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Atomic interferometry methods used to measure the Newtonian gravitationalconstant. To improve the accuracy, one should measure the phase of an atomicinterferometer at extreme values of atomic vertical velocities and coordinates.Owing to symmetry, the horizontal components of atomic velocities andcoordinates are also extreme. We propose using a source mass consisting of 3 ormore parts, since only in this case one can find such an arrangement of partsthat all atomic variables become extreme. Nonlinear dependences of the phase onthe uncertainties of atomic positions and velocities near those extreme valuesrequired us to modify the expression for the phase relative standard deviation(RSD). Moreover, taking into account nonlinear terms in the phase dependence onthe atomic coordinates and velocities leads to a phase shift. In the lastexperiment to measure the Newtonian gravitational constant by atomicinterferometry, this shift was not included. We took the shift into account,got a value of 199ppm for it, and this leads to a decrease in the value of theNewton constant by 0.02%. In addition, we showed that at equal sizes of theatomic cloud in the vertical and horizontal directions, as well as at equalatomic vertical and transverse temperatures, systematic errors due to thefinite size and temperature of the cloud disappear. The calculation also showedthat when using the 13-ton source mass proposed recently, the measurementaccuracy can reach 17ppm for a source mass consisting of 4 quarters. We assumedthat the source mass consisting of a set of cylinders is used for measurements.We have obtained a new analytical expression for the gravitational field of ahomogeneous cylinder.

Newtonian gravitational constant measurement. All atomic variables become extreme when using a source mass consisting of 3 or more parts