{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 16: Cosmology and Modern Astrophysics - The Beginning and the End"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.1, Page 581"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"H0 = 22; # Value of Hubble constant, km/s per million ly\n",
"parsec = 3.26; # The value of 1 parsec, light years\n",
"\n",
"#Calculations&Result\n",
"print \"The value of Hubble constant = %d km/s per Mpc\"%math.ceil(H0*parsec)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The value of Hubble constant = 72 km/s per Mpc\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.2, Page 583"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"M = 1; # Let the current mass of the universe be unity\n",
"m_u = 1; # Mass equivalent of 1 amu, u\n",
"N_n = 2; # Number of neutrons in helium\n",
"N_p = 2; # Number of protons in helium\n",
"\n",
"#Calculations\n",
"M_p = 0.75*M*m_u; # Total mass of protons\n",
"M_He = 0.25*M*m_u; # Total mass of helium\n",
"N_fp = M_p/M_He*(N_n + N_p); # Total number of free protons for every He-4\n",
"N_P = N_fp + N_p; # Total number of protons per He-4\n",
"ratio = N_P/N_n; # Current ratio of protons to the neutrons in the universe\n",
"\n",
"#Result\n",
"print \"The current ratio of protons to the neutrons in the universe = %d\"%ratio"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The current ratio of protons to the neutrons in the universe = 7\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.3, Page 607"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"m_n = 939.566; # Rest mass of the neutron, MeV/c^2\n",
"m_p = 938.272; # Rest mass of the proton, MeV/c^2\n",
"e = 1.6e-019; # Energy equivalent of 1 eV, J\n",
"c = 1; # For simplicity assume speed of light of light to be unity\n",
"T = 1e+010; # Temperature of the universe, K\n",
"\n",
"#Calculations\n",
"delta_m = m_n - m_p; # Mass difference between a proton and a neutron, MeV/c^2\n",
"k = 1.38e-023; # Boltzmann constant, J/k\n",
"# As from Maxwell-Boltzmann distribution from thermodynamics, N = exp(-m*c^2/(k*T)), so\n",
"ratio = math.exp(delta_m*c**2*1e+006*e/(k*T)); # Ratio of protons to neutrons in the universe at 10 billion kelvin\n",
"\n",
"#Result\n",
"print \"The ratio of protons to neutrons in the universe at 10 billion kelvin = %3.1f\"%ratio"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The ratio of protons to neutrons in the universe at 10 billion kelvin = 4.5\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.4, Page 589"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"M = 1.99e+030; # Mass of the sun, kg\n",
"G = 6.67e-011; # Universal gravitational constant, N-Sq.m/kg^2\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"R = 6.96e+008; # Radius of the sun, m\n",
"m = 1.67e-027; # Rest mass of the proton, kg\n",
"\n",
"#Calculations\n",
"PE = 3./5*(G*M**2/R); # Self potential energy of the sun, J\n",
"# As KE = 1./3*(M/m_p)*m_p*v**2, solving for v\n",
"v = math.sqrt(2*PE/M); # Velocity of a proton inside the sun, m/s\n",
"# From kinetic theory of gases, v = sqrt(3*k*T/m), solving for T\n",
"T = m*v**2/(3*k); # The mean temperature of the sun, K\n",
"\n",
"#Result\n",
"print \"The mean temperature of the sun = %1.0e K\"%T"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The mean temperature of the sun = 9e+06 K\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.5, Page 590"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"M_sun = 1.99e+030; # Mass of the sun, kg\n",
"m_n = 1.675e-027; # Rest mass of the neutron, kg\n",
"h = 6.62e-034; # Planck's constant, Js\n",
"\n",
"#Calculations\n",
"h_bar = h/(2*math.pi); # Planck's constant, Js\n",
"G = 6.67e-011; # Universal gravitational constant, N-Sq.m/kg^2\n",
"N = 2*M_sun/m_n; # Number of neutrons in the neutron star\n",
"V = (6.5*h_bar**2/(N**(1./3)*m_n**3*G))**3; # Volume of the neutron star, metre cube\n",
"R = (3./(4*math.pi)*V)**(1./3); # The radius of neutron star, m\n",
"\n",
"#Result\n",
"print \"The radius of the neutron star of 2 solar masses = %d km\"%math.ceil(R/1e+003)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The radius of the neutron star of 2 solar masses = 11 km\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.7, Page 598"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"c = 1; # For simplicity assume speed of light to be unity, m/s\n",
"d = 1.6e+005; # Distance of the supernova 1987A from the earth, ly\n",
"m = 16; # Mass of heavier neutrino, eV/c^2;\n",
"E = 20e+006; # Energy of the neutrino, eV\n",
"\n",
"#Calculations\n",
"delta_t = d/(2*c)*(m/E)**2; # Difference between the travel times of the lighter and the massive neutrinos, y\n",
"\n",
"#Result\n",
"print \"The difference between the travel times of the lighter and the massive neutrinos = %3.1f s\"%(delta_t*(365.25*24*60*60))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The difference between the travel times of the lighter and the massive neutrinos = 1.6 s\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.8, Page 602"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"c = 3.00e+008; # Speed of light, m/s\n",
"H = 22; # Hubble constant, km/s per million ly\n",
"G = 6.67e-011; # Universal gravitational constant, N-Sq.m/kg^2\n",
"\n",
"#Calculations\n",
"rho_c = 3/(8*math.pi)*H**2/G*1e+003/(c*365.25*24*60*60*1e+006)**2; # The critical density of the universe, g/cc\n",
"\n",
"#Result\n",
"print \"The critical density of the universe = %3.1e g/cc\"%rho_c"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The critical density of the universe = 9.7e-30 g/cc\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16.9, Page 604"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"H0 = 71; # Hubble constant, km/s per Mpc\n",
"\n",
"#Calculations\n",
"tau = 1./H0*1e+006*3.26*9.46e+012/3.16e+007; # The upper limit of the age of the universe, y\n",
"\n",
"#Result\n",
"print \"The upper limit of the age of the universe = %4.2e y\"%tau"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The upper limit of the age of the universe = 1.37e+10 y\n"
]
}
],
"prompt_number": 8
}
],
"metadata": {}
}
]
}