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
the reader's computer).
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

Table of Contents for the Digital Edition of 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
Index of Advertisers
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
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