# JED - June 2016 - 47

```E W101
p (min)

h (km)

a (km)

90

281

6652

105

1001

7372

120

1688

8059

135

2346

8717

150

2980

9351

165

3594

9965

180

4189

10560

195

4768

11139

5332

11703

5883

12254

240

6422

12793

255

6949

13320

270

7466

13837

285

7974

14345

300

8473

14844
15335

315

8964

330

9447

15818

345

9923

16294

360

10392

16763

375

10854

17225

390

11311

17682

405

11761

18132
18577

420

12206

435

12646

19017

450

13081

19452

465

13510

19881

480

13936

20307

495

14357

20728

510

14773

21144

525

15186

21557

540

15595

21966

Altitude of Satellite (km)

Table 2: Altitude and Semimajor Axis of Circular Orbits vs.
Satellite Period

RELATIONSHIP BETWEEN THE SIZE
OF AN ORBIT AND ITS PERIOD
Kepler's third law is stated as follows:
a3 = CP 2
where: a is the semi-major axis of the ellipse of
the orbit
C is a constant
P is the period of the orbit.
Note that the semi-major axis of the ellipse is the
radius of a circular orbit. To simplify our lives, we
will determine the constant C by considering a circular (i.e., constant altitude) Earth satellite orbit.
Let's look at a satellite that circles the Earth every hour and a half and has an altitude of 281.4 km
or a radius (from the center of the Earth) of 6,653
km. The constant is:
C = a3 / P 2
For our 281.4-km-high satellite, C is calculated
as:
6653 km3 / 90 min2 = 36,355,285 km3 per min2
This constant value can be used to determine
the relationship between the semi-major axis of
any Earth satellite and its orbital period. You can
subtract the Earth's radius of 6,371 km to find the
average altitude of the satellite. For simplicity in
this EW101 column series, we will use circular orbit
(i.e., constant altitude) satellites in our examples
and problems.
Table 2 shows the altitude of a circular Earth
satellite vs. the period of its orbit for satellites with
periods of 1 .5 hours to 9 hours. Figure 3 is a graph
of the altitude of a circular satellite vs. its period. Go
straight up from the period (300 minutes in this case)
to the line and then left to the altitude (8,475 km).
Another orbit of particular interest is for the
stationary satellite that hovers over a single point
on the Earth's surface. Because the Earth rotates
366 times per year (to face the sun 365 times) the
period of the satellite is 23 hours, 56 minutes and
4.09 seconds (about 1436 minutes). From
Kepler's 3rd law, the radius of this orbit is
42,165.7 km and its altitude is 35,795 km. An
additional orbit of interest is that of each of
the GPS satellites. They complete two orbits
per day. The radii of their 12 hour orbits are
26,612 km (i.e., 20, 241 km altitude).

WHAT'S NEXT

Period of Satellite (minutes)

Figure 3: The altitude of a circular satellite is a function of its orbital period.
Figure 3: The altitude of a circular satellite is a function
of its orbital period.

Next month, we will continue our discussion of orbits with a quick review of spherical trigonometry. Then, we will be prepared
to get into the material we really want to
cover, which is the relationships between
suggestions, Dave Adamy can be reached at
dave@lynxpub.com. a

The Journal of Electronic Defense | June 2016

210
225

centricity of the orbit. This defines the
orbit's shape. It is a number between 0
and 1. The distance from the center of
the Earth at the satellite's closest approach (the perigee) is a (1-e), and its
minimum altitude is less than this by
the radius of the Earth. The maximum
distance from the satellite to the center
of the Earth (the apogee) is a(1+e), and
its maxim altitude is this distance less
the radius of the Earth. For a circular
orbit, the eccentricity is zero, and the
altitude is constant.
The next four elements of the ephemeris are illustrated in Figure 2. All of
the angles described are angles as seen
from the center of the Earth.
i is the inclination of the orbit relative to the equatorial plane. This determines the maximum latitude covered by
the orbit. An equatorial satellite has 0°
inclination, and a polar orbit has 90°
inclination.
n is the right ascension of the ascending node. This is the longitude of
the point at which the satellite crosses
the equator going north - relative to
the direction of the vernal equinox.
The vernal equinox direction is along
the line of intersection of the plane of
the Earth's orbit around the sun and the
equatorial plane.
w is the argument of perigee. This is
the angle between the ascending node
and the perigee of the satellite's orbit
(in the orbital plane).
v is the true anomaly. This is the
angle between the perigee and the satellite location along its orbital path.

47

```

# JED - June 2016

The View From Here
Conferences Calendar
Courses Calendar
From the President
The Monitor
Washington Report
World Report
Technology Survey: Communications and IED Jammers
SIGINT History
EW 101
Report from the 45th Annual Collaborative EW Symposium
AOC News
2016 AOC International Election Guide
JED Quick Look
JED - June 2016 - cover1
JED - June 2016 - cover2
JED - June 2016 - 3
JED - June 2016 - 4
JED - June 2016 - 5
JED - June 2016 - The View From Here
JED - June 2016 - 7
JED - June 2016 - Conferences Calendar
JED - June 2016 - 9
JED - June 2016 - Courses Calendar
JED - June 2016 - 11
JED - June 2016 - From the President
JED - June 2016 - 13
JED - June 2016 - 14
JED - June 2016 - The Monitor
JED - June 2016 - 16
JED - June 2016 - 17
JED - June 2016 - 18
JED - June 2016 - 19
JED - June 2016 - 20
JED - June 2016 - 21
JED - June 2016 - Washington Report
JED - June 2016 - 23
JED - June 2016 - World Report
JED - June 2016 - 25
JED - June 2016 - Advances in COMINT/ DF Systems
JED - June 2016 - 27
JED - June 2016 - 28
JED - June 2016 - 29
JED - June 2016 - 30
JED - June 2016 - 31
JED - June 2016 - 32
JED - June 2016 - Technology Survey: Communications and IED Jammers
JED - June 2016 - 34
JED - June 2016 - 35
JED - June 2016 - 36
JED - June 2016 - 37
JED - June 2016 - 38
JED - June 2016 - 39
JED - June 2016 - 40
JED - June 2016 - 41
JED - June 2016 - 42
JED - June 2016 - SIGINT History
JED - June 2016 - 44
JED - June 2016 - 45
JED - June 2016 - EW 101
JED - June 2016 - 47
JED - June 2016 - Report from the 45th Annual Collaborative EW Symposium
JED - June 2016 - 49
JED - June 2016 - AOC News
JED - June 2016 - 2016 AOC International Election Guide
JED - June 2016 - 52
JED - June 2016 - 53
JED - June 2016 - 54
JED - June 2016 - 55
JED - June 2016 - 56
JED - June 2016 - Index of Advertisers
JED - June 2016 - JED Quick Look
JED - June 2016 - cover3
JED - June 2016 - cover4
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