# JED - June 2017 - 43

```EW 101

Space EW - Part 13

Intercept from Space Using
a Directional Antenna

HORIZON PLOT ON THE EARTH

North
Pole

Satellite

Difference of
longitude to
edge point

Rotation of
edge point
Edge point of
horizon trace

SVP

Center of
Earth

D
Latitude
of SVP
Latitude
of horizon
edge point

f

e
d
Equator

E

In the January 2017 "EW101" column, we develF
oped the formula for the geocentric angle from the
sub-vehicle point (SVP) to the horizon. Now we will
Fig. 2: The location
a point
on of
thepoint
horizon
relative
to relative
the satellite
Fig. 2: of
The
location
on the
horizon
to thesub-vehicle
satellite
show how to generate an Earth-surface contour of the
point (SVP) issub-vehicle
shown in this
spherical
point
(SVP) istriangle.
shown in this spherical triangle.
horizon. For the rest of this column, we will do examNow consider the spherical triangle of Figure 2, formed by
ples for a 300-km-high satellite with its sub-vehicle
the sub-vehicle point, the North Pole, and the edge point of
point at 100° East longitude and 30° North latitude.
the horizon trace on the Earth's surface.
Considering the plane triangle in Figure 1 this month,
angle C = acos(side a/side c)
* Side d is the same as angle C in Figure 1 (i.e., the geocentric
where a is the radius of the Earth and c is the altitude of the
angle from the SVP to the edge of the horizon).
satellite plus the radius of the Earth.
* Side e is 90° - the latitude of the SVP (i.e., 60°)
Thus, the geocentric angle (C) to the horizon from the SVP
* Side f is 90° - the latitude of the edge point of the horizon
is:
* Angle F is assigned as we are calculating the horizon edge
C = arcos [RE/ (h + RE)].
points. It will be chosen every few degrees from 0° to 360°
For a 300-km-high satellite, C would be acos[6371/6671] = 17.2°
* Angle D is the difference in longitude between the SVP and
the calculated edge point of the horizon.
You can calculate a table of the latitude and longiElevation of local
tude points for the edge of the horizon with the resohorizon from nadir
A
Satellite
lution you like (the computer won't mind generating
and plotting a lot of points).
SVP
As an example, we will manually calculate only
c
H
Edge of
one
point for our chosen satellite. Let's choose the
horizon
B
horizon edge point 45° East of North. This makes
angle F = 45°
b
side e is 60° and side d is angle C from Figure 1
RE
a
Lo
(i.e., 17.2°).
ca
90°
l
From the law of cosines for sides for spherical
ho
Geocentric
RE
riz
triangles:
on
angle to
Cos f = cos e *cos d + sin e *sin d * cos F
horizon
So: f = acos[cos e * cos d + sin e * sin d *cos F]
C
Center
Let's choose the edge point 45° East of North. This
of Earth
makes angle F = 45°
Side f is then: acos[cos60º * cos 17.2° + sin 60º *
1: The
geocentric
the sub-vehicle
point (SVP)
the is
Fig. Fig.
1: The
geocentric
angleangle
from from
the sub-vehicle
point (SVP)
to the to
horizon
sin 17.2° * cos 45º]
horizonfrom
is calculated
this plane triangle.
calculated
this planefrom
triangle.

The Journal of Electronic Defense | June 2017

L

ast month, we dealt with intercept from a
satellite with a non-directional antenna.
Now we are adding a directional antenna.
We will show how to define the outline
of the horizon from the satellite in terms
of the latitude and longitude of points
around the horizon. Then, we will calculate the
antenna look-angles to any point on the Earth's surface that can be seen by the satellite.

Geocentric angle
to horizon
edge point

43

```

# 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
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