## Gravitational Experiments in the LaboratoryThis book provides an account of the precise experiments exploring the nature of universal gravitation that can be performed in a laboratory. Experiment design is discussed, including an analysis of the effects of noise and other disturbances. Critical accounts are given of the principal experiments testing the principle of equivalence and the inverse square law, and measuring the constant of gravitation. The book will be of value to those engaged in either theoretical or experimental studies of gravitation, and who wish to understand the nature and problems of laboratory experiments in this field. 1. Introduction; 2. The linear oscillator driven by thermal noise and with electrical damping; 3. External sources of noise, and design of experiments; 4. The weak principle of equivalence; 5. Verification of the weak principle of equivalence for free particles; 6. Newtonian attractors of extended bodies; 7. Experimental tests of the inverse square law; 8. The constant of gravitation; 9. Conclusion; References; Index. |

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### Contents

1 Introduction | 1 |

2 The linear oscillator driven by thermal noise and with electrical damping | 9 |

3 External sources of noise and design of experiments | 34 |

4 The weak principle of equivalence | 58 |

5 Verification of the weak principle of equivalence for free particles | 97 |

6 Newtonian attractions of extended bodies | 109 |

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### Common terms and phrases

amplitude angle angular angular resolution apparatus attracting masses axis beam balance calculated coeﬂicient component deﬁned density detector determination of G deviation diameter direct deﬂection discussed displacement distance Earth effect electrons Eotvos equation of motion equilibrium position experimental feedback ﬁnite ﬁrst ﬁxed ﬂuctuation frequency function gravitational attraction gravitational constant gravitational experiments gravitational ﬁeld gravitational force gravitational mass ground noise hollow cylinder inertial mass inﬂuence inverse square law laboratory least detectable length linear oscillator located measurement of G mechanical method moment of inertia neutrons Newtonian non-linear non-Newtonian null experiment observations optical lever particle period plane potential precision principle of equivalence radial ratio reduced relative resonance rotating sensitivity shown in Fig signal signiﬁcant simple pendulum sphere spherical stationary point suspension ﬁbre temperature test bodies test mass thermal noise torque torsion balance torsion pendulum tungsten vacuum chamber velocity vibration voltage weak principle wire