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+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:9c5b783b7af2e7759af05c065786293bfda0657b22d7595e2418aaa43901e7b0"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "Chapter 2: Orbits and Launching Methods"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.1, Page 23"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "u=3.986*(10**14)         #Earth's Gravitational constant(m^3/sec^2)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "n=(2*3.14)/(24*60*60)    #Mean Motion(rad/sec)\n",
+      "a=((u/n**2)**(0.33333))/1000      #Radius of the orbit by kepler's 3rd law(km)\n",
+      "a=round(a,2)\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"The Radius of the circular orbit with 1 day period is:\", a,\"km\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The Radius of the circular orbit with 1 day period is: 42247.94 km\n"
+       ]
+      }
+     ],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.2, Page 29"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Variable Declaration\n",
+      "NN=14.22296917        #Mean Motion (1/day)\n",
+      "u=3.986005*(10**14)   #Earth's Gravitational COnstant(m^3/sec^2)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "n0=(NN*2*3.142)/(24*60*60)                  #Mean Motion(rad/sec)\n",
+      "a=((u/n0**2)**(0.33333))/1000   #Radius of the orbit by kepler's 3rd law(km)\n",
+      "a=round(a,2)\n",
+      "#Result\n",
+      "\n",
+      "print \"The Semimajor axis for given satellite parameters is:\", a,\"km\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The Semimajor axis for given satellite parameters is: 7193.97 km\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.3, Page 29"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "R=6371   #Mean Earth's radius(km)\n",
+      "e=0.0011501  #Eccentricity\n",
+      "a=7192.3     #Semimajor axis(km)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "ra=a*(1+e)   #Radius Vector at apogee(km)\n",
+      "rp=a*(1-e)   #Radius Vector at perigee(km)\n",
+      "ha=round(ra-R,2)      #Apogee height(km)\n",
+      "hp=round(rp-R,2)      #Perigee height(km)\n",
+      "\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"The Apogee height for given orbital parameters is:\", ha,\"km\"\n",
+      "print \"The Apogee height for given orbital parameters is:\", hp,\"km\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The Apogee height for given orbital parameters is: 829.57 km\n",
+        "The Apogee height for given orbital parameters is: 813.03 km\n"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.4, Page 31"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "aE=6378.141   #Earth's equitorial radius(km)\n",
+      "e=0.002  #Eccentricity\n",
+      "p=12     #period from perigee to perigee (hours)\n",
+      "K1=66063.1704  #Constant (km^2)\n",
+      "u=3.986005*(10**14)         #Earth's Gravitational constant(m^3/sec^2)\n",
+      "\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "n=(2*math.pi)/(12*60*60)  #Mean Motion(rad/sec)\n",
+      "anp=((u/n**2)**(0.3333))/1000      #Radius of the orbit by kepler's 3rd law(km)\n",
+      "k2=(1-e**2)**1.5\n",
+      "# Solving for perturbed value of semimajor axis\n",
+      "import scipy\n",
+      "import scipy.optimize\n",
+      "def f(a):\n",
+      "    y=(n-((u/a**3)**0.5)*(1+K1/a**2*k2))\n",
+      "    return y\n",
+      "a=scipy.optimize.fsolve(f,2)\n",
+      "a=a/1000  #Converting a into km\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"The nonperturbed value of semimajor axis is\", anp,\"km\"\n",
+      "print \"The perturbed value of semimajor axis is\", a,\"km\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The nonperturbed value of semimajor axis is 26564.7679852 km\n",
+        "The perturbed value of semimajor axis is [ 26610.22410209] km\n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.5, Page 34"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "i=98.6328      #Angle(degrees)\n",
+      "e=0.0011501    #eccentricity\n",
+      "n=14.23304826  #Mean Motion(1/day)\n",
+      "a=7192.3       #Semimajor axis(km)\n",
+      "K1=66063.1704  #Known constant(km^2)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "n0=(2*180*n)  #Mean Motion (deg/sec)\n",
+      "K=(n0*K1)/((a**2)*((1-e**2)**2))  #Constant (deg/day)\n",
+      "w=-K*math.cos(i*3.142/180)    #Rate of regression of nodes(deg/day)\n",
+      "W=K*(2-2.5*(math.sin(i*3.142/180))**2)   #Rate of rotation of line of apsides(deg/day)\n",
+      "w=round(w,3)\n",
+      "W=round(W,3)\n",
+      "#Results\n",
+      "\n",
+      "print \"The rate of regression of nodes is:\", w,\"deg/day\"\n",
+      "print \"The rate of rotation of line of apsides is:\", W,\"deg/day\"\n",
+      "\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The rate of regression of nodes is: 0.984 deg/day\n",
+        "The rate of rotation of line of apsides is: -2.902 deg/day\n"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.6, Page 34"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Variable Declaration\n",
+      "\n",
+      "w=0.982  #rate of regression of nodes from Example 2.5(deg/day)\n",
+      "W=-2.903 #rate of rotation of line of apsides from Example 2.5)deg/day)\n",
+      "n=14.23304826  #Mean Motion(1/day)\n",
+      "W0=113.5534   #Argument of perigee(deg)\n",
+      "w0=251.5324   #Right ascension of the ascending node(deg)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "PA=1/n   #Period \n",
+      "w=round(w0+w*PA,2)  #New value of rate of regression of nodes(deg)\n",
+      "W=round(W0+W*PA,2)  #New Value of rate of rotation of line of apsides(deg)\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"New value of rate of regression of nodes is:\", w,\"deg\"\n",
+      "print \"New value of rate of rotation of line of apsides is:\", W,\"deg\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "New value of rate of regression of nodes is: 251.6 deg\n",
+        "New value of rate of rotation of line of apsides is: 113.35 deg\n"
+       ]
+      }
+     ],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.7, Page 38"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Calculation\n",
+      "\n",
+      "ndays=400*365    #Nominal number of days in 400years\n",
+      "nleapyrs=400/4   #Nominal number of leap years\n",
+      "gregoriandays=ndays+nleapyrs-3  #number of days in 400 years of Gregorian calendar\n",
+      "gregavg=round(gregoriandays/float(400),2)    #number of days in 400 years of Gregorian calendar\n",
+      "\n",
+      "#Result\n",
+      "print gregoriandays\n",
+      "print \"The average length of the civil year in gregorian calender is:\", gregavg,\"days\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "146097\n",
+        "The average length of the civil year in gregorian calender is: 365.24 days\n"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.8, Page 38"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Calculation and Results\n",
+      "\n",
+      "if 1987%4==0:\n",
+      "  print \"1987 is a leap year\"\n",
+      "else:\n",
+      "  print \"1987 is not a leap year\"\n",
+      "\n",
+      "\n",
+      "if 1988%4==0:\n",
+      "  print \"1988 is a leap year\"\n",
+      "else:\n",
+      "  print \"1988 is not a leap year\"\n",
+      "\n",
+      "\n",
+      "if 2000%400==0:\n",
+      "  print \"2000 is a leap year\"\n",
+      "else:\n",
+      "  print \"2000 is not a leap year\"\n",
+      "\n",
+      "\n",
+      "if 2100%400==0:\n",
+      "  print \"2100 is a leap year\"\n",
+      "else:\n",
+      "  print \"2100 is not a leap year\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "1987 is not a leap year\n",
+        "1988 is a leap year\n",
+        "2000 is a leap year\n",
+        "2100 is not a leap year\n"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.9, Page 38"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Calculation\n",
+      "days=324   #Number of days\n",
+      "hours=math.floor(24*0.95616765)  # Number of hours\n",
+      "decimalfraction1=24*0.95616765-hours\n",
+      "minutes=math.floor(60*decimalfraction1)  # Number of minutes\n",
+      "decimalfraction2=60*decimalfraction1-minutes\n",
+      "seconds=round(60*decimalfraction2,2)  # Number of seconds\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print decimalfraction1,decimalfraction2\n",
+      "print \"An Epoch day has\", days,\"days\",hours,\"hours\",minutes,\"minutes\",seconds,\"seconds\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "0.9480236 0.881416\n",
+        "An Epoch day has 324 days 22.0 hours 56.0 minutes 52.88 seconds\n"
+       ]
+      }
+     ],
+     "prompt_number": 12
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.10, Page 39"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "\n",
+      "#Variable Declaration\n",
+      "\n",
+      "y=2000      #year\n",
+      "mon=12      #month\n",
+      "dy=18       #day\n",
+      "hours=13    #hours of the day\n",
+      "minutes=0   #Minutes of the day\n",
+      "seconds=0   #Seconds of the day\n",
+      "\n",
+      "\n",
+      "#Calculation\n",
+      "d=dy+(hours/24)+(minutes/(24*60))+seconds  #Days in December \n",
+      "if mon<=2:\n",
+      "   y=y-1\n",
+      "   mon=mon+12\n",
+      "else:\n",
+      "   y=y\n",
+      "   mon=mon\n",
+      "\n",
+      "A=math.floor(y/100)      #Converting years to days\n",
+      "B=2-A+math.floor(A/4)    #Converting years to days\n",
+      "C=math.floor(365.25*y)     #rounding the days \n",
+      "D=math.floor(30.6001*(mon+1)) #Converting months to days\n",
+      "JD=B+C+D+d+1720994.5     #Adding reeference to number of days\n",
+      "\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"The Julian day of given day is:\", JD,\"Days\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The Julian day of given day is: 2451896.5 Days\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.11, Page 41"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Variable Declaration\n",
+      "\n",
+      "JDref=2415020   #Reference Julian days\n",
+      "JC=36525\n",
+      "JD=2451897.0417 #Julian days with reference from Example 2.10\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "T=round((JD-JDref)/JC,4)  #Time in julian Centuries\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"The time for given date is:\", T,\"Julian Centuries\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The time for given date is: 1.0096 Julian Centuries\n"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.12, Page 43"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Variable Declaration\n",
+      "\n",
+      "n=14.23304826  #Mean Motion (rev/day)\n",
+      "M0=246.6853    #Mean Anomaly (degrees)\n",
+      "t0=223.79688452 #Time of anomaly\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "T=round(t0-(M0/(n*360)),3)  #Time of perigee passage\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "\n",
+      "print \"The time of perigee passage for NASA elements is:\", T,\"days\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The time of perigee passage for NASA elements is: 223.749 days\n"
+       ]
+      }
+     ],
+     "prompt_number": 15
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.13, Page 44"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#Variable Declaration\n",
+      "\n",
+      "M=205  #Mean anomaly(degrees)\n",
+      "e=0.0025  #Eccentricity\n",
+      "E=math.pi #Initial guess value for eccentric anomaly\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "import scipy\n",
+      "import scipy.optimize\n",
+      "def f(E):\n",
+      "    y=M-E+e*math.sin(E)\n",
+      "    return y\n",
+      "E=scipy.optimize.fsolve(f,3.142)\n",
+      "E=round(E,3)\n",
+      "\n",
+      "print \"The Eccentric anomaly is:\",E,\"degrees\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The Eccentric anomaly is: 204.998 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.14, Page 45"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#Variable Declaration\n",
+      "\n",
+      "n=14.2171401*2*math.pi/86400  #Mean motion (rad/sec)\n",
+      "M=204.9779+0.001*180*5/math.pi #Mean anomaly(rad)\n",
+      "e=9.5981*10**-3   #Eccentricity\n",
+      "a=7194.9   #Semimajor axis(km)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "v=(M*math.pi/180)+2*e*math.sin(M*math.pi/180)+(5*e**2*math.sin(2*M*math.pi)/(4*180)) #True Anomaly (radians)\n",
+      "v=v*180/math.pi  #True anomaly(degrees)\n",
+      "r=a*(1-e**2)/(1+e*math.cos(v))  #Magnitude of radius vector after 5s(km)\n",
+      "v=round(v,2)\n",
+      "r=round(r,2)\n",
+      "\n",
+      "#Results\n",
+      "\n",
+      "print \"The true anomaly is:\",v,\"degrees\"\n",
+      "print \"The magnitude of radius vector 5s after epoch is:\",r,\"km\"\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The true anomaly is: 204.79 degrees\n",
+        "The magnitude of radius vector 5s after epoch is: 7252.02 km\n"
+       ]
+      }
+     ],
+     "prompt_number": 17
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.15, Page 46"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#Variable Declaration\n",
+      "\n",
+      "v=204.81   #True anomaly(degrees) from Example 2.14\n",
+      "r=7257     #Magnitude of radius vector(km) from Example 2.14\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "rP=r*math.cos(v*math.pi/180)  #P coordinate of radius vector(km)\n",
+      "rQ=r*math.sin(v*math.pi/180)  #Q coordinate of radius vector(km)\n",
+      "rP=round(rP,2)\n",
+      "rQ=round(rQ,2)\n",
+      "#Result\n",
+      "\n",
+      "print \"r in the perifocal coordinate system is\", rP,\"Pkm\", rQ,\"Qkm\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "r in the perifocal coordinate system is -6587.21 Pkm -3045.11 Qkm\n"
+       ]
+      }
+     ],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Exanple 2.17, Page 50"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#Variable Declaration\n",
+      "\n",
+      "T=1.009638376  #Time in Julian centuries from Example 2.11\n",
+      "UT=13  #Universal time(hours)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "GST=(99.6910+36000.7689*T+0.004*T**2)*3.142/180  #GST(radians)\n",
+      "UT=2*math.pi*UT/24  #Universal time converted to fraction of earth rotation (radians)\n",
+      "\n",
+      "GST=GST+UT \n",
+      "\n",
+      "\n",
+      "GST=(math.fmod(GST,2*math.pi))*180/math.pi#using fmod multiplr revolutions are removed (degrees)\n",
+      "GST=round(GST,2)\n",
+      "\n",
+      "#Result\n",
+      "\n",
+      "print \"The GST for given date and time is \", GST,\"degrees\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The GST for given date and time is  287.18 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.18, Page 51"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#Variable Declararion\n",
+      "\n",
+      "WL=-89.26  #Expressing the longitude in degrees west\n",
+      "GST=282.449  #GST from Example 2.17 (degrees)\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "EL=2*math.pi+WL  #Longitude in degrees East \n",
+      "LST=(GST+EL)*math.pi/180       #LST(radians)\n",
+      "LST=(math.fmod(LST,2*math.pi))*180/math.pi   #fmod removes multiple revolutions(Degrees)\n",
+      "LST=round(LST,2)\n",
+      "\n",
+      "#Results\n",
+      "\n",
+      "print \"LST for Thunder Bay on given day is:\" ,LST,\"Degrees\"\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "LST for Thunder Bay on given day is: 199.47 Degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 20
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.19, Page 52"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import math\n",
+      "#Variable Declaration\n",
+      "\n",
+      "LST=167.475 #LST(degrees)\n",
+      "LE=48.42    #Latitude at thunder bay(degrees)\n",
+      "H=200       #Height above sea level(metres)\n",
+      "aE=6378.1414 #Semimajor axis(km)\n",
+      "eE=0.08182   #Eccentricity\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "l=(aE/math.sqrt(1-eE**2*math.sin(LE*3.142/180)**2)+H/1000)*math.cos(LE*3.142/180)  \n",
+      "\n",
+      "z=((aE*(1-eE**2))/math.sqrt(1-eE**2*math.sin(LE*3.142/180)**2)+H/1000)*math.sin(LE*3.142/180)  \n",
+      "\n",
+      "RI=round(l*math.cos(LST*3.142/180),2) #I component of radius vector at thunder bay(km)\n",
+      "\n",
+      "RJ=round(l*math.sin(LST*3.142/180),2) #J component of radius vector at thunder bay(km)\n",
+      "\n",
+      "RK=round(z,2)      #Z component of radius vector at thunder bay(km)\n",
+      "\n",
+      "R=math.sqrt(RI**2+RJ**2+RK**2)\n",
+      "R=round(R,2)\n",
+      "\n",
+      "\n",
+      "#Results\n",
+      "\n",
+      "print \"The Radius vector components are\" ,RI,\"ikm+\",RJ,\"jkm+\",RK,\"kkm\"\n",
+      "print \"The Magnitude of radius component is\" ,R,\"km\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The Radius vector components are -4139.81 ikm+ 918.02 jkm+ 4748.46 kkm\n",
+        "The Magnitude of radius component is 6366.21 km\n"
+       ]
+      }
+     ],
+     "prompt_number": 21
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.20, Page 55"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Variable Declaration\n",
+      "\n",
+      "PI=-1280  #I component of range vector for a satellite(km)\n",
+      "PJ=-1278  #J component of range vector for a satellite(km)\n",
+      "PK=66     #K component of range vector for a satellite(km)\n",
+      "GST=240   #GST(degrees)\n",
+      "LE=48.42  #Latitude(Degrees)\n",
+      "PE=-89.26 #Longitude(Degrees)\n",
+      "H=200     #Height above mean sea level(metres)\n",
+      "aE=6378.1414 #Semimajor axis(km)\n",
+      "eE=0.08182   #Eccentricity\n",
+      "\n",
+      "import math\n",
+      "#Calculation\n",
+      "\n",
+      "l=(aE/math.sqrt(1-eE**2*math.sin(LE*3.142/180)**2)+H/1000)*math.cos(LE*3.142/180)  \n",
+      "\n",
+      "z=((aE*(1-eE**2))/math.sqrt(1-eE**2*math.sin(LE*3.142/180)**2)+H/1000)*math.sin(LE*3.142/180)  \n",
+      "\n",
+      "SE=(math.atan(z/l))*180/3.142 #Geocentric latitude angle (degrees)\n",
+      "LST=240+PE\n",
+      "\n",
+      "from numpy import matrix\n",
+      "from numpy import linalg\n",
+      "a=math.sin(SE*3.142/180)*math.cos(LST*3.142/180)\n",
+      "b=math.sin(SE*3.142/180)*math.sin(LST*3.142/180)\n",
+      "c=-math.cos(SE*3.142/180)\n",
+      "d=-math.sin(LST*3.142/180)\n",
+      "e=math.cos(LST*3.142/180)\n",
+      "f=0\n",
+      "g=math.cos(SE*3.142/180)*math.cos(LST*3.142/180)\n",
+      "h=math.cos(SE*3.142/180)*math.sin(LST*3.142/180)\n",
+      "i=math.sin(SE*3.142/180)\n",
+      "\n",
+      "D = matrix( [[a,b,c],[d,e,f],[g,h,i]]) \n",
+      "\n",
+      "P=matrix( [[PI],[PJ],[PK]] )\n",
+      "\n",
+      "R=D*P  #Components of range of earth station\n",
+      "Ro=math.sqrt(R[0,0]**2+R[1,0]**2+R[2,0]**2) #Magnitude of range of earth station(km)\n",
+      "Ro=round(Ro,2)  \n",
+      "El=math.asin(R[2,0]/Ro) #Antenna elevation angle for the earth station(radians) \n",
+      "El=round(El*180/3.142,2) #Converting El to degrees\n",
+      "alpha=(math.atan(R[1,0]/R[2,0]))*180/3.142\n",
+      "if (R[0,0]<0 and R[1,0]>0):\n",
+      "   Aza=alpha\n",
+      "else:\n",
+      "   Aza=0\n",
+      "if (R[0,0]>0 and R[1,0]>0):\n",
+      "   Azb=180-alpha\n",
+      "else:\n",
+      "   Azb=0\n",
+      "if (R[0,0]>0 and R[1,0]<0):\n",
+      "   Azc=180+alpha\n",
+      "else:\n",
+      "   Azc=0\n",
+      "if (R[0,0]<0 and R[1,0]<0):\n",
+      "   Azd=360-alpha\n",
+      "else:\n",
+      "   Azd=0\n",
+      "Az=round(Aza+Azb+Azc+Azd,2)  #Azimuth angle (degrees)\n",
+      "\n",
+      "print \"The magnitude of range of earth station is\" ,Ro,\"km\"\n",
+      "print \"The antenna elevation angle for the earth station are\",El,\"degrees\"\n",
+      "print \"The Azimuth angle for the earth station is\",Az,\"degrees\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The magnitude of range of earth station is 1809.98 km\n",
+        "The antenna elevation angle for the earth station are 12.03 degrees\n",
+        "The Azimuth angle for the earth station is 102.24 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 22
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Example 2.21, Page 58"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Variable Declaration\n",
+      "\n",
+      "rI=-4685.3  #I component of radius vector from Example 2.16(km)\n",
+      "rJ=5047.7   #J component of radius vector from Example 2.16(km)\n",
+      "rK=-3289.1  #K component of radius vector from Example 2.16(km)\n",
+      "aE=6378.1414 #Semimajor axis (km)\n",
+      "eE=0.08182   #Eccentricity\n",
+      "\n",
+      "#Calculation\n",
+      "\n",
+      "r=math.sqrt(rI**2+rJ**2+rK**2)\n",
+      "a=math.pi  #Guess value for LST(radians)\n",
+      "b=math.atan(rK/rI)   #Guess Value for latitude(radians)\n",
+      "c=r-aE   #Guess value for height(km)\n",
+      "\n",
+      "from scipy.optimize import fsolve\n",
+      "\n",
+      "\n",
+      "def equations(p):\n",
+      "    L,h,LST = p\n",
+      "    return (rI-((aE/math.sqrt(1-eE**2*math.sin(L)**2))+h)*math.cos(L)*math.cos(LST),rJ-((aE/math.sqrt(1-eE**2*math.sin(L)**2))+h)*math.cos(L)*math.sin(LST),rK-((aE*(1-eE**2)/math.sqrt(1-eE**2*math.sin(L)**2))+h)*math.sin(L))\n",
+      "\n",
+      "L,h,LST =  fsolve(equations, (b,c,a))\n",
+      "L=round(L*180/3.142,2)  #Converting L into degrees\n",
+      "h=round(h)\n",
+      "LST=round(LST*180/3.142,1) #Converting LST into degrees\n",
+      "\n",
+      "print \"The latitude of subsatellite is\",L,\"degrees\"\n",
+      "print \"The height of subsatellite is\",h,\"km\"\n",
+      "print \"The LST of subsatellite is\",LST,\"degrees\""
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "The latitude of subsatellite is -25.65 degrees\n",
+        "The height of subsatellite is 1258.0 km\n",
+        "The LST of subsatellite is 132.9 degrees\n"
+       ]
+      }
+     ],
+     "prompt_number": 23
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file