{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "=========================================================================================================================" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# How to determine the horizon of the visible universe in a Jupyter Notebook" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "=========================================================================================================================" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 20 correlations establishing the theoritical value of the horizon of the visible universe see [Observable_universe](https://en.wikipedia.org/wiki/Observable_universe) and [Schwarzschild_radius](https://en.wikipedia.org/wiki/Schwarzschild_radius)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# with ± 0.0001 billion (10^9) years 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", "* Apery Constant $\\xi(3)=1.202056903159594$ [Apery Constant](https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant)\n", "* Atiyah's $\\Gamma=25.178097241906$ [Michael_Atiyah](https://en.wikipedia.org/wiki/Michael_Atiyah)\n", "* Lucas Mersenne number [Edouard Lucas](https://en.wikipedia.org/wiki/%C3%89douard_Lucas)\n", "* OM Monster [Monster_group](https://en.wikipedia.org/wiki/Monster_group) also known as Fischer–Griess monster\n", "* OB Baby Monster [Baby_monster_group](https://en.wikipedia.org/wiki/Baby_monster_group) baby monster group B\n", "* OP Pariah Group [Pariah_group](https://en.wikipedia.org/wiki/Pariah_group) six sporadic simple groups\n", "* Eddington Electric Constant $a=137.0359990836958$ also known as the inversed fine structure constant CODATA2018\n", "* $c=299792458.0$ m/s CODATA2018\n", "* $h=6.62607015.10^{-34}$ $J.Hz^{-1}$ Planck constant CODATA2018\n", "* $\\hbar=1.0545718176461565.10^{-34}$ $J.s$ Planck constant over 2 pi 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", "* $\\lambda_{wi}=2.897771955.10^{-3}$ m K (exact) Wien wavelength displacement law constant CODATA2018\n", "* $k_B=1.380 649.10^{-23}$ J K^-1 (exact) Boltzmann constant 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": "markdown", "metadata": {}, "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": "code", "execution_count": 190, "metadata": {}, "outputs": [], "source": [ "from scipy import constants\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 191, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "299792458.0\n", "6.62607015e-34\n", "1.0545718176461565e-34\n", "137.0359990836958\n", "1.00115965218128\n", "1.202056903159594\n", "1.6449340668482264\n", "2.718281828459045\n", "0.5772156649015329\n", "25.178097241906\n", "573007.364905975\n", "3.8615926796089057e-13\n", "6.739167620022749e-19\n", "2.1030891033555923e-16\n", "1837.152646 1836.15267343 1838.68366173\n", "9.1093837015e-31 1.67262192369e-27 1.67492749804e-27\n", "1.000027430752471\n", "113.91063459990004\n", "1.380649e-23 2.72582\n", "0.0008400718024707187\n", "6.67545372e-11\n", "1.6163947113699356e-35\n", "1.1761048867371158e-24\n", "2.389015908333496e+22\n", "0.002897771955\n", "4.965114232061555\n", "0.0013440173951173593\n", "5.294654020152911e-11\n", "5.294654020152911e-11\n", "170141183460469231731687303715884105727\n", "808017424794512875886459904961710757005754368000000000\n", "4154781481226426191177580544000000\n", "2663849798329448283764291471531459318169741293570162121768960000000000000\n" ] } ], "source": [ "c=constants.c\n", "print(c)\n", "h=constants.h\n", "print(h)\n", "hbar=constants.hbar\n", "print(hbar)\n", "a=137.0359990836958\n", "print(a)\n", "d_e=1.00115965218128\n", "print(d_e)\n", "xi3=1.202056903159594\n", "print(xi3)\n", "xi2=np.pi**2/6\n", "print(xi2)\n", "#print(c,h,hbar,a,d_e,xi3,xi2)\n", "e=np.e\n", "print(e)\n", "gamma=np.euler_gamma\n", "print(gamma)\n", "Gamma=(constants.fine_structure**-1*gamma)/np.pi\n", "print(Gamma)\n", "# F**(2/3)=2*137*Gamma\n", "# Fermi's mass given by \n", "F=(2*137*Gamma)**1.5\n", "print(F)\n", "lambdabare=constants.hbar/(constants.m_e*constants.c)\n", "print(lambdabare)\n", "lambdabar_F=lambdabare/F\n", "print(lambdabar_F)\n", "lambdabar_p=(constants.hbar/(constants.m_p*constants.c))\n", "print(lambdabar_p)\n", "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)\n", "m_e=constants.m_e\n", "m_p=constants.m_p\n", "m_n=constants.m_n\n", "print(m_e,m_p,m_n)\n", "beta=(H-p)**(-1)\n", "print(beta)\n", "j=(8*np.pi**2)/np.log(2)\n", "print(j)\n", "k_B=constants.Boltzmann\n", "T_cmb=2.72582\n", "print(k_B,T_cmb)\n", "lambdabar_cmb=(constants.hbar*constants.c)/(k_B*T_cmb)\n", "print(lambdabar_cmb)\n", "# Planck's length CODATA2018 (hbar.G/c^3)^1/2 = 1.61639471.10^-35\n", "# l_P=1.616255*10**(-35) CODATA2018\n", "G_s=6.67545372*10**-11\n", "print(G_s)\n", "l_P=((constants.hbar*G_s)/constants.c**3)**0.5\n", "print(l_P)\n", "ƛ_w=(constants.hbar/(constants.m_e*constants.c))/F**2\n", "print(ƛ_w)\n", "lambdabar_w=(constants.hbar/(constants.m_e*constants.c))/F**2\n", "P=lambdabare/l_P\n", "print(P)\n", "#2.897 771 955... e-3 m.K - NIST CODATA 2018\n", "b=2.897771955*10**(-3)\n", "#lambdawien=(h*c)/(k_B*)\n", "# b=lambda/lambdawien\n", "print(b)\n", "𝜔=(h*c)/(k_B*b)\n", "print(𝜔)\n", "l_ph=(lambdabare*(np.pi*(a**2))**2)\n", "print(l_ph)\n", "aprime=137.1106292\n", "# Hydrogen Atom Radius\n", "r_H=(lambdabare*aprime)\n", "print(r_H)\n", "# Hydrogen Atom Radius\n", "r_H=(lambdabare*aprime)\n", "print(r_H)\n", "Lucas=(2**127)-1\n", "print(Lucas)\n", "OM=2**46 * 3**20 * 5**9 * 7**6 * 11**2 * 13**3 * 17 * 19 * 23 * 29 * 31 * 41 * 47 * 59 * 71 # 808017424794512875886459904961710757005754368000000000\n", "print(OM)\n", "OB=2**41 * 3**13 * 5**6 * 7**2 * 11 * 13 * 17 * 19 * 23 * 31 * 47 # 4154781481226426191177580544000000\n", "print(OB)\n", "OP=2**8 * 3**7 * 5**6 * 7 * 11 * 31 * 37 * 67 * 2**9 * 3**4 * 5 * 7**3 * 11 * 19 * 31 * 2**14 * 3**3 * 5**3 * 7 * 13 * 29 * 2**21 * 3**3 * 5 * 7 * 11**3 * 23 * 29 * 31 * 37 * 43 * 2**7 * 3**5 * 5 * 17 * 19 * 2**3 * 3 * 5 * 7 * 11 * 19\n", "print(OP)" ] }, { "cell_type": "code", "execution_count": 213, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('hubble-table.csv', )" ] }, "execution_count": 213, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# URL= 'https://github.com/laguer/hubble-table/hubble-table.csv'\n", "URL= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/hubble-table.csv'\n", "from urllib.request import urlretrieve\n", "urlretrieve (URL, 'hubble-table.csv')" ] }, { "cell_type": "code", "execution_count": 193, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "('constant-table.csv', )" ] }, "execution_count": 193, "metadata": {}, "output_type": "execute_result" } ], "source": [ "URL= 'https://raw.githubusercontent.com/LaGuer/hubble-table/master/constant-table.csv'\n", "from urllib.request import urlretrieve\n", "urlretrieve (URL, 'constant-table.csv')" ] }, { "cell_type": "code", "execution_count": 218, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Formula in LatexFormula in plaingly_valuem_value
4$$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e√2$$(lambdabare**2/l_P)(j/16)**16( e**e )**2*d_e*...1.381200e+101.306715e+26
5$$((a/\\sqrt(137)(4πF)^2)ƛe4 l_ph^3(\\lambda_CMB...((a/np.sqrt(137)*(4np.pi*F)**2)*lambdabar**4*...1.381189e+101.306715e+26
6$$2\\betaƛ_ej**{17}(4π)^2√137$$2*beta*lambdabare*(j**17)*(4*np.pi)**2*np.sqr...1.381198e+101.306715e+26
7$$ƛ_e(3j^j /2H)^{1/6}$$lambdabare*(3*j**j /(2*H))**(1/6)1.381199e+101.306715e+26
8$$(βFP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$beta*F*P**(3/2)*(n/p)**(7/2)/(2*np.pi)*lambda...1.381198e+101.306716e+26
\n", "
" ], "text/plain": [ " Formula in Latex \\\n", "4 $$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e√2$$ \n", "5 $$((a/\\sqrt(137)(4πF)^2)ƛe4 l_ph^3(\\lambda_CMB... \n", "6 $$2\\betaƛ_ej**{17}(4π)^2√137$$ \n", "7 $$ƛ_e(3j^j /2H)^{1/6}$$ \n", "8 $$(βFP^{3/2}(n/p)^{7/2}/2\\pi).ƛ_e$$ \n", "\n", " Formula in plain gly_value \\\n", "4 (lambdabare**2/l_P)(j/16)**16( e**e )**2*d_e*... 1.381200e+10 \n", "5 ((a/np.sqrt(137)*(4np.pi*F)**2)*lambdabar**4*... 1.381189e+10 \n", "6 2*beta*lambdabare*(j**17)*(4*np.pi)**2*np.sqr... 1.381198e+10 \n", "7 lambdabare*(3*j**j /(2*H))**(1/6) 1.381199e+10 \n", "8 beta*F*P**(3/2)*(n/p)**(7/2)/(2*np.pi)*lambda... 1.381198e+10 \n", "\n", " m_value \n", "4 1.306715e+26 \n", "5 1.306715e+26 \n", "6 1.306715e+26 \n", "7 1.306715e+26 \n", "8 1.306716e+26 " ] }, "execution_count": 218, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "#from StringIO import StringIO\n", "#df = pd.read_csv('hubble-table.csv')\n", "df = pd.read_csv(\"hubble-table.csv\", dtype = {\"gly_value\" : \"float64\",\"m_value\" : \"float64\"}, skiprows = [10], sep = \",\")\n", "#df = pd.read_csv(\"hubble-table.csv\", dtype = {\"gly_value\" : \"float64\",\"m_value\" : \"float64\"}, usecols=range(1), skiprows = [10], sep = \",\")\n", "#df1 = pd.read_csv(\"constant-table.csv\", dtype = {\" c_value\" : \"float64\"}, skiprows = [1], sep = \",\")\n", "#df = pd.to_csv('hubble-table.csv', float_format='%.3f')\n", "df.tail ()\n", "#df.head ()" ] }, { "cell_type": "code", "execution_count": 219, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Formula in LatexFormula in plaingly_valuem_value
0$$2hbar^2/(G.m_e.m_p.m_n)$$2*hbar**2/(G_s*m_e*m_p*m_n)1.380048e+011.305626e+26
1$$ƛ_e.exp((e{^4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$\\t(lambdabare**2/l_P)*((j/16)**16)*( e**e )**...1.381000e+101.306719e+26
2$$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l{ph}^3(ƛ_{CMB...((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabar...1.381170e+101.306242e+26
3$$ƛ_eF_e(Pe^e)^2/√(pn)$$lambdabare*F_e*(P*e**e)**2/np.sqrt(pn)1.381260e+101.306715e+26
4$$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e√2$$(lambdabare**2/l_P)(j/16)**16( e**e )**2*d_e*...1.381200e+101.306715e+26
\n", "
" ], "text/plain": [ " Formula in Latex \\\n", "0 $$2hbar^2/(G.m_e.m_p.m_n)$$ \n", "1 $$ƛ_e.exp((e{^4e-1/a}-ln2(P^4/a^3 ))/2)^{1/2}$$ \n", "2 $$((a/\\sqrt(137)(4\\pi.F)^2)ƛ_e^4l{ph}^3(ƛ_{CMB... \n", "3 $$ƛ_eF_e(Pe^e)^2/√(pn)$$ \n", "4 $$(ƛ_e^2/l_P)(j/16)^16( e^e )^2.d_e√2$$ \n", "\n", " Formula in plain gly_value \\\n", "0 2*hbar**2/(G_s*m_e*m_p*m_n) 1.380048e+01 \n", "1 \\t(lambdabare**2/l_P)*((j/16)**16)*( e**e )**... 1.381000e+10 \n", "2 ((a/(np.sqrt(137)*(4*np.pi*F)**2))*(lambdabar... 1.381170e+10 \n", "3 lambdabare*F_e*(P*e**e)**2/np.sqrt(pn) 1.381260e+10 \n", "4 (lambdabare**2/l_P)(j/16)**16( e**e )**2*d_e*... 1.381200e+10 \n", "\n", " m_value \n", "0 1.305626e+26 \n", "1 1.306719e+26 \n", "2 1.306242e+26 \n", "3 1.306715e+26 \n", "4 1.306715e+26 " ] }, "execution_count": 219, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "#from StringIO import StringIO\n", "#df = pd.read_csv('hubble-table.csv')\n", "df = pd.read_csv(\"hubble-table.csv\", dtype = {\"gly_value\" : \"float64\",\"m_value\" : \"float64\"}, skiprows = [10], sep = \",\")\n", "#df = pd.read_csv(\"hubble-table.csv\", dtype = {\"gly_value\" : \"float64\",\"m_value\" : \"float64\"}, usecols=range(1), skiprows = [10], sep = \",\")\n", "#df1 = pd.read_csv(\"constant-table.csv\", dtype = {\" c_value\" : \"float64\"}, skiprows = [1], sep = \",\")\n", "#df = pd.to_csv('hubble-table.csv', float_format='%.3f')\n", "#df.tail ()\n", "df.head ()" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
symbolvalue
32G_s6.67545372e-11
33Lucas170141183460469231731687303715884105727
34OM8080174247945128758864599049617107570057543680...
35OB4154781481226426191177580544000000
36OP2663849798329448283764291471531459318169741293...
\n", "
" ], "text/plain": [ " symbol value\n", "32 G_s 6.67545372e-11\n", "33 Lucas 170141183460469231731687303715884105727\n", "34 OM 8080174247945128758864599049617107570057543680...\n", "35 OB 4154781481226426191177580544000000\n", "36 OP 2663849798329448283764291471531459318169741293..." ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df1 = pd.read_csv(\"constant-table.csv\", dtype = {\"value\" : \"float64\"}, skiprows = [2], sep = \",\")\n", "#df = pd.to_csv('hubble-table.csv', float_format='%.3f')\n", "#df1.head ()\n", "df1.tail ()" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Formula in Latex object\n", " Formula in plain object\n", " gly_value float64\n", " m_value float64\n", "dtype: object" ] }, "execution_count": 217, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.dtypes" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# 3**210" ] }, { "cell_type": "code", "execution_count": 22, "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": [ "# Universe Horizon Radius calculus in 3 minutes (method 1)\n", "$$R_U=\\frac{2.\\hbar^2}{G.m_e.m_p.m_n}$$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.3056258355517771e+26\n" ] } ], "source": [ "R_U=2*constants.hbar**2/(G_s*constants.m_e*constants.m_p*constants.m_n)\n", "print(R_U)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Yields 13.802861522337478 Gly (G) and 13.80047597102314 Gyr (G_s)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "13.80047597102314" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "R_U/(constants.light_year*10**9)" ] }, { "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }