{
"metadata": {
"name": "AKmaini"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": "Chapter 11: Satellites and Satellite Communications\n"
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 1, Pg No: 567"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n# Variable Declaration\nh = 150; # height of satellite from earth in km\nG = 6.67*10**-11; # Gravitational constant\nM = 5.98*10**24; # mass of the earth in kg\nRe = 6370; # radius of earth in km\n\n# Calculations\nu = G*M\nV = math.sqrt(u/((Re + h)*10**3)) # orbital velocity\nV1 = V/1000; # orbital velocity in km/s\n\n# Result\nprint 'Orbital velocity = %3.3f'%V1,'km/s';",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Orbital velocity = 7.821 km/s\n"
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 2, Pg No: 568"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\nAp_Pe_diff = 30000; # difference between apogee and perigee in Km\na = 16000; # semi major axis of orbit\n\n# Calculations\ne = Ap_Pe_diff/float(2*a); # Eccentricity\n\n# Result\nprint 'Eccentricity = %3.2f'%e;",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Eccentricity = 0.94\n"
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 3, Pg No:568"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Decalaration\na1 = 18000; # semi major axis of the elliptical orbits of satellite 1\na2 = 24000; # semi major axis of the elliptical orbits of satellite 2\n\n# Calculations\n#T = 2*%pi*sqrt(a^3/u);\n#let K = T2/T1;\nK = (float(a2)/a1)**(3/float(2)); # Ratio of orbital periods\n\n# Result\nprint 'The orbital period of satellite-2 is %3.2f' %K,' times the orbital period of satellite-1';\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "The orbital period of satellite-2 is 1.54 times the orbital period of satellite-1\n"
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 4, Pg No:569"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\n\nh = 35800; # height of satellite orbit from earth in km\nG = 6.67*10**-11; # Gravitational constant\nM = 5.98*10**24; # mass of the earth in kg\nRe = 6364; # radius of earth in km\ni = 2; # inclination angle\n\n# Calculations\nu = G*M\nr = Re+h\nVi = math.sqrt(u/r*10**3)* math.tan(i*math.pi/180); # magnitude of velocity impulse\nV = Vi/1000; # magnitude of velocity impulse in m/s\n\n#Result\nprint 'Magnitude of velocity impulse = %d' %V,' m/s';",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Magnitude of velocity impulse = 107 m/s\n"
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 5, Pg No: 571"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\nh = float(13622); # ht of circular orbit from earth's surface\nRe = 6378; # Radius of earth in km\n\n# Calculations\nR = Re+h; # Radius of circular orbit\npimax = 180 - (2*math.acos(Re/R))*(180/math.pi); # Maximum shadow angle\neclipmax_time = (pimax/360)*24; # maximum daily eclipse duration\n\n# Result\nprint ' Maximum shadow angle = %3.1f\u00b0' %pimax\nprint ' Maximum daily eclipse duration = %3.2f'%eclipmax_time,' hours';",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": " Maximum shadow angle = 37.2\u00b0\n Maximum daily eclipse duration = 2.48 hours\n"
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 6, Pg No:572"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n# Variable Declaration\n\nh = 35786; # ht of geo.stationary orbit above earth surface\nT = 365; # time in days\nr = 6378 # radius of earth in km\n\n# ie(t) = 23.4*sin(2*%pi*t/T)\n# for a circular orbit of 20000 km radius ,phi = 37.4\u00b0 ,Therefore, the time from first day of eclipse to equinox is given by substituting ie(t) = 37.4/2 = 18.7\u00b0\nphi = 37.4\nie = (phi/2)*(math.pi/180)\nk = 23.4*(math.pi/180)\nt = (365/(2*math.pi))*math.asin((ie/k)) \n# for geostationary orbit\nphimax = 180 - 2*(math.acos(r/(r+h)))*(180/math.pi)\nt_geo = (365/(2*math.pi))*math.asin((8.7*math.pi/180)/k)\n\n# Result\nprint 'Total time from first day of eclipse to last day of eclipse = %3.1f' %t,' days';\nprint 'Total time from first day of eclipse to last day of eclipse for geostationary orbit = %3.2f' %t_geo, 'days'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Total time from first day of eclipse to last day of eclipse = 53.8 days\nTotal time from first day of eclipse to last day of eclipse for geostationary orbit = 22.13 days\n"
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 7, Pg No:600"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\nm = 100; # mass of satellite\nV = 8000; # orbital velocity in m/s\nRe = 6370; # radius of earth in Km\nH = 200; # satellite height above earth surface\n\n# Calculations\nCF = (m*V**2)/((Re+H)*10**3); #centrifugal force\n\n# Result\nprint 'Centrifugal Force = %d' %CF,' Newtons';",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Centrifugal Force = 974 Newtons\n"
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 8, Pg No:601"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\n\nApogee = 30000; # Apogee pt of satellite elliptical orbit\nPerige = 1000; # perigee pt of satellite elliptical orbit\n\n# Calculations\na = (Apogee + Perige)/2; # semi major axis\n\n# Result\nprint 'Semi-major axis = %d' %a,' Km';",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Semi-major axis = 15500 Km\n"
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 9, Pg No:603"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math\n\n# Variable Declaration\nfarth = 30000; # farthest point in satellite elliptic eccentric orbit\nclosest = 200; # closest point in satellite elliptic eccentric orbit\nRe = float(6370); # Radius of earth in km\n\n# Calculations\nApogee = farth + Re; # Apogee in km\nPerigee = closest + Re; # perigee in km\na = (Apogee + Perigee)/(2); # semi-major axis\ne = (Apogee - Perigee)/(2*a); # orbit eccentricity\n\n# Result\nprint 'Apogee = %d' %Apogee,' km';\nprint 'Perigee = %d' %Perigee,' km';\nprint 'Orbit eccentricity = %3.3f' %e;",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Apogee = 36370 km\nPerigee = 6570 km\nOrbit eccentricity = 0.694\n"
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 10, Pg No:604"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\ne = 0.5; # orbit eccentricity\nae = 14000; # from fig. the distance from center of ellipse to the centre of earth\n\n# Calculations\na = ae/(e); # semi major axis\napogee = a*(1 + e); # Apogee in km\nperige = a*(1 - e); # perigee in km\n\n# Result\nprint 'Apogee = %d' %apogee,' km'\nprint 'Perigee = %d' %perige,' km'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Apogee = 42000 km\nPerigee = 14000 km\n"
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 11, Pg No:604"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\nG = 6.67*10**-11; # Gravitational constant\nM = 5.98*10**24; # mass of the earth in kg\nRe = 6370*10**3; # radius of earth in m\n\n# Calculations\nu = G*M\nVesc = math.sqrt(2*u/Re);\nVes = Vesc/1000; # escape velocity in km/s\n\n# Result\nprint 'Escape velocity = %3.1f' %Ves,' km/s';",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Escape velocity = 11.2 km/s\n"
}
],
"prompt_number": 36
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 12, Pg No:605"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# variable Declartion\na = 25000*10**3; # semimajor axis in m from fig\nG = 6.67*10**-11; # Gravitational constant\nM = 5.98*10**24; # mass of the earth in kg\nh = 0\n\n# Calculations\nu = G*M;\nT = 2*math.pi*math.sqrt((a**3)/u)\nhr = T/3600 # conv. from sec to hrs and min\nt = T%3600 # conv. from sec to hrs and min\nmi = t/60 # conv. from sec to hrs and min\n\n# Result\nprint 'Orbital time period = %d' %hr,' Hours',' %d'%mi, 'minutes'",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Orbital time period = 10 Hours 55 minutes\n"
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example 13, Pg No:605"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import math;\n\n# Variable Declaration\napogee = float(35000); # farthest point in kms\nperigee = 500; # closest point in kms\nr = float(6360); # radius of earth in kms\nG = 6.67*10**-11 # gravitational constant\nM = 5.98*10**24; # mass of earth in kgs\n\n# calculations\n#funcprot(0)\napogee_dist = apogee + r # apogee distance in kms\nperigee_dist= perigee+r ; # perigee distance in kms\na = (apogee_dist + perigee_dist)/2; # semi-major axis of elliptical orbit\nT = (2*math.pi)*math.sqrt((a*10**3)**3/(G*M)); # orbital time period\nhr = T/3600 # conv. from sec to hrs and min\nt = (T%3600) # conv. from sec to hrs and min\nmi = t/60 # conv. from sec to hrs and min\nu = G*M\nVapogee = math.sqrt(u*((2/(apogee_dist*10**3)) - (1/(a*10**3))))/1000; # velocity at apogee point\nVperigee = math.sqrt((G*M)*((2/(perigee_dist*10**3)-(1/(a*10**3)))))/1000 # velocity at perigee point\n\n#Result\nprint 'Orbital Time Period = %d'%hr,' Hrs'' %d'%mi,' min'\nprint 'Velocity at apogee = %3.3f' %Vapogee,' Km/s'\nprint'Velocity at perigee = %3.3f' %Vperigee,' Km/s'\nprint'Note: Calculation mistake in textbook in finding velocity at apogee point'\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Orbital Time Period = 10 Hrs 20 min\nVelocity at apogee = 1.656 Km/s\nVelocity at perigee = 9.987 Km/s\nNote: Calculation mistake in textbook in finding velocity at apogee point\n"
}
],
"prompt_number": 57
}
],
"metadata": {}
}
]
}