Precision measurement of the Newtonian
gravitational constant using cold atoms.
Take for example the simple Law of Gravity envisioned by Newton in 1660s that force of gravity equals the product of masses divided by the square of the distance between the two masses and multiplied by a
gravitational constant. This very simple but prophetic mathematical formulation has been providing the basis for precisely calculating the trajectories of all space missions, even beyond the solar system, undertaken to-date.
[M.sub.gj] is gravitational mass of mass j, G(t) is the
gravitational constant in time t and [R.sub.ij] is the distance between the two objects j and i.
We assume Planck constant, Boltzmann constant, and the speed of light as h = [K.sub.B] = c = 1 and define the
gravitational constant 8[pi]G by the relation [K.sup.2] = 8[pi]/[M.sup.2.sub.pl] (where [M.sub.pl] is Planckmass).
Drawn from the proceedings of the XXII International Conference on Laser Spectroscopy (ICOL2015), held in Singapore in June and July of 2015, the eight papers in this volume discuss quantum walks with neutral atoms in state-dependent optical lattices; the role of muonic atoms in nuclear structure; the development and optimization of Doppler broadening thermometry using acetylene as a molecular target; antiferromagnetism with ultracold atoms; the generation and transfer of stable optical frequencies in optical clocks with trapped ions; precision measurement of the Newtonian
gravitational constant by atom interferometry; optical sideband cooling in a Penning trap; and Bose-Einstein condensation of photons vs.
where [M.sub.i](t) and [M.sub.j](t) are the masses of the ith agent and the jth agent, respectively, G(t) is the
gravitational constant at the ith time, [epsilon] is a small constant, and [R.sub.ij] is the Euclidian distance between the ith agent and the jth agent [17].
where: G is the
gravitational constant, M and m are the masses of the two objects, r is the distance between the two objects, c is the speed of light, p is the half normal chord for the object m moving around the object M along with a curve, and the value of p is given by: p = a(l-[e.sup.2]) (for ellipse), p = a ([e.sup.2]-l) (for hyperbola), p = [y.sup.2]/2x (for parabola).
where [rand.sub.j] is a random number in the interval [0, 1], G(t) is the
gravitational constant at time t, [M.sub.i] and [M.sub.j] are masses of agents i and j, [epsilon] is a small value and [R.sub.ij] (t) is the Euclidean distance between two agents, i and j.