences on frequency, temperature, and material parameters.

We have characterized the stress and its effects on surface morphology for multi-layer thin films of about 3μm total thickness, consisting of three or seven layers of Ti and Cu. These films constitute the electrostatic suspension electrodes for the gyroscope housings of the Relativity Mission Gravity Probe B. Full understanding of surface morphology is critical for meeting the complex requirements of this application.The residual stresses have been measured using a laser curvature technique, while the surface morphology was studied by scanning electron microscopy (SEM). We find that the surface morphology depends strongly on the stress, which evolves with the Ti-Cu multi-layer period. Average stress and the resulting surface roughness decrease for thinner Cu layers (increased total number of layers). Seven layer Ti-Cu films with low stress and very smooth surface have been successfully used for the electrodes of the gyroscope housings.

Techniques based on superconductivity are crucial in providing the means of achieving the high accuracy and low noise required by experimental tests of gravitational theories. We discuss applications of superconductivity to two space-based experiments: the Gravity Probe B Relativity Mission (GP-B), and the Satellite Test of the Equivalence Principle (STEP). Superconducting shields attenuate the dc magnetic field to less than 10−11 T and provide an ac shielding factor in excess of 1012. The readout of the GP-B gyroscopes is based on the London magnetic dipole generated by a rotating superconductor and detected with state-of-the-art dc SQUIDs, which are also used in STEP.