Magnetic Gravity

Sanchez Exponential

The following equation:

${\frac {\alpha _{g}}{2\pi \alpha ^{2}}}={\frac {Gm_{e}}{2\pi \alpha ^{2}ch}}={\frac {Gm_{e}\epsilon _{0}}{\alpha \pi q_{e}^{2}}}={\frac {Gm_{e}2ch\epsilon _{0}^{2}}{\pi q_{e}^{4}}}={\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}}={\frac {\ell _{P}^{2}}{2\pi r_{e}^{2}}}=$

$=\exp({\frac {\pi }{4}}{\sqrt {2}}\alpha -{\frac {1}{{\sqrt {2}}\alpha }})=e^{-96.891}=2^{-139.784}=10^{-42.079}={\texttt {8.33E-43}}$

because of $\exp(\ln(x))=x$ on

$\exp(\ln({\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}}))=\exp({\frac {\pi }{4}}{\sqrt {2}}\alpha -{\frac {1}{{\sqrt {2}}\alpha }})$

because of $\exp(x)=\exp(x)$ on

$\ln({\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}})={\frac {\pi }{4}}{\sqrt {2}}\alpha -{\frac {1}{{\sqrt {2}}\alpha }}$

because of $x=0+x$ on

$0={\frac {\pi }{4}}{\sqrt {2}}\alpha -\ln({\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}})-{\frac {1}{{\sqrt {2}}\alpha }}$

because of $\alpha =r_{e}/r_{c}$ on

$0=r_{e}^{1}{\frac {\pi }{4}}{\frac {\sqrt {2}}{r_{c}}}-\ln({\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}})-r_{e}^{-1}{\frac {r_{c}}{\sqrt {2}}}$

because of $\int r^{n}\partial r=(n+1\neq 0)?{\frac {1}{n+1}}r^{n+1}:\ln(r)$ on

$0=\int _{r_{e}}^{r_{e}+\partial r}\left(r^{0}{\frac {\pi }{4}}{\frac {\sqrt {2}}{r_{c}}}-r^{-1}{\frac {Gh}{(2\pi c)^{3}r_{e}^{2}}}+r^{-2}{\frac {r_{c}}{\sqrt {2}}}\right)\partial r$

because of $\int _{0}^{1}{\sqrt {1-c^{2}}}\partial c={\frac {\pi }{4}}$ on

$0=\int _{r_{e}}^{r_{e}+\partial r}\left({\frac {\int _{0}^{1}{\sqrt {1-c^{2}}}\partial c}{r_{c}/{\sqrt {2}}}}-{\frac {{\frac {Gm_{e}}{{\sqrt {2}}\pi c^{2}r}}{\frac {h}{{\sqrt {2}}\pi cm_{e}}}}{4\pi r_{e}^{2}}}+{\frac {4\pi r_{c}/{\sqrt {2}}}{4\pi r^{2}}}\right)\partial r$

because of $\int _{0}^{t(c)}{\sqrt {1-({\frac {v(t)}{c}})^{2}}}\partial t=T\land {\frac {\partial r}{\partial s}}=({\frac {\partial t}{\partial s}})^{-1}\land {\frac {2Gm_{e}}{c^{2}}}=r_{s}\land {\frac {h}{2\pi cm_{e}}}=r_{c}$ on

$0=\int _{r_{e}}^{r_{e}+\partial r}\left({\frac {\partial r}{\partial s}}T-{\frac {r_{s}}{2\pi {\sqrt {2}}r}}{\frac {r_{c}}{\sqrt {2}}}{\frac {1}{4\pi r_{e}^{2}}}+{\frac {4\pi r_{c}/{\sqrt {2}}}{4\pi r^{2}}}\right)\partial r$

See Also

• Vixra.org: Calculation of the gravitational constant G using electromagnetic parameters