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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 15: General Relativity"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.1, Page 562"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"g = 9.8; # Acceleration due to gravity, m/sec^2\n",
"H = 10000; # Altitude of the aeroplane above the surface of earth, m\n",
"c = 3.00e+008; # Speed of light in free space, m/s\n",
"T = 45*3600; # Time taken by the airplane to from eastward to westward trip, s\n",
"\n",
"#Calculations\n",
"delta_T_G = g*H*T/(c**2*1e-009); # Time difference in the two clocks due to gravitational redshift, ns\n",
"C = 4e+007; # Circumference of the earth, m \n",
"v = 300; # Speed of the jet airplane, m/s\n",
"T0 = C/v; # Time of flight of jet airplane very near the surface of the earth, s\n",
"bita = v/c; # Boost parameter\n",
"# As from special relativity time dilation relation, T = T0*sqrt(1-bita^2), solving for T0 - T = delta_T_R, we have\n",
"delta_T_R = T0*(1-math.sqrt(1-bita**2))/1e-009; # Time difference in the two clocks due to special relativity, ns\n",
"\n",
"#Result\n",
"print \"The gravitational time dilation effect of %d ns is larger than the approximate %4.1f ns of that of special relativity.\"%(math.ceil(delta_T_G), delta_T_R)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The gravitational time dilation effect of 177 ns is larger than the approximate 66.7 ns of that of special relativity.\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.2, Page 567"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"c = 3.00e+008; # Speed of light in free space, m/s\n",
"G = 6.67e-011; # Newton's gravitational constant, N-Sq.m/per kg square\n",
"M_S = 2.0e+030; # Mass of the sun, kg\n",
"M_E = 6.0e+024; # Mass of the earth, kg\n",
"\n",
"#Calculations\n",
"r_S = 2*G*M_S/(c**2*1e+003); # Schwarzschild radius for sun, km\n",
"r_E = 2*G*M_E/(c**2*1e-003); # Schwarzschild radius for earth, mm\n",
"\n",
"#Results\n",
"print \"The Schwarzschild radius for sun = %d km\"%math.ceil(r_S)\n",
"print \"The Schwarzschild radius for earth = %d mm\"%math.ceil(r_E)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Schwarzschild radius for sun = 3 km\n",
"The Schwarzschild radius for earth = 9 mm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15.3, Page 568"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"import scipy\n",
"from scipy.integrate import quad\n",
"\n",
"#Variable declaration\n",
"c = 3.00e+008; # Speed of light in free space, m/s\n",
"G = 6.67e-011; # Newton's gravitational constant, N-Sq.m/per kg square\n",
"h = 6.62e-034; # Planck's constant, Js\n",
"\n",
"#Calculations\n",
"h_bar = h/(2*math.pi); # Reduced Planck's constant, Js\n",
"sigma = 5.67e-008; # Stefan-Boltzmann constant, W per Sq.m per K^4\n",
"k = 1.38e-023; # Boltzmann constant, J/K\n",
"M0 = 1.99e+030; # Mass of the sun, kg\n",
"alpha = 2*sigma*h_bar**4*c**6/((8*math.pi)**3*k**4*G**2); # A constant, kg^3/s\n",
"T = lambda M: 1/alpha*M**2\n",
"t,err = scipy.integrate.quad(T,0, 3*M0)\n",
"\n",
"#Result\n",
"print \"The time required for the 3-solar-mass black hole to evaporate = %3.1e y\"%(t/(365.25*24*60*60))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The time required for the 3-solar-mass black hole to evaporate = 5.7e+68 y\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
|
