User:Qtheory/Gravitational waves-Atomic orbitals

Atomic orbitals & Gravitational waves as standing waves of Planck momentum

Postulates atomic orbitals and gravitational waves as standing waves of momentum with vector components. For a summary of the theory, refer to the online book. For gravitational wave frequency, refer to the online calculator.

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Electric (standard model)
i.e: A = electron, B = proton
 * $$\lambda_e \;=\; \lambda_A \;+\; \lambda_B $$ (wavelength)
 * $$\lambda_e = \frac{m_P.l_p}{m_A}\;+\;\frac{m_P.l_p}{m_B} $$
 * $$r_e = \alpha.n^2.\lambda_e $$ (radius)
 * $$v_e = \frac{c}{\alpha.n}  $$ (velocity)
 * $$a_e = \frac{c^2}{\alpha^3.n^4.\lambda_e} $$ (acceleration)
 * $$T_e = \frac{2.\pi.\alpha^2.n^3.\lambda_e}{c} $$ (period)
 * $$E_n = \frac{m_e.c^2}{2.\alpha^2.n^2} $$ (energy levels)

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Gravity (proposed)
SR = Schwarzschild radius

i.e: A = earth, B = moon
 * $$\lambda_g = \frac{2.G.(m_A+m_B)}{c^2} $$
 * $$\lambda_g = SR_A + SR_B $$ (wavelength)
 * $$r_g = \alpha.n^2.\lambda_g $$ (radius)
 * $$v_g^2 = \frac{c^2}{2.\alpha.n^2} $$ (velocity)
 * $$a_g = \frac{c^2}{2.\alpha^2.n^4.\lambda_g} $$ (acceleration)
 * $$T_g^2 = \frac{8.\pi^2.\alpha^3.n^6.\lambda_g^2}{c^2} $$ (period)
 * $$E_n = \frac{m.c^2}{4.\alpha.n^2} $$ (energy levels)

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Gravitational Waves (proposed)

 * $$r_1 = \alpha.n_1^2.\lambda_g $$


 * $$r_2 = \alpha.n_2^2.\lambda_g $$


 * $$\delta.\mu_{GPE} = \frac{G.M.m}{r_1}\;-\;\frac{G.M.m}{r_2} $$


 * $$\frac{G.M.m}{r_n}\; = \;\frac{l_p.c^2}{m_P} \;.\; M.m \;.\; \frac{1}{\alpha.n^2.\lambda_{M+m}} \; = \; \frac{h.c}{2.\pi.\alpha.n^2.\lambda_{M+m}} \;.\;\frac{M.m}{m_P^2} $$


 * $$R_g = \frac{1}{2.\pi.r}. (\frac{1}{n_1^2}-\frac{1}{n_2^2}) =\frac{1}{2.\pi.\alpha.\lambda_{M+m}}. (\frac{1}{n_1^2}-\frac{1}{n_2^2}) $$


 * $$f = R_g.c. (\frac{1}{n_1^2}-\frac{1}{n_2^2})  $$


 * $$E_{tot}= \;h.f.\;\frac{M.m}{m_P^2} $$


 * $$N_{graviton}= \frac{M.m}{m_P^2} $$


 * $$E_{graviton}= h.R_g.c. (\frac{1}{n_1^2}-\frac{1}{n_2^2}) $$


 * $$E_{tot}=E_{graviton}\;.\;N_{graviton} $$

where


 * Ngraviton = number of gravitons
 * Egraviton = energy per graviton
 * Etot = total energy required
 * Rg = Rydberg for gravity
 * mP = Planck mass
 * lp = Planck length
 * n = integer; 1,2,3,4... (corresponds to principal quantum number)

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