# JED - August 2016 - 43

```E W

101

Each location is defined by its
latitude and longitude.

Satellite

A SPHERICAL TRIANGLE ON
THE EARTH'S SURFACE

As shown in the figure,
there is a spherical triangle
with its corners at the North
pole, the SVP and the receiver
location. Using the notation
we discussed last month for
spherical triangles, the angle
"A" is at the North pole, the
Angle "B" is at the SVP and the
angle "C" is at the receiver location. The side "c" (opposite
the angle C) is (90° - the latiE
tude of the SVP). The side "b"
(opposite the angle B) is (90° the latitude of the receiver location). The side "a" (opposite
E
the angle A) is the geocentric
angle between the SVP and the
Remember from last month
that the sides of the spherical triangle are great circle
segments, and the angles are
the intersection angles of the
43
planes containing the sides.
The "length" of a side of a
Figure 3: The propagation distance between a transmitting satellite and a receiver on the Earth's surface can
be calculated from the plane triangle formed by the satellite location, the receiver location and the center of
spherical triangle is the angle
the Earth.
as seen from the center of the
unit sphere (in this case Figure
the center3:
of The
the Earth).
earth is 7371
km, and angle
"a" (from our spherical
triangle)
propagation distance
between
a transmitting
satellite
and a
We know the sides b and c and the angle A; we want to
is 35.1°.
determine side a. Thus, we will use the law of cosines for sides
Using the law of cosines-for-sides formula for plane trianbyour
theknowns
satellite
location,
location,
and
the center
the3,Earth.
given last month, but with
and unknowns
placed
gles (from last
month) and
the dimensions
fromof
Figure
appropriately in the equation:
d2 = (H + R E)2 + (R E)2 - 2((H + R E)(R E) cos a
cos a = cos b cos c + sin b sin c cos A
= 73712 + 63712 - 2(7371)(6371)(.818)
Where: a, b, c and A are as defined above.
= 54,331,641 + 40,589,641 - 76,827,609 = 18,093,673
Now, let's plug in some locations:
d (the propagation distance) is the square root of
Let the SVP be at longitude 200°/latitude 45° and the re18,093,673 = 4254 km
ceiver at longitude 230°/latitude 20°.
The spherical cosines-for-sides equation is now:
cos a = cos(90 - 45) cos(90 - 20) + sin(90 - 45) sin(90Let the transmission frequency be 2 GHz. The propagation
mode to and from satellites is line of sight, so the loss formula is:
20) cos(230 - 200)
L = 32.44 + 20 log(d) + 20 log(F)
= cos(45) cos(70) + sin(45) sin(70) cos(30)
= .707 x .342 + .707 x .940 x .866 = .242 + .576
Where: L is the link loss in dB
= .818
d is the link distance in km
Side a then equals the arc cos of .818 = 35.1°
F is the frequency in MHz.
L = 32.44 + 72.60 + 66.02 = 171 dB

d

H

a

R

Center
of Earth

THE PROPAGATION DISTANCE

The propagation distance between the transmitter (in
the satellite) and the receiver can now be determined from
the plane triangle shown in Figure 3. Let the satellite be at
1000 km altitude; the radius of the Earth is 6371 km. Then
the distance between the satellite and the center of the

WHAT'S NEXT
Next month, we will continue our discussion of space
EW with consideration of satellite Earth traces. For your
dave@lynxpub.com. a

The Journal of Electronic Defense | August 2016

R

Location

```

# JED - August 2016

The View From Here
Conferences Calendar
Courses Calendar
From the President
The Monitor
World Report
Cyber Blitz: US Army Gains New Insight for EW/Cyber Operational Integration
Technology Survey: Solid State Power Amplifiers for EW, Radar and Communications Applications
EW 101
Threat Monitor
AOC Election
JED Quick Look
JED - August 2016 - cover1
JED - August 2016 - cover2
JED - August 2016 - 3
JED - August 2016 - 4
JED - August 2016 - 5
JED - August 2016 - The View From Here
JED - August 2016 - 7
JED - August 2016 - insert1
JED - August 2016 - insert2
JED - August 2016 - Conferences Calendar
JED - August 2016 - 9
JED - August 2016 - Courses Calendar
JED - August 2016 - 11
JED - August 2016 - From the President
JED - August 2016 - 13
JED - August 2016 - 14
JED - August 2016 - The Monitor
JED - August 2016 - 16
JED - August 2016 - 17
JED - August 2016 - 18
JED - August 2016 - 19
JED - August 2016 - 20
JED - August 2016 - 21
JED - August 2016 - World Report
JED - August 2016 - 23
JED - August 2016 - Cyber Blitz: US Army Gains New Insight for EW/Cyber Operational Integration
JED - August 2016 - 25
JED - August 2016 - 26
JED - August 2016 - 27
JED - August 2016 - 28
JED - August 2016 - 29
JED - August 2016 - 30
JED - August 2016 - 31
JED - August 2016 - 32
JED - August 2016 - 33
JED - August 2016 - 34
JED - August 2016 - Technology Survey: Solid State Power Amplifiers for EW, Radar and Communications Applications
JED - August 2016 - 36
JED - August 2016 - 37
JED - August 2016 - 38
JED - August 2016 - 39
JED - August 2016 - 40
JED - August 2016 - 41
JED - August 2016 - EW 101
JED - August 2016 - 43
JED - August 2016 - Threat Monitor
JED - August 2016 - 45
JED - August 2016 - 46
JED - August 2016 - AOC Election
JED - August 2016 - 48
JED - August 2016 - Index of Advertisers
JED - August 2016 - JED Quick Look
JED - August 2016 - cover3
JED - August 2016 - cover4
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