1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
|
{
"metadata": {
"name": "",
"signature": "sha256:cf5342643c702b9d8304367e59517c8b40b2c0d171b088582d18b96d8620a619"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3: The Geostationary Orbit"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.1, Page 71"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"\n",
"Pss=-90 #Location of geostationary satellite(degrees)\n",
"PE=-100 #Longitude of the earth station antenna(degrees)\n",
"LE=35 #Latitude of the earth station antenna(degrees)\n",
"\n",
"#Calculation\n",
"\n",
"B=PE-Pss #Angle between planes containing a and c(degrees)\n",
"b=math.acos(math.cos(B)*math.cos(LE)) #Angle of plane containing b(radians)\n",
"A=math.asin(math.sin(abs(B*3.142/180))/math.sin(b)) #Angle between planes containing b and c (radians)\n",
"\n",
"A=A*180/3.142 #Converting A into degrees\n",
"#LE>0 and B<0 by observation\n",
"Az=round(180-A,2) #Azimuth angle(degrees)\n",
"\n",
"#Result\n",
"\n",
"print \"The azimuth angle for the given earth station antenna is\", Az,\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The azimuth angle for the given earth station antenna is 164.55 degrees\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.2, Page 73"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable Declaration\n",
"\n",
"R=6371 #Radius of earth (km)\n",
"aGSO= 42164 #Circumference of earth(km)\n",
"b=0.632 #values of b from Example 3.1 (radians)\n",
"#Calculation\n",
"import math\n",
"d=math.sqrt(R**2+aGSO**2-2*R*aGSO*math.cos(b)) #Range of earth station antenna (km)\n",
"El=math.acos(aGSO*math.sin(b)/d)*180/math.pi #Elevation angle(degrees)\n",
"d=round(d)\n",
"El=round(El)\n",
"#Results\n",
"\n",
"print \"The range of earth station antenna is\", d,\"km\"\n",
"print \"Elevation angle is\", El,\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The range of earth station antenna is 37214.0 km\n",
"Elevation angle is 48.0 degrees\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.3, Page 77"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"\n",
"LE=49 #Latitude of earth station(degrees)\n",
"aGSO=42164 #Circumference of earth(km)\n",
"R=6371 #Radius of earth(km)\n",
"\n",
"#Calculation\n",
"d=(R**2+aGSO**2-2*R*aGSO*math.cos(LE*3.142/180))**0.5 #Range of earth station antenna\n",
"\n",
"El0=math.acos(aGSO*math.sin(LE*3.142/180)/d) #Elevation angle(radians)\n",
"\n",
"El0=El0*180/3.142 #Converting El0 to degrees\n",
"\n",
"delta=round(90-El0-LE) #Angle of tilt required for polar mount\n",
"\n",
"#Results\n",
"\n",
"\n",
"print \"The Angle of tilt required for polar mount is\", delta,\"degrees\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The Angle of tilt required for polar mount is 7.0 degrees\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.4, Page 78"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"\n",
"LE=48.42 #Latitude of earth station(degrees)\n",
"PE=-89.26 #Longitute of earth station(degrees)\n",
"Elmin=5 #Minimum angle of elevation(degrees)\n",
"aGSO=42164 #Circumference of earth(km)\n",
"R=6371 #Radius of earth(km)\n",
"\n",
"#Calculation\n",
"\n",
"Smin=90+Elmin\n",
"S=math.asin(R*math.sin(Smin*3.142/180)/aGSO)*180/math.pi #Angle subtended at the satellite(degrees)\n",
"\n",
"b=180-Smin-S #Angle of plane containing b(degrees)\n",
"B=math.acos(math.cos(b*3.142/180)/math.cos(LE*3.142/180))*180/math.pi#Angle between the planes containing a and c(degrees)\n",
"\n",
"#Results\n",
"\n",
"print \"The satellite limit east of the earth station is at\", round(PE+B),\"Degrees approximately\"\n",
"print \"The satellite limit west of the earth station is at\", round(PE-B),\"Degrees approximately\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The satellite limit east of the earth station is at -20.0 Degrees approximately\n",
"The satellite limit west of the earth station is at -158.0 Degrees approximately\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3.5, Page 80"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#Variable Declaration\n",
"y=2000 #year\n",
"d=223.153 #day\n",
"n=1.002716 #mean motion(1/day)\n",
"w=272.5299 #rate of regression of nodes(degrees)\n",
"e=0.000352 #Eccentricity\n",
"W=247.9161 #Rate of regression of line of apsides(degrees)\n",
"M=158.0516 #Mean Anomaly at given time\n",
"JD00=2451543.5 #Julian days for Jan 0.0 2000\n",
"\n",
"#Calculation\n",
"\n",
"JD=JD00+d #Julian days for given day\n",
"JDref=2415020 #Reference Julian days\n",
"JC=36525\n",
"T=round((JD-JDref)/JC,4) #Time in julian Centuries\n",
"UT=d-223 #Universal Time, fraction of the day\n",
"GST=(99.6910+36000.7689*T+0.004*T**2)*3.142/180 #GST(radians)\n",
"UT=2*math.pi*UT #Universal time converted to fraction of earth rotation (radians)\n",
"\n",
"GST=(GST+UT)*180/3.1421\n",
"\n",
"\n",
"GST=(math.fmod(GST,360))#using fmod multiplr revolutions are removed (degrees)\n",
"GST=round(GST,3)\n",
"v=M+2*e*M #True Anomaly(degrees)\n",
"\n",
"Pssmean=W+w+M-GST #longitude for INTELSAT(degrees)\n",
"Pssmean=math.fmod(Pssmean,360) #fmod removes multiple revolutions\n",
"Pss=w+W+v-GST#longitude for INTELSAT(degrees)\n",
"Pss=math.fmod(Pss,360)#fmod removes multiple revolutions\n",
"\n",
"#Results\n",
"print \"The longitude of INTELSAT 805 is\", round(Pss,3),\"Degrees\"\n",
"print \"The average longitude of INTELSAT 805 is\", round(Pssmean,3),\"Degrees\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The longitude of INTELSAT 805 is 304.625 Degrees\n",
"The average longitude of INTELSAT 805 is 304.514 Degrees\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}
|
