The maximum iteration number is 500, the number of agents (N) is 50, and the initial gravitational constant
([G.sub.0]) is 100.
where t is the time variable, corresponds to current iteration; [t.sub.max] is the maximum iteration, [G.sub.0] is the initial gravitational constant
(set to 100), and [alpha] is the algorithm control variable (set to 20) .
Physics shows that all the basic phenomena of nature and the laws that govern them have particular constants or ratios associated with them--the gravitational constant
, the electric charge, the mass of the electron, Planck's constant from quantum mechanics, and others.
That left two unknowns, the mass of the Earth and the gravitational constant
. If one of these could be determined, the other could be calculated at once.
wher e G and C are expressed in units of mass; dm is the element of (active gravitational(29)) mass; r is the distance between dm and P; f is the gravitational constant
; l is the distance between dm and the rotation axis of the earth; |Omega~ is the angular velocity of the earth.
A team of researchers from NASA and Massachusetts Institute of Technology (MIT) studied changes in the orbit of Mercury to determine the rate at which solar mass is being lost, which has implications for our knowledge of some other solar parameters and also the stability of the gravitational constant
with [LAMBDA] being the cosmological constant and [kappa] being the D-dimensional gravitational constant
defined as [kappa] = 2(D - 3) [[OMEGA].sub.D-1][G.sub.D], where [G.sub.D] is the Newton's constant in D-dimensions (the units for the D-dimensional gravitational constant
are [G.sub.D] = [G.sub.4][L.sub.D-4], where [G.sub.4] is the gravitational constant
in 4-spacetime dimensions and L is a unit of length).
Several long, detailed papers are presented, covering a general review of atom interferometry, interferometry with composite quantum objects, use of internal excitation, general relativity and gravitational waves, quantum mechanics and matter waves oscillating at the Compton frequency, Bloch oscillations, precision measurement of the gravitational constant
, inertial sensing, measurement of local gravity, several contributions on gravitational wave detection, measurement of electromagnetic interactions, Bose-Einstein condensates, phase estimation, and interferometry beyond classical limits.
The value and sign of the gravitational constant
G are of no consequence on an astronomical scale.