I appreciate your responses, which were pretty much as anticipated. However, you are both wrong. It is true that the falloff in the near field of the electric dipole of a hydrogen atom (having but a single electron and a single proton) is third order, but the falloff in the far field is second order.
It is true that the dipole field is well understood for the static case. However, when it is moved, things change. If you don't believe, this you can prove it to yourself by trying to solve a very simple puzzle at
www.science-site.net/puzzle.htm .
This puzzle may seem simple to solve at first, but it is not.
Take into consideration the fact that the gravitational force is very tiny in comparison to the Coulomb force (by a factor of about 10^41 times). Therefore, any nonlinearity in the electrical forces can produce forces in excess of the gravitational force. Note that the dipole equation is nonlinear.
The scenario that I chose for the hydrogen atom is one electron rotating around a fixed proton and two stationary atoms spaced apart. Therefore one must consider the proton-proton and electron-electron negative force and the electron-proton positive forces. Then space the atoms apart and add all of the forces together. They do not add up to zero, and the resulting force is greater than that of gravity by a small amount.