**Metrological Approaches**

**Chapter 4**

**Provisional chapter**

or more with

**Measuring 'Big G', the Newtonian Constant, with a**

**Measuring 'Big G', the Newtonian Constant, with a** 

A new approach is described and discussed to the determination of the Newtonian gravitational constant G, which is based on the very powerful measurement of the frequency difference between two similar oscillators. The rate of change of time delay between the two is equal to their relative frequency difference, and small variations of either one can then be detected via delay monitoring with resolution limited only by time resolution and frequency stability of the two oscillators. The latter should be highly sensitive to gravitational field, to measure *G*, which triggers the choice of simple pendulums as field detectors. Since the relative effect on frequency readily obtainable in the lab by wellcontrolled variations of the gravitational field is on the order of 10−7, stabilities on the order of 10−12 are needed of the relative frequency difference if measurement of the fifth decimal digit of *G* is the target of the experiment. It is argued that such high stability is possible with a pendulum properly designed for being locally isochronous and showing

an adequately high *Q* factor. The latter is projected to reach possibly 107

**Keywords:** Newtonian constant, simple pendulum, pendulum frequency stability,

The presently official value of the Newtonian constant *G* is listed in the most recent CODATA report (2014) as 6.674 08 × 10−11 m3 kg−1 s−2, with a quoted relative uncertainty of 4.7 × 10−5, which still makes it the least well known of all constants of nature, despite improvements

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.75635

**Frequency Metrology Approach**

**Frequency Metrology Approach**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75635

Andrea De Marchi

Andrea De Marchi

**Abstract**

the discussed design.

**1. Introduction**

time stability, isochronous pendulum

derived from a flurry of efforts undertaken in the last decades.

#### **Measuring 'Big G', the Newtonian Constant, with a Frequency Metrology Approach Measuring 'Big G', the Newtonian Constant, with a Frequency Metrology Approach**

DOI: 10.5772/intechopen.75635

#### Andrea De Marchi Andrea De Marchi

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.75635

#### **Abstract**

A new approach is described and discussed to the determination of the Newtonian gravitational constant G, which is based on the very powerful measurement of the frequency difference between two similar oscillators. The rate of change of time delay between the two is equal to their relative frequency difference, and small variations of either one can then be detected via delay monitoring with resolution limited only by time resolution and frequency stability of the two oscillators. The latter should be highly sensitive to gravitational field, to measure *G*, which triggers the choice of simple pendulums as field detectors. Since the relative effect on frequency readily obtainable in the lab by wellcontrolled variations of the gravitational field is on the order of 10−7, stabilities on the order of 10−12 are needed of the relative frequency difference if measurement of the fifth decimal digit of *G* is the target of the experiment. It is argued that such high stability is possible with a pendulum properly designed for being locally isochronous and showing an adequately high *Q* factor. The latter is projected to reach possibly 107 or more with the discussed design.

**Keywords:** Newtonian constant, simple pendulum, pendulum frequency stability, time stability, isochronous pendulum
