Precision Spheres for Gravity Probe B Experiment (GP-B)

 Abstract: Spherical gyroscope rotors for a fundamental experiment in General Relativity were manufactured out of fused silica and single crystal silicon. We describe the manufacturing process and the associated measurements.

Introduction.

    The General Theory of Relativity predicts two effects which should contribute to the drift of a perfect gyroscope in a polar orbit around the earth: a geodetic effect and a frame dragging. For a gyroscope in the form of a perfectly homogeneous sphere and for an orbit of 650 km altitude, the predicted drift rates are 6.6 arc sec per year for the geodetic effect and 0.042 arc sec per year for the frame dragging; Schiff, L.I.(ref.1). The aim of the Gravity Probe B experiment is to detect and measure these two effects to an accuracy better than 0.0005 arc sec per year.

    However, imperfections of the gyroscope rotor spheres such as asphericity and inhomogeneity also cause drifts due to classical torques. It is therefore essential that these unwanted drifts be small compared to the effects to be measured. From an analysis of the electrical torques on the rotors it was determined that in order to reduce the drift rate due to asphericity to less than 0.0001 arc sec per year, the rotor spheres have to be polished to 1 micro inch (25 nm) or to deviate no more than ± 0.5 micro inch (12 nm) from a perfect sphere. Similar requirements are also set for the niobium thin film coating which is subsequently applied to the rotor spheres, because a non uniform coating can cause mass unbalance. Problems associated with the coating are discussed by Gill, D. et al. (ref.2).

    The spheres were manufactured at the Hansen Experimental Physics Laboratory out of fused silica and out of single crystal silicon. Both materials are well established and have extensive industrial use.
[Editor's Note: While both types of rotors were made, in final flight qualification testing the Homosil fused silica performed better, exceeding specifications. Unfortunately, the single crystal silicon rotors did not pass final flight qualification testing.]

    Fused silica was originally chosen for the rotors because it is available with highly homogeneous density, which can be tested by measuring the uniformity of the index of refraction. Homosil fused silica (ref.3) was tested and selected for homogeneity by the manufacturer using interferometry. Multipath refractive index measurements in three perpendicular directions, performed at the Physics Dept. of the Univ. of Aberdeen, confirmed the manufacturer results;  De Freitas, J.M. et al. (ref.4).

    On the other hand single crystal silicon has several desirable properties. Float zone refined single crystal silicon has 1 ppm typical homogeneity, which is an order of magnitude better than our requirement. In comparison to fused silica, silicon has smaller thermal expansion coefficient (4·10^-8 K^-1 at 2 deg. K) and higher thermal conductivity (?*) [but lower specific heat (?*)]. Therefore, an effort was made to manufacture silicon spheres of a similar precision as the fused silica spheres. The Wacker company was selected as a silicon supplier (ref.5).

    The present plan is to use two gyroscope rotors spheres made of fused silica and two made of single crystal silicon. This paper will describe the manufacturing of such spheres and the related precision measurements.

    We will first describe the specially developed machines and the methods of fabrication as well as the precision instrumentation, measurement methods and data analysis. This is followed by the discussion of lapping and polishing process. We conclude with the results obtained.