\(g=-g_{ o }e^{ -\cfrac { x }{ r_{ e } } }\)
Consider,
\(g=-g_{ o }e^{ -i\cfrac { x }{ r_{ e } } }\)
where \(ix\) is perpendicular to \(x\) and if \(x\) is a set of radial lines from a origin then \(ix\) is the circular front with radius \(x\). On this front, the value of \(g\) is a constant, given by the expression above.
If we vary gravity by a driving force such that gravity varies in time,
\( g_{ w }=ge^{ iwt }=-g_{ o }e^{i (-\cfrac { x }{ r_{ e } } +wt) }\)
Consider,
\( \cfrac { \partial ^{ 2 }g_{ w } }{ \partial t^{ 2 } } =w^{ 2 }g_{ o }e^{i (-\cfrac { x }{ r_{ e } } +wt) }\)
and
\( \cfrac { \partial ^{ 2 }g_{ w } }{ \partial x^{ 2 } } =\cfrac { g_{ o } }{ r^{ 2 }_{ e } } e^{i (-\cfrac { x }{ r_{ e } } +wt) }\)
If
\( w^{ 2 }g_o=c^{ 2 }\cfrac { g_{ o } }{ r^{ 2 }_{ e } } \)
then,
\( \cfrac { \partial ^{ 2 }g_{ w } }{ \partial t^{ 2 } } =c^{ 2 }\cfrac { \partial ^{ 2 }g_{ w } }{ \partial x^{ 2 } } \)
That is to say, we have a gravity wave that satisfy the above wave equation. It is assumed here that gravity wave travels at light speed \(c\).
\(w^2=(2\pi f)^2=\cfrac { c^{ 2 } }{ r^{ 2 }_{ e } } \)
then
\(f=\cfrac{1}{2\pi}\cfrac{c}{r_e}\)=1/(2pi)*299792458/6371000=7.489 Hz
This value is very close to the fundamental Schumann resonances at 7.83 Hz and could the underlying cause of it. For the case of Mars of radius, \(r_m\) = 3390000 m, the fundamental Schumann Resonance will then be,
\(f_{mars}=\cfrac{1}{2\pi}\cfrac{c}{r_m}\)=1/(2pi)*299792458/3390000=14.075 Hz
If Gravitational Wave (GW) can be detected as electromagnetic wave (EMW), that means space is a carrier of both EMW and GW. Could it be that EMW and GW is one and the same thing. From previously, we also have
\(f=\cfrac{1}{2\pi}\cfrac{c}{r}\)
where \(r\) is the radius of the helical path of the dipole not the wavelength of the EMW.
