It has been pointed out that the Newtonian second law can be tested in the very small acceleration regime by using the combined movement of the Earth and Sun around the Galactic center of mass. It has been shown that there are only two brief intervals during the year in which the experiment can be completed, which correspond to only two specific spots on the Earth surface. An alternative experimental setup is presented to allow the measurement to be made on Earth at any location and at any time.
This test will help answer the question does the universe have dark matter or are the apparent mass discrepancies inside galaxies the result o needing modifications to the Newtonian dynamics in the limit of low
accelerations. However, if gravity is modified then the test has to be done in space.
Several experimental setups could be developed to achieve the regime of very small accelerations, as discussed in this manuscript. In all cases, the main idea is to add an auxiliary device that can produce an extra acceleration such that the total acceleration over a test particle is cancelled out.
A possible experiment setup is presented below:
• For a 1-m radius ring, the considerations presented in the last section imply an upper limit to the detection area of the order of 10^−8m2. Because of the smallness of the area, the width of the ring surface should be large enough to avoid possible errors caused by the pointing process (say, a ring surface width of between 1 and 5cm) .
• To measure the effect of small accelerations on test particles, the surface of the ring could consist of a homogeneous crystal lattice of known molecular structure, and mechanical and electronic properties. The characteristics of the crystal, such as the particle diameter, lattice and dielectric constant, Curie temperature, conductance and the lattice exact phonon mode frequencies could be used for the baseline calibration of the crystal lattice (for lattice dynamics theory. In this case, the detection of the small acceleration regime could be achieved statistically by comparing the calibration laboratory spectral pattern (a control template) with the experimental spectral pattern of the frequencies from the reloaded experimental data.
The experiment could be improved by decreasing the number of atoms in the crystal lattice (nanocrystallite), thus triggering the decrease in the number of oscillation modes. A nanocrystallite of size 2-3 nanometers consists of N about 100 atoms. In this case, the full number of oscillation modes in the lattice of such a nanocrystallite is 3N. With this small number, the oscillation modes are isolated each from other and do not interact among themselves. This provides a possible conceptual design of a detector
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