Geodesics are introduced and the geodesic equation analysed for the geometries introduced in chapter 2, using variation principles of classical mechanics. Geodesic motino on a sphere is described as well as the Coriolis effect and the Sagnac effect. Newtonian gravity is derived as the non-relativistic limit of geodesic motion in space-time. Geodesics in an expanding universe and heat death is described. Geodesics in Schwarzschild space-time are treated in detail: the precession of the perihelion of Mercury; the bending of light by the Sun; Shapiro time delay; black holes and the event horizon. Gravitational waves and gravitational lensing are also covered.

This chapter discusses the design properties and operational practices of the helium–neon ring laser gyroscope in fine detail. We look atmonolithic ring laser design and explore the advantage of upscaling, which eventually necessitates a heterolithic cavity structure. This requires us to revisit the scale factor stability, beam wander and strain effects. Topics like backscatter correction, sensor sensitivity and a variety of different operation modes, such as single laser mode or the mode-locked regime, are presented and critically discussed. The mitigation of all sorts of obvious and also a large number of unsuspected ring laser error sources is intensively treated and illustrated with a rich body of measurement examples, before the importance and limitations of the cavity mirrors is addressed. This leads us to explore several alternative transitions of neon, before the design and realization of large sensor arrays is described. With the realization of the ROMY ring laser array in the shape of a tetrahedron, we have recovered the full Earth rotation vector. Furthermore, ROMY is also the first six degree of freedom sensor for teleseismic events.

The essence of a well performing ring laser gyro is the complete reciprocity of the traveling wave oscillator. In addition to this, the scale factor needs to be sufficiently large and above all extremely stable. In an active ring laser gyroscope, the gain medium inside the resonator causes a modification to the scale factor of the instrument, which is important to quantify correctly in order to relate the observed optical beat note properly to the experienced rate of rotation of the sensor. For highly accurate rotation sensing, these effects have to be known with extremely high accuracy. This chapter introduces the important helium–neon-based ring laser gyroscope design features.

This preface of the book provides the driving motivation for the development of ultra-stable and highly sensitive inertial rotation sensing for applications in the geosciences. It identifies the exact observation of the rotation rate and the orientation of the rotation axis of the Earth as the important connecting link between the terrestrial reference frame and the long-term-stable celestial reference frame. The former is important because we navigate in this frame, while the latter is the frame in which navigation satellite motion is defined. With the precise knowledge of Earth rotation, one can transform from one reference frame to the other. At this point in time, space geodesy still awaits a self-contained continuously observing high resolution inertial sensor for this demanding task. Large ring laser gyroscopes are currently the only promising technique for this task.