gravitational-constant.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to determine the gravitational constant in a Jupyter Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlations establishing the theoritical value of the gravitational constant see [Gravitational constant](https://en.wikipedia.org/wiki/Gravitational_constant)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with ± ...  m^3⋅kg^−1⋅s^−2 approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "List of physical (NIST CODATA2018) and mathematical constants used:\n",
    "\n",
    "* $\\pi=3.141592653589793$\n",
    "* Euler natural logarithm $e=2.718281828459045$\n",
    "* Euler Mascheroni $\\gamma=0.5772156649015329$\n",
    "* Atiyah's $\\Gamma=25.178097241906$\n",
    "* Eddington Electric Constant $a=137.0359990836958$ also known as the inversed fine structure constant CODATA2018\n",
    "* $c=299792458.0$ m/s CODATA2018\n",
    "* $h=6.62607015.10^{-34}$ $J.Hz^{-1}$ CODATA2018\n",
    "* $\\hbar=1.0545718176461565.10^{-34}$ $J.s$ CODATA2018\n",
    "* $l_P=1.616255.10^{-35}$ m Planck length CODATA2018\n",
    "* $m_P=2.176434.10^{-8}$ kg Planck mass CODATA2018\n",
    "* ƛ$_e$ $=3.861 592 6796.10^{-13}$m Reduced (Electron) Compton Wavelength CODATA2018\n",
    "* ƛ$_p$ $=2.103 089 103 36.10^{-16}$m Reduced (Proton) Compton Wavelength CODATA2018\n",
    "* $t_K=9600.60(1)$s non-Doppler Kotov Periodicity (1000 ppb)\n",
    "* Fermi coupling constant : $1.1663787.10^{-5}$    (GeV)-2          (51 ppb)\n",
    "* Fermi's ratio   F = Fermi's mass / m_e = 573007.3625        (25 ppb)\n",
    "* Fermi-Atiyah's ratio : $F_A = (2\\Gamma . 137)^{3/2}$ ≈ 573007.3652        (0.22 ppb)\n",
    "* Mass of the electron $m_e=9.1093837015.10^{-31}$ kg CODATA2018\n",
    "* Mass of the proton $m_p=1.672 621 923 69.10^{-27}$ kg CODATA2018\n",
    "* Magnetic Moment of the electron/Bohr magneton: $d_e$ ≈ 1.00115965218128 (2 × 10-4  ppb)\n",
    "* Magnetic moment anomaly $1159.65218091.10^{−6}$ ± 0.00000026 [Particle Data Group Leptons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-leptons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "* Boson $W=80.379 GeV$ ± 0.012 [Particle Data Group Bosons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-gauge-higgs-bosons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "* Boson $Z=91.1876 GeV$ ± 0.0023 [Particle Data Group Bosons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-gauge-higgs-bosons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "* Lepton $e=0.5109989461 MeV$ [Particle Data Group Leptons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-leptons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "* Baryon $p=938.272081 MeV$ [Particle Data Group Baryons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-baryons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "* Baryon $n=939.565413 MeV$ [Particle Data Group Baryons](http://pdg.lbl.gov/2019/tables/rpp2019-sum-baryons.pdf) M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) and 2019\n",
    "* $G=6.6743.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$ Newtonian constant of gravitation CODATA2018\n",
    "* $G_q=6.6755.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$ Newtonian constant of gravitation measured by T.Quinn et al. (2013) BIPM Sevres [Improved determination of G using two methods](https://www.bipm.org/utils/en/pdf/PhysRevLett.111.101102.pdf)\n",
    "* $G_s=6.67545372.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$ Newtonian constant of gravitation estimate by Francis M. Sanchez (Jan 2020)\n",
    "* Galaxies Doppler radius $R=c.f /\\Delta.f$=Universe Schwarzschild radius: $2G.M/c^2$\n",
    "* Hubble-Lemaître radius: $c/H_0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import constants\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.141592653589793\n",
      "2.718281828459045\n"
     ]
    }
   ],
   "source": [
    "pi=np.pi\n",
    "print(pi)\n",
    "e=np.e\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15684240429131529254685698284890751184639406145730291592802676915731672495230992603635422093849215049"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3**210"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "170141183460469231731687303715884105727\n",
      "4154781481226426191177580544000000\n"
     ]
    }
   ],
   "source": [
    "Lucas=(2**127)-1\n",
    "print(Lucas)\n",
    "OB=2**41 * 3**13 * 5**6 * 7**2 * 11 * 13 * 17 * 19 * 23 * 31 * 47\n",
    "print(OB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137.0359990836958\n",
      "299792458.0\n",
      "9600.6\n"
     ]
    }
   ],
   "source": [
    "a=constants.fine_structure**-1\n",
    "print(a)\n",
    "c=constants.c\n",
    "print(c)\n",
    "t_K=9600.60 # Non-Doppler Kotov Periodicity\n",
    "print(t_K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5772156649015329\n",
      "25.178097241906\n",
      "113.91063459990004\n"
     ]
    }
   ],
   "source": [
    "# Euler Mascheroni gamma\n",
    "gamma=np.euler_gamma\n",
    "print(gamma)\n",
    "# Atiyah's Gamma\n",
    "Gamma=a*np.euler_gamma/np.pi\n",
    "print(Gamma)\n",
    "j=8*pi**2/np.log(2) # Joel Sternheimer Constant 113.91063459990004\n",
    "print(j)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.62607015e-34\n",
      "1.0545718176461565e-34\n"
     ]
    }
   ],
   "source": [
    "h=constants.h\n",
    "print(h)\n",
    "hbar=constants.hbar\n",
    "print(hbar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "573007.364905975\n"
     ]
    }
   ],
   "source": [
    "# Fermi's mass given by \n",
    "F=(2*137*Gamma)**1.5\n",
    "print(F)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "H=1837.152646"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.1093837015e-31\n",
      "1.67262192369e-27\n",
      "1.67492749804e-27\n",
      "1.673532837064e-27\n"
     ]
    }
   ],
   "source": [
    "# in kg\n",
    "m_e=constants.m_e\n",
    "print(m_e)\n",
    "m_p=constants.m_p\n",
    "print(m_p)\n",
    "m_n=constants.m_n\n",
    "print(m_n)\n",
    "m_H=H*9.1093837015e-31\n",
    "print(m_H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1837.152646 1836.15267343 1838.68366173\n"
     ]
    }
   ],
   "source": [
    "H=1837.152646   # (0.06 ppb)\n",
    "p=1836.15267343 # 1836.1526734400013 #(0.06 ppb)\n",
    "n=1838.68366173 # 1838.6836617324586 #(0.5 ppb)\n",
    "print(H,p,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.616255e-35\n"
     ]
    }
   ],
   "source": [
    "# Planck length\n",
    "l_P=1.616255*10**-35\n",
    "print(l_P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.00115965218091\n"
     ]
    }
   ],
   "source": [
    "# electron magnetic moment excess\n",
    "d_e=1.00115965218091\n",
    "print(d_e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8615926796089057e-13\n"
     ]
    }
   ],
   "source": [
    "# hbar/m_e*c\n",
    "lambdabare=hbar/(m_e*c)\n",
    "print(lambdabare)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.67545372e-11\n"
     ]
    }
   ],
   "source": [
    "# Using G_s the Newtonian constant of gravitation estimate by Francis M. Sanchez (Jan 2020)\n",
    "G_s=6.67545372*10**-11\n",
    "print(G_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$(2^{127}-1)=\\frac{d_e^2.(m_H/m_p)^6.\\hbar.c}{G.m_p.m_H}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0023206491550007\n"
     ]
    }
   ],
   "source": [
    "print(d_e**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0056003070680364"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(H/p)**6*d_e**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.6919364684510842e+38"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((2**127)-1)/1.0056003084810168"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.4768312351697826e+39"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(d_e**2*(H*p)**6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In this instance G yields to 6.675453722212173e-11 $m^{3}.kg^{-1}.s^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.67545372064888e-11"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (d_e**2*(H*p)**6)*constants.hbar*constants.c\n",
    "(((constants.hbar*constants.c/1.6919364684510842e+38)/constants.m_e**2)/p)/H"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{F^5}{a^3}≈\\frac{𝜂.ƛ_𝑒}{l_P}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.1773330957966155e+28"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F**5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0047961630695443\n"
     ]
    }
   ],
   "source": [
    "𝜂=419/417\n",
    "print(𝜂)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3890159033751643e+22"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(F**5/a**3)/𝜂"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.616394714724715e-35"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#1.616394709.10**-35\n",
    "(lambdabare)/((F**5/a**3)/𝜂)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4006815185774947e+22"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(419/(419-2))*(constants.hbar/(constants.m_e*constants.c))/l_P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### In this instance G yields  6.675453747678621e-11 $m^{3}.kg^{-1}.s^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.675453747678621e-11\n"
     ]
    }
   ],
   "source": [
    "G_2=(1.616394714720987e-35**2*c**3)/hbar\n",
    "print(G_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067138908886458e+26\n"
     ]
    }
   ],
   "source": [
    "R_2=2*hbar**2/(G_2*m_e*m_p*m_H)\n",
    "print(R_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.81197672500849"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_2/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R=$ƛ$_e.2^{128}.(1 - (137^2 + \\pi^2 + e^2)/p.H)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1837.152646 1836.152673 1838.68366173\n"
     ]
    }
   ],
   "source": [
    "H=1837.152646\n",
    "p=1836.152673\n",
    "n=1838.68366173 #(0.5 ppb)\n",
    "print(H,p,n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067139010079756e+26\n"
     ]
    }
   ],
   "source": [
    "# Universe radius\n",
    "R=lambdabare*2**128*(1-(137**2+pi**2+e**2)/(p*H))\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976831969892"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.8615926796089057e-13\n"
     ]
    }
   ],
   "source": [
    "print(lambdabare)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0545718176461565e-34\n"
     ]
    }
   ],
   "source": [
    "print(hbar)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.1093837015e-31 1.67262192369e-27 1.673532837064e-27\n"
     ]
    }
   ],
   "source": [
    "print(m_e,m_p,m_H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$G_3=2.\\hbar^2/(R.m_e.m_p.m_H)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### G yields $6.675453699616791.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.675453695983206e-11\n"
     ]
    }
   ],
   "source": [
    "G_3=2*hbar**2/(R*m_e*m_p*m_H)\n",
    "print(G_3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  $R=$ƛ$_e.2^{137}.(\\gamma.n^3)^2/137^3.\\Gamma^{11}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067139119716594e+26\n"
     ]
    }
   ],
   "source": [
    "R2=(lambdabare*2**137*(gamma*n**3)**2)/(137**3*Gamma**11)\n",
    "print(R2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.81197694785612"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R2/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$G_4=2.\\hbar^2/(R.m_e.m_p.m_H)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### G yields $6.675453643607926.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.67545363997434e-11\n"
     ]
    }
   ],
   "source": [
    "G_4=2*hbar**2/(R2*m_e*m_p*m_H)\n",
    "print(G_4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R=$ƛe$.g(6)/(1+ √(137^2+√136)/j.n)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067138950061902e+26\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy import constants\n",
    "R_12=((hbar/(m_e*constants.c))*np.exp(2**(6+(1/2)))/6)/(1+np.sqrt(137**2+np.sqrt(136))/(j*n))\n",
    "print(R_12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976768530968"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_12/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### G yields $6.675453726643811.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.675453726643811e-11\n"
     ]
    }
   ],
   "source": [
    "G_12=2*hbar**2/(R_12*m_e*m_p*m_H)\n",
    "print(G_12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $R =  \\frac{2.ƛe(p.n/H^2).g(5)^2}{ln^2 (2 – 1/j.a^2)} $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067138946181524e+26\n"
     ]
    }
   ],
   "source": [
    "R_13=(2*(hbar/(m_e*c))*(p*n/H**2)*(np.exp(2**(5+(1/2)))/5)**2)/(np.log(2-1/(j*a**2)))**2\n",
    "print(R_13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976764429406"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_13/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### G yields $6.675453728626135.10^{-11}$ $m^{3}.kg^{-1}.s^{-2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.675453728626135e-11\n"
     ]
    }
   ],
   "source": [
    "G_13=2*hbar**2/(R_13*m_e*m_p*m_H)\n",
    "print(G_13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Universe Radius calculus based on $ƛ_w$, $\\gamma$ and $\\Gamma$ (method 11) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$R_{ƛ_w}=ƛ_w.(2^{70}.\\gamma.n^3/\\Gamma^4)^2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ƛ_w=ƛ_e/F^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "137.0359990836958\n"
     ]
    }
   ],
   "source": [
    "a=constants.fine_structure**-1\n",
    "print(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.178097241906\n"
     ]
    }
   ],
   "source": [
    "# Atiyah's Gamma\n",
    "Gamma=a*np.euler_gamma/np.pi\n",
    "print(Gamma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.1761048867371158e-24\n"
     ]
    }
   ],
   "source": [
    "ƛ_w=(constants.hbar/(constants.m_e*constants.c))/F**2\n",
    "print(ƛ_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.3067139119716592e+26\n"
     ]
    }
   ],
   "source": [
    "R_w=(((2**70*np.euler_gamma*n**3)/Gamma**4)**2)*ƛ_w\n",
    "print(R_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.67545363997434e-11\n"
     ]
    }
   ],
   "source": [
    "G_w=2*hbar**2/(R_w*m_e*m_p*m_H)\n",
    "print(G_w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.811976947856119"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_w/(constants.light_year*10**9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other estimates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Universe mass calculus given by the relation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$m_P$ is the Planck Mass , $m_e$ the electron mass, $m_p$ the proton mass, $m_n$ the neutron mass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{align}\n",
       "\\frac{m_P^4}{m_e\\cdot m_p\\cdot\\ m_n} = M_U \\\\\n",
       "\\end{align}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "\\begin{align}\n",
    "\\frac{m_P^4}{m_e\\cdot m_p\\cdot\\ m_n} = M_U \\\\\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.176434e-08\n"
     ]
    }
   ],
   "source": [
    "# Planck's mass\n",
    "m_P=2.176434*10**(-8)\n",
    "print(m_P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.2437889614753534e-31\n"
     ]
    }
   ],
   "source": [
    "print(m_P**4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5520124761382513e-84"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constants.m_e*constants.m_p*constants.m_n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.792233511611562e+52"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m_P**4/(constants.m_e*constants.m_p*constants.m_n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Universe Mass $8.792233511611562.10^{52}$ kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.792233511611562e+52\n"
     ]
    }
   ],
   "source": [
    "M_U=(m_P**4)/(constants.m_e*constants.m_p*constants.m_n)\n",
    "print(M_U)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.919879446372421e+32\n"
     ]
    }
   ],
   "source": [
    "M_U1=(R*constants.c**2)/2*G_s\n",
    "print(M_U1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following example, one can write the equation with Latex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{eqnarray}\n",
       "\\ R = \\frac{2\\cdot \\hbar^2}{G.m_e.m_p.m_n} \\\\\n",
       "\\ M_U = \\frac{{R}{c}^2}{2G} = \\frac{{m_P}^4}{m_em_pm_n} \\\\\n",
       "\\frac{r_H}{ƛ_e} = \\frac{\\sum\\frac{1}{n}}{\\sum\\frac{1}{n^2}}\\\\\n",
       "\\end{eqnarray}"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Latex\n",
    "Latex(r\"\"\"\\begin{eqnarray}\n",
    "\\ R = \\frac{2\\cdot \\hbar^2}{G.m_e.m_p.m_n} \\\\\n",
    "\\ M_U = \\frac{{R}{c}^2}{2G} = \\frac{{m_P}^4}{m_em_pm_n} \\\\\n",
    "\\frac{r_H}{ƛ_e} = \\frac{\\sum\\frac{1}{n}}{\\sum\\frac{1}{n^2}}\\\\\n",
    "\\end{eqnarray}\"\"\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":star:\n",
    "\n",
    "# Docs\n",
    "\n",
    "This project aims at providing a repository dedicated to Dr Francis Michel Sanchez's work in holography and cosmology; it is just a mere continuation of what was initiated and published in a set of theoritical physics articles.\n",
    "\n",
    "\n",
    "## Publications by Francis M. Sanchez\n",
    "* Please, cite this paper (http://vixra.org/pdf/1811.0146v8.pdf) if you employ this package in your research work.\n",
    "* [Vixra Publications](http://vixra.org/author/francis_m_sanchez)\n",
    "* [Rxiv Publications](http://rxiv.org/author/f_m_sanchez)\n",
    "* [A coherent resonant cosmology approach and its implications in microphysics and Biophysics Pages 375-407 of Quantum Systems in Physics, Chemistry](https://www.springer.com/fr/book/9783319502540?token=gbgen&wt_mc=GoogleBooks.GoogleBooks.3.EN#)\n",
    "* [From Coherent Cosmic Oscillations to the Steady-State Cyclic Ultrafast](https://rxiv.org/abs/1401.0228)\n",
    "* [Evidence for a Steady-State, Holographic, Tachyonic and Super-Symmetric Cosmology](https://www.researchgate.net/publication/267430152_Evidence_for_a_Steady-State_Holographic_Tachyonic_and_Super-Symmetric_Cosmology)\n",
    "* [academia.edu Correcting Five Historical Faults in Modern Cosmology](https://www.academia.edu/30843365/Correcting_Five_Historical_Faults_in_Modern_Cosmology)\n",
    "\n",
    "## Publications by V.A. Kotov\n",
    "* [Nature: Observations of solar oscillations with periods of 160 minutes](https://www.nature.com/articles/277635a0)\n",
    "* [Back to Cosmos](https://rxiv.org/abs/1904.0218)\n",
    "* [V.A Kotov publications](https://www.researchgate.net/scientific-contributions/4140366_V_A_Kotov)\n",
    "\n",
    "\n",
    "## Videos\n",
    "\n",
    "* [L'enigme des grands nombres Part1](https://www.youtube.com/watch?v=ev_eIqLtK8s)\n",
    "* [L'enigme des grands nombres Part2](https://www.youtube.com/watch?v=i4w392nYqns)\n",
    "* [L'enigme des grands nombres Part3](https://www.youtube.com/watch?v=b4WvI0yVXnE)\n",
    "* [Exposés de Francis Sanchez playlist created by J.Bailhache](https://www.youtube.com/playlist?list=PLQXUNrzoAeFbmfHo3jgWzzExlVoBn2JUw)\n",
    "* [Khelif/Torgoz/Sanchez' Debate on LE FORMALISME EN PHYSIQUE ET EN SCIENCE](https://www.youtube.com/watch?v=TEK2hCI2we0)\n",
    "\n",
    "* [La science du 3eme millenaire playlist created by J.Bailhache](https://www.youtube.com/playlist?list=PLQXUNrzoAeFbLOuEsltAUWJWCcAEgeGJE)\n",
    "* [Francis Sanchez Cosmologie 23/03/2017](https://www.youtube.com/watch?v=NmvvIQjxBw8)\n",
    "* [La complexité mathématique face à la simplicité cosmique - Exposé de Francis Sanchez](https://www.youtube.com/watch?v=dyUlUahgHGg)\n",
    "* [La méthode scientifique en question et les constantes fondamentales - Exposé](https://www.youtube.com/watch?v=zUt1hxTdiuA)\n",
    "* [Jean Maruani chez lui et Francis Sanchez autour du nombre 237 29. 12. 17](https://www.youtube.com/watch?v=05g416VWjnw)\n",
    "* [Pr. Michel Grosmann: Holographie quanto-cosmique](https://www.youtube.com/watch?v=M7bJnekDIt0)\n",
    "* [Pr. Renée Veysseyre: La constante d'Atiyah réunifie Physique et Mathématique](https://www.youtube.com/watch?v=mbPpKqakDAU)\n",
    "* [Christian Bizouard, astronome: Omniprésence astrophysique du cycle de Kotov](https://www.youtube.com/watch?v=DGeBC73kKvQ)\n",
    "* [Pr. Francis Sanchez: Historique, Principe Calculatoire, Axe Topologique et Principe Holique](https://www.youtube.com/watch?v=IgKSrfsqFEs)\n",
    "\n",
    "## Books\n",
    "\n",
    "* [Bizouard, Kotov, Sanchez wrote in 20th Natural Philosophy Alliance Proceedings by David de Hilster, published by Lulu.com in 2013]()\n",
    "* [Quantum Systems in Physics, Chemistry, Springer Ed](https://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9783319502557)\n",
    "* [The Worldwide List of Alternative Theories and Critics](https://books.google.com/books?isbn=2902425171)\n",
    "* [The Dirac Electron: From Quantum Chemistry to Holistic Cosmology by J.Maruani](https://onlinelibrary.wiley.com/doi/abs/10.1002/jccs.201500374#)\n",
    "* [solar 22 years cycle](https://link.springer.com/article/10.1007%2Fs10509-016-2985-8)\n",
    "* [Current Issues in Cosmology](https://www.cambridge.org/gb/academic/subjects/physics/cosmology-relativity-and-gravitation/current-issues-cosmology?format=HB&isbn=9780521858984)\n",
    "* ```@inproceedings{Sanchez2015RemarkablePO,\n",
    "  title=Remarkable Properties of the Eddington Number 137 and Electric Parameter 137 . 036 excluding the Multiverse Hypothesis},\n",
    "  author={Francis M. Sanchez and Valery A. Kotov,\n",
    "  year=2015```\n",
    "\n",
    "## Papers\n",
    "\n",
    "* [College de France (2004): Discussions sur les oscillations cosmiques, les nombres sans dimension et les periodicites en microphysique et cosmologie - College de France 27th Feb 2004](https://lempel.pagesperso-orange.fr/occ_cdf.pdf)\n",
    "\n",
    "More to come soon stay tuned.../.:stars:."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "========================================================================================================================="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}