{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"chapter 2: Satellite Orbits and Trajectories"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.1, page no-36"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Declaration\n",
"r1=6370.0 # Earth's Orbit in km\n",
"r2=630.0 # Height of satellite from surface in km\n",
"G=6.67*10**-11 # Gravitational constant inNm^2/kg^2\n",
"M=5.98*10**24 # Mass of earth in kg\n",
"\n",
"#Calculation\n",
"R=r1+r2\n",
"v=math.sqrt(G*M/(R*10**3))\n",
"\n",
"#Result\n",
"print(\"The velocity of sattelite %.2fkm/s\"%(math.floor(v/10)*10**-2))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of sattelite 7.54km/s\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.2, page no-37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Declaration\n",
"A=45000.0 #Apogee in km\n",
"P=7000.0 #Perigee in km\n",
"\n",
"\n",
"#Calculation\n",
"#(a)\n",
"a=(A+P)/2\n",
"#(b)\n",
"e=(A-P)/(2*a)\n",
"#(c)\n",
"e=(math.floor(e*100))/100\n",
"d=a*e\n",
"\n",
"#Result\n",
"print(\"(a)\\nSemi-major axis of elliptical orbit is %d km\"%a)\n",
"print(\"\\n(b)\\nEccentricity = %.2f\"%e)\n",
"print(\"\\n(c)\\nThe distance between centre of earth and centre of ellipse is %d km \"%d)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)\n",
"Semi-major axis of elliptical orbit is 26000 km\n",
"\n",
"(b)\n",
"Eccentricity = 0.73\n",
"\n",
"(c)\n",
"The distance between centre of earth and centre of ellipse is 18980 km \n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.3, page no-37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"ma=42000.0 # Major axis distance in Km\n",
"P=8000.0 # Perigee distance in Km\n",
"\n",
"\n",
"#Calculation\n",
"A=ma-P\n",
"e=(A-P)/ma\n",
"\n",
"#Result\n",
"print(\"Apogee=%dkm\\n Eccentricity=%.2f\"%(A,e))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Apogee=34000km\n",
" Eccentricity=0.62\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.4, page no-37"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration\n",
"e=0.6 #Eccentricity\n",
"d=18000.0 #distance between earth's centre and centre of ellipse\n",
"\n",
"\n",
"#Calculation\n",
"a=d/e\n",
"A=a*(1+e)\n",
"P=a*(1-e)\n",
"\n",
"\n",
"#Result\n",
"print(\"Semi-major axis of elliptical orbit is %d km\\n Apogee distance=%dkm\\n Perigee distance=%dkm\"%(a,A,P))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Semi-major axis of elliptical orbit is 30000 km\n",
" Apogee distance=48000km\n",
" Perigee distance=12000km\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.5, page no-38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"AP_diff=30000.0 #difference between apogee and perigee in km\n",
"AP_sum=62800.0 #Apogee+perigee\n",
"\n",
"\n",
"#Calculation\n",
"E=AP_diff/AP_sum\n",
"\n",
"\n",
"#Result\n",
"print(\"Orbit Eccentricity= %.3f\"%E)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Orbit Eccentricity= 0.478\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.6, page no-38"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"R=7000.0*10**3 # sattelite orbit in m\n",
"mu=39.8*10**13 # constant G*M in Nm^2/kg\n",
"A=47000.0*10**3 # appogee distance in m\n",
"P=7000.0*10**3 # perigee distance in m\n",
"\n",
"\n",
"#Calculation\n",
"v=math.sqrt(mu/R)\n",
"a=(A+P)/2\n",
"v1=math.sqrt(mu*((2/R)-(1/a)))\n",
"\n",
"\n",
"#Result\n",
"print(\"Velocity of satellite A at point X is v=%.2fkm/s\\nVelocity of satellite B at point X is V=%.3fkm/s\"%(v/1000,v1/1000))\n",
"#value in book is different at 3rd decimal place."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity of satellite A at point X is v=7.54km/s\n",
"Velocity of satellite B at point X is V=9.949km/s\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.7, page no-39"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Declaration\n",
"R=42000.0*10**3 #sattelite orbit in m\n",
"mu=39.8*10**13 #constant G*M in Nm^2/kg\n",
"A=42000.0*10**3 #appogee distance in m\n",
"P=7000.0*10**3 #perigee distance in m\n",
"\n",
"#Calculation\n",
"v=math.sqrt(mu/R)\n",
"a=(A+P)/2\n",
"v1=math.sqrt(mu*((2/R)-(1/a)))\n",
"\n",
"#Result\n",
"print(\"Velocity of satellite A at point X is v=%.3fkm/s\\n Velocity of satellite B at point X is V=%.3fkm/s\"%(v/1000,v1/1000))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity of satellite A at point X is v=3.078km/s\n",
" Velocity of satellite B at point X is V=1.645km/s\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.8, page no-40"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"R=25000.0*10**3 #sattelite orbit in m\n",
"mu=39.8*10**13 #constant G*M in Nm^2/kg\n",
"A=43000.0*10**3 #appogee distance in m\n",
"P=7000.0*10**3 #perigee distance in m\n",
"\n",
"#Calculation\n",
"v=math.sqrt(mu/R)\n",
"a=(A+P)/2\n",
"v1=math.sqrt(mu*((2/R)-(1/a)))\n",
"\n",
"#Result\n",
"print(\"Velocity of satellite A at point X is v=%.3fkm/s\\n Velocity of satellite B at point X is V=%.3fkm/s\"%(v/1000,v1/1000))\n",
"#value in book is different at 3rd decimal place."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity of satellite A at point X is v=3.990km/s\n",
" Velocity of satellite B at point X is V=3.990km/s\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.9, page no-40"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"a=(50000.0/2)*10**3 #Semi-major axis in m\n",
"mu=39.8*10**13 #constant G*M in Nm^2/kg\n",
"\n",
"\n",
"#Calculation\n",
"T=2*math.pi*math.sqrt((a**3)/mu) #math.pi gives variation in answer\n",
"h=T/(60*60)\n",
"x=T%3600\n",
"m=x/60\n",
"s=x%60\n",
"\n",
"#Result\n",
"print(\"Orbital time period is given by, T = %dsec\\n\\t\\t\\t\\t = %dh %dm %ds\"%(T,math.floor(h),math.floor(m),math.floor(s)))\n",
"#value in book is different for seconds."
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Orbital time period is given by, T = 39368sec\n",
"\t\t\t\t = 10h 56m 8s\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.10, page no-42"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"a1=18000.0*10**3 #Semi-major axis for first satellite in m\n",
"a2=24000.0*10**3 #Semi-major axis f0r 2nd satellite in m\n",
"\n",
"#Calculation\n",
"T2_by_T1=(a2/a1)**(3.0/2.0)\n",
"\n",
"#Result\n",
"print(\"Orbital time period of sattelite 2 is %.2f times that of sattelite 1\"%T2_by_T1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Orbital time period of sattelite 2 is 1.54 times that of sattelite 1\n"
]
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.11, page no-42"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"a=25000.0*10**3 #appogee distance in m\n",
"b=18330.0*10**3 #perigee distance in m\n",
"\n",
"\n",
"#Calculation\n",
"e=(math.sqrt(a**2-b**2)/a)\n",
"\n",
"\n",
"#Result\n",
"print(\"Apogee distance = a(1+e)= %dkm\\n Perigee distance = a(1-e)= %dkm\\n\"%(a*(1+e)/1000,math.ceil(a*(1-e)/1000)))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Apogee distance = a(1+e)= 42000km\n",
" Perigee distance = a(1-e)= 8000km\n",
"\n"
]
}
],
"prompt_number": 26
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.12, page no-43"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"e=0.6 # eccentricity of elliptical orbit\n",
"a=0.97 # area of shaded region\n",
"b=2.17 # Area of non-shaded region\n",
"t=3 # time taken by satellite to move from pt B to A\n",
"\n",
"\n",
"#Calculation\n",
"x=b/a\n",
"y=x*t\n",
"\n",
"#Result\n",
"print(\"Time taken by satellite to move from A to B is %.3f hours \"%y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Time taken by satellite to move from A to B is 6.711 hours \n"
]
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.13, page no-44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"A=42000.0 # Apogee in km\n",
"P=8000.0 # Perigee in km\n",
"v_p=9.142 # velocity at perigee point\n",
"\n",
"\n",
"#Calculation\n",
"v_a=v_p*P/A\n",
"\n",
"\n",
"#Result\n",
"print(\"Velocity at apogee = %.3f km/s\"%v_a)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Velocity at apogee = 1.741 km/s\n"
]
}
],
"prompt_number": 28
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.14, page no-44"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Declaration\n",
"theta=56.245 #angle made by direction of satellite with local horizontal\n",
"d=16000.0 #distance of particular point\n",
"P=8000.0 #Perigee in m\n",
"v_p=9.142 #velocity at perigee point\n",
"\n",
"\n",
"#Calculation\n",
"v=(P*v_p)/(d*math.floor(math.cos(theta*math.pi/180)*1000)/1000)\n",
"\n",
"\n",
"#Result\n",
"print(\"The velocity of satellite at that particular point is %.3f km/s\"%v)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The velocity of satellite at that particular point is 8.236 km/s\n"
]
}
],
"prompt_number": 29
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.16, page no-49"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"A1=12000.0 # first Apogee distance\n",
"P=8000.0 # Perigee distance\n",
"v1=1.0 # assume v1 as 1\n",
"v2=1.2*v1 # 20% higher than v1 \n",
"\n",
"\n",
"#Calculation\n",
"x=(v2/v1)**2\n",
"k=(((1+(P/A1))/x)-1)\n",
"k=math.floor(k*10**4)/10**4\n",
"A2=P/k\n",
"\n",
"\n",
"#Result\n",
"print(\"A2 = %.0fkm\"%math.ceil(A2))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A2 = 50826km\n"
]
}
],
"prompt_number": 30
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.17, page no-50"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"vp=8.0 # horizontal velocity of satellite in km/s\n",
"r=1620.0 # distance from earth's surface in km\n",
"R=6380.0 # Earth's radius in km\n",
"d=10000.0 # distance of point at which velocity to be calculated\n",
"theta=30.0 # angle made by satellite with local horzon at that point\n",
"\n",
"\n",
"#Calculation\n",
"P=r+R\n",
"v=(vp*P)/(d*math.cos(theta*math.pi/180))\n",
"\n",
"#Result\n",
"print(\"v = %.2f km/s\"%v)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"v = 7.39 km/s\n"
]
}
],
"prompt_number": 31
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.18, page no-50"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable Declaration\n",
"r=620.0 # distance from earth's surface in km\n",
"vp=8.0 # horizontal velocity of satelliteat 9000km height in km/s\n",
"R=6380.0 # Earth's radius in km\n",
"d=9000.0 # distance of point at which velocity to be calculated\n",
"theta=30.0 # angle made by satellite with local horzon at that point\n",
"mu=39.8*10**13 # Nm**2/kg\n",
"\n",
"\n",
"#Calculation\n",
"P=r+R\n",
"m=vp*d*math.cos(theta*math.pi/180)/P #m=sqrt((2mu/P)-[2mu/(A+P)])\n",
"m=(m*10**3)**2\n",
"x=(2*mu/(P*10**3))-m #x=[2mu/(A+P)]\n",
"x=math.floor(x/10**4)*10**4\n",
"k=(2*mu)/x #k=A+P\n",
"k=math.ceil(k/10**4)*10**4\n",
"A=k-(P*10**3)\n",
"\n",
"#Result\n",
"print(\"A = %.0f km\"%(A/1000))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"A = 16170 km\n"
]
}
],
"prompt_number": 32
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.19, page no-58"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"#variable declaration\n",
"R=6380 #Earth's radius in km\n",
"T=86160 #Orbital period of Geostationary satellite in km\n",
"mu=39.8*10**13 #in Nm^2/k\n",
"\n",
"#calculations\n",
"\n",
"r=(T*math.sqrt(mu)/(2*math.pi))**(2.0/3.0) # Answer matches to the answer given in the book if value of pi is taken as 3.14 \n",
"\n",
"#Result\n",
"print('Radius of satellite is, r = %.0f km'%(r/1000))\n",
"print('Therefore, height of satellite orbit above earth surface is %.0f km '%((r/1000)-R))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Radius of satellite is, r = 42142 km\n",
"Therefore, height of satellite orbit above earth surface is 35762 km \n"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 2.20, page no-59"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#variable declaration\n",
"\n",
"R=6380 #radius of earth in km\n",
"P=400 #Perigee distance in km\n",
"A=40000 #Apogee distance in km\n",
"mu=39.8*10**13 #in Nm^2/k\n",
"\n",
"#calculation\n",
"\n",
"a=(A+P+R+R)/2 #semi-major axis of the elliptical orbit\n",
"\n",
"T=(2*math.pi*(a*10**3)**(3.0/2.0))/math.sqrt(mu)\n",
"\n",
"h=T/(60*60)\n",
"x=T%3600\n",
"m=x/60\n",
"s=x%60\n",
"\n",
"#Result\n",
"print('T = %dsec\\n = %dh %dm %ds\\n\\nThis approximately equal to 12 hour'%(T,math.floor(h),math.floor(m),math.floor(s)))\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"T = 43158sec\n",
" = 11h 59m 18s\n",
"\n",
"This approximately equal to 12 hour\n"
]
}
],
"prompt_number": 34
}
],
"metadata": {}
}
]
}