# JED - June 2017 - 44

```E W101
So: n = sqrt[m2 +k2 -2mk cosN] = sqrt[66172 + 63712 - 2 *
= acos[0.500 * 0.955 + 0.866 * 0.296 * 0.707] = acos[0.659]
6671
* 6371 * cos(2.6°)] = sqrt[175002] = 418 km
= 48.8°
Then, from the law of sines for plane triangles: sin K/k =
Which makes the latitude of the calculated horizon edge
sin N/n
point 90° - 48.8° = 41.2° North
So: K = asin [k * sin N / n] = asin[6371*sin(2.6°)/418] =
Now, from the law of sines for spherical triangles,
asin[6371*.045/418] = 68.6°
Sin D / sin d = sin F/sin f
Now, we can find angle M = 180° - 2.6° - 68.6° = 108.8°
So: D = asin[(sin d * sin F)/sin f] = asin[(sin 17.2° *
The local horizon at the bore-sight point is 90° above nadir,
sin 45°)/sin 48.8°]
so the satellite is
= asin[(0.295 * 0.707) / 0.752º] = asin 0.277 = 16.1º
108.8° - 90° = 18.8° above the horizon
Since the satellite SVP is at 100° East latitude, the longitude of the calculated horizon edge point is 100° +
16.1° = 116.1 º East Longitude.
Calculation of the rest of the horizon points and
Longitude
North
the plotting is left as an exercise for the reader (and
Pole
Target
Azimuth of

ANTENNA POINTING

The Journal of Electronic Defense | June 2017

44

antenna
direction

Latitude of bore-sight
on Earth surface

Now, we will calculate the azimuth and elevation
Sub-vehicle
point
(from nadir) required to direct the satellite antenna
G
bore-sight at an Earth surface target at a specific
Latitude
of sub-vehicle
j
latitude and longitude. The SVP is the same as stated
point
h
above, and the target is at 102° East longitude, 32°
North latitude. Note that this is well within the area
H
Center
g
that the satellite can see. First, consider the spherical
of Earth
J
triangle of Figure 3 formed by the SVP, the target location and the North pole.
Fig. 3: The spherical triangle formed by the North pole, the sub-vehicle point and
h = 90° - latitude of SVP (i.e., 60°)
a target at a specified longitude and latitude allows calculation of the satellite
antenna
azimuth
look angle
to that
target.
j = 90° - latitude of target (i.e., 58°)
Fig. 3:
The spherical
triangle
formed
by the North pole,
the sub-vehicle point and a target at a specified longitude and latitude
g = geocentric angle from the SVP to the target
allows calculation of the satellite antenna azimuth look angle to that target.
G = the difference in longitude between the SVP and
the target (i.e., 2°)
Antenna
Range to Earth
elevation
surface target
J = the azimuth to which the antenna must be
Satellite
K
angle
directed
From the law of cosines for sides:
n
H
Cos g = cos h * cos j + sin h * sin j * cos G
Target
M
So g = acos[cos 60° *cos 58° + sin 60º * sin 58° *
cos 2°] = acos[ 0.500 * 0.530 + 0.866 * 0.848 * 0.999]
m
= acos [0.738] = 2.6°
RE
Then, from the law of sines for spherical triangles:
k
Sin J / sin j = sin G / sin g
Geocentric
RE
So J = asin[(sin G * sin j) / sin g] = asin[(sin 2° *
angle of
boresight
sin 58º) / sin 2.6°] = asin[(0.035 * 0.848)/ 0.045] =
to Earth
asin[.660] = 41.3°
N
Center
Now consider the plane triangle in Figure 4 formed
of Earth
by the satellite, the target, and the center of the
Earth.
Fig. 4: The elevation of the antenna (above nadir) and the range from the satellite
m = RE + height of satellite
Fig. 4: The elevation of the antenna (above nadir) and the range from the satellite to a
to a target
on the Earth surface can be calculated from this plane triangle.
target on the Earth surface can be calculated from this plane triangle.
k=RE
n = the propagation range from the satellite to the
target
WHAT'S NEXT
K = the elevation (from nadir) from the satellite to the target
Next month, we will put all of these angles and distances
N = the geocentric angle from the satellite to the target
together and run some EW calculations. We will determine the
M = the angle from the center of the Earth to the satellite as
signal strength that a transmitter on this satellite would put
seen from the target
on the target, determine the antenna gain and sensitivity a
Angle N in Figure 4 is side g from Figure 3 (i.e., 2.6°)
satellite receiver would require to intercept a signal from the
Using the law of cosines for plane triangles: n2 = m2 + k2
target, and calculate the ERP required to perform radar and
- 2nk cosN
communications jamming from this satellite. a

```

# JED - June 2017

The View From Here
Conferences Calendar
Courses Calendar
From the President
The Monitor
World Report
DIRCM Past & Present
Technology Survey: GaN Transistors
EW 101
Report from the 42nd Annual Collaborative EW Symposium
AOC News
2017 AOC International Election Guide
JED Quick Look
JED - June 2017 - intro
JED - June 2017 - cover1
JED - June 2017 - cover2
JED - June 2017 - 3
JED - June 2017 - 4
JED - June 2017 - 5
JED - June 2017 - The View From Here
JED - June 2017 - 7
JED - June 2017 - Conferences Calendar
JED - June 2017 - 9
JED - June 2017 - Courses Calendar
JED - June 2017 - 11
JED - June 2017 - From the President
JED - June 2017 - 13
JED - June 2017 - 14
JED - June 2017 - insert1
JED - June 2017 - insert2
JED - June 2017 - The Monitor
JED - June 2017 - 16
JED - June 2017 - 17
JED - June 2017 - 18
JED - June 2017 - 19
JED - June 2017 - 20
JED - June 2017 - 21
JED - June 2017 - World Report
JED - June 2017 - 23
JED - June 2017 - DIRCM Past & Present
JED - June 2017 - 25
JED - June 2017 - 26
JED - June 2017 - 27
JED - June 2017 - 28
JED - June 2017 - 29
JED - June 2017 - 30
JED - June 2017 - 31
JED - June 2017 - 32
JED - June 2017 - 33
JED - June 2017 - 34
JED - June 2017 - Technology Survey: GaN Transistors
JED - June 2017 - 36
JED - June 2017 - 37
JED - June 2017 - 38
JED - June 2017 - 39
JED - June 2017 - 40
JED - June 2017 - 41
JED - June 2017 - 42
JED - June 2017 - EW 101
JED - June 2017 - 44
JED - June 2017 - Report from the 42nd Annual Collaborative EW Symposium
JED - June 2017 - AOC News
JED - June 2017 - 47
JED - June 2017 - 2017 AOC International Election Guide
JED - June 2017 - 49
JED - June 2017 - 50
JED - June 2017 - 51
JED - June 2017 - 52
JED - June 2017 - 53
JED - June 2017 - 54
JED - June 2017 - 55
JED - June 2017 - JED Quick Look
JED - June 2017 - Index of Advertisers
JED - June 2017 - 58
JED - June 2017 - cover3
JED - June 2017 - cover4
https://www.nxtbook.com/naylor/JEDM/JEDM0318
https://www.nxtbook.com/naylor/JEDM/JEDM0218
https://www.nxtbook.com/naylor/JEDM/JEDM0118
https://www.nxtbook.com/naylor/JEDM/JEDM1217
https://www.nxtbook.com/naylor/JEDM/JEDM1117
https://www.nxtbook.com/naylor/JEDM/JEDM1017
https://www.nxtbook.com/naylor/JEDM/JEDM0917
https://www.nxtbook.com/naylor/JEDM/JEDM0817
https://www.nxtbook.com/naylor/JEDM/JEDM0717
https://www.nxtbook.com/naylor/JEDM/JEDM0617
https://www.nxtbook.com/naylor/JEDM/JEDM0517
https://www.nxtbook.com/naylor/JEDM/JEDM0417
https://www.nxtbook.com/naylor/JEDM/JEDM0317
https://www.nxtbook.com/naylor/JEDM/JEDM0217
https://www.nxtbook.com/naylor/JEDM/JEDM0117
https://www.nxtbook.com/naylor/JEDM/JEDM1216
https://www.nxtbook.com/naylor/JEDM/JEDM1116
https://www.nxtbook.com/naylor/JEDM/JEDM1016
https://www.nxtbook.com/naylor/JEDM/JEDM0916
https://www.nxtbook.com/naylor/JEDM/JEDM0816
https://www.nxtbook.com/naylor/JEDM/JEDM0716
https://www.nxtbook.com/naylor/JEDM/JEDM0616
https://www.nxtbook.com/naylor/JEDM/JEDM0516
https://www.nxtbook.com/naylor/JEDM/JEDM0416
https://www.nxtbook.com/naylor/JEDM/JEDM0316
https://www.nxtbook.com/naylor/JEDM/JEDM0216
https://www.nxtbook.com/naylor/JEDM/JEDM0116
https://www.nxtbook.com/naylor/JEDM/JEDM1215
https://www.nxtbook.com/naylor/JEDM/JEDM1115
https://www.nxtbook.com/naylor/JEDM/JEDM1015
https://www.nxtbook.com/naylor/JEDM/JEDM0915
https://www.nxtbook.com/naylor/JEDM/JEDM0815
https://www.nxtbook.com/naylor/JEDM/JEDM0715
https://www.nxtbook.com/naylor/JEDM/JEDM0615
https://www.nxtbook.com/naylor/JEDM/JEDM0515
https://www.nxtbook.com/naylor/JEDM/JEDM0415
https://www.nxtbook.com/naylor/JEDM/JEDM0315
https://www.nxtbook.com/naylor/JEDM/JEDM0215
https://www.nxtbook.com/naylor/JEDM/JEDM0115
https://www.nxtbook.com/naylor/JEDM/JEDM1214
https://www.nxtbook.com/naylor/JEDM/JEDM1114
https://www.nxtbook.com/naylor/JEDM/JEDM1014
https://www.nxtbook.com/naylor/JEDM/JEDM0914
https://www.nxtbook.com/naylor/JEDM/JEDM0814
https://www.nxtbook.com/naylor/JEDM/JEDM0714
https://www.nxtbook.com/naylor/JEDM/JEDM0614
https://www.nxtbook.com/naylor/JEDM/JEDM0514
https://www.nxtbook.com/naylor/JEDM/JEDM0414
https://www.nxtbook.com/naylor/JEDM/JEDM0314
https://www.nxtbook.com/naylor/JEDM/JEDM0214
https://www.nxtbook.com/naylor/JEDM/JEDM0114
https://www.nxtbook.com/naylor/JEDM/JEDM1213
https://www.nxtbook.com/naylor/JEDM/JEDM1113
https://www.nxtbook.com/naylor/JEDM/JEDM1013
https://www.nxtbook.com/naylor/JEDM/JEDM0913
https://www.nxtbook.com/naylor/JEDM/JEDM0813
https://www.nxtbook.com/naylor/JEDM/JEDM0713
https://www.nxtbook.com/naylor/JEDM/JEDM0613
https://www.nxtbook.com/naylor/JEDM/JEDM0513
https://www.nxtbook.com/naylor/JEDM/JEDM0413
https://www.nxtbook.com/naylor/JEDM/JEDM0313
https://www.nxtbook.com/nxtbooks/naylor/JEDM0213
https://www.nxtbook.com/nxtbooks/naylor/JEDM0113
https://www.nxtbook.com/nxtbooks/naylor/JEDM1212
https://www.nxtbook.com/nxtbooks/naylor/JEDM1112
https://www.nxtbook.com/nxtbooks/naylor/JEDM1012
https://www.nxtbook.com/nxtbooks/naylor/JEDM0912
https://www.nxtbook.com/nxtbooks/naylor/JEDM0812
https://www.nxtbook.com/nxtbooks/naylor/JEDM0712
https://www.nxtbook.com/nxtbooks/naylor/JEDM0612
https://www.nxtbook.com/nxtbooks/naylor/JEDM0512
https://www.nxtbook.com/nxtbooks/naylor/JEDM0412
https://www.nxtbook.com/nxtbooks/naylor/JEDM0312
https://www.nxtbook.com/nxtbooks/naylor/JEDM0212
https://www.nxtbook.com/nxtbooks/naylor/JEDM0112
https://www.nxtbook.com/nxtbooks/naylor/JEDM1211
https://www.nxtbook.com/nxtbooks/naylor/JEDM1111
https://www.nxtbook.com/nxtbooks/naylor/JEDM1011
https://www.nxtbook.com/nxtbooks/naylor/JEDM0911
https://www.nxtbook.com/nxtbooks/naylor/JEDM0811
https://www.nxtbook.com/nxtbooks/naylor/JEDM0711
https://www.nxtbook.com/nxtbooks/naylor/JEDM0611
https://www.nxtbook.com/nxtbooks/naylor/JEDM0511
https://www.nxtbook.com/nxtbooks/naylor/JEDM0411
https://www.nxtbook.com/nxtbooks/naylor/JEDM0311
https://www.nxtbook.com/nxtbooks/naylor/JEDM0211
https://www.nxtbook.com/nxtbooks/naylor/JEDM0111
https://www.nxtbook.com/nxtbooks/naylor/JEDM1210
https://www.nxtbook.com/nxtbooks/naylor/JEDM1110
https://www.nxtbook.com/nxtbooks/naylor/JEDM1010
https://www.nxtbook.com/nxtbooks/naylor/JEDM0910
https://www.nxtbook.com/nxtbooks/naylor/JEDM0810
https://www.nxtbook.com/nxtbooks/naylor/JEDM0710
https://www.nxtbook.com/nxtbooks/naylor/JEDM0610
https://www.nxtbook.com/nxtbooks/naylor/JEDM0510
https://www.nxtbook.com/nxtbooks/naylor/JEDM0410
https://www.nxtbook.com/nxtbooks/naylor/JEDM0310
https://www.nxtbook.com/nxtbooks/naylor/JEDM0210
https://www.nxtbook.com/nxtbooks/naylor/JEDM0110
https://www.nxtbook.com/nxtbooks/naylor/JEDM1209
https://www.nxtbook.com/nxtbooks/naylor/JEDM1109
https://www.nxtbook.com/nxtbooks/naylor/JEDM1009
https://www.nxtbook.com/nxtbooks/naylor/JEDM0909
https://www.nxtbook.com/nxtbooks/naylor/JEDM0809
https://www.nxtbook.com/nxtbooks/naylor/JEDM0709
https://www.nxtbook.com/nxtbooks/naylor/JEDM0609
https://www.nxtbook.com/nxtbooks/naylor/JEDM0509
https://www.nxtbook.com/nxtbooks/naylor/JEDM0409
https://www.nxtbook.com/nxtbooks/naylor/JEDM0309
https://www.nxtbook.com/nxtbooks/naylor/JEDM0209
https://www.nxtbook.com/nxtbooks/naylor/JEDM0109
https://www.nxtbook.com/nxtbooks/naylor/JEDM0908
https://www.nxtbookmedia.com