ORBITAL ASSESMENT FOR THE OPERATION OF AN ELECTRONICALLY
STEERABLE PHASED-ARRAY MODULE (ESPAM) ON A SOLAR POWER
SATELLITE (SPS)
Cadet Matthew S. Wilcoxen
United States Air Force Academy, Department of Astronautics
Colorado Springs, Colorado
ABSTRACT
Transmitting wireless power at high levels of efficiency is essential to the feasibility of the SPS
Program. Existing SPS designs fulfill this constraint by means of modern microwave technology
that can take the D.C. power produced by the massive solar array, convert it to microwave
energy, and then beam it to a rectenna on Earth. While the microwave energy is being received, a
separate system can then convert the energy back into D.C. power. Such a process requires a
high level of accuracy for political and efficiency reasons. This level of accuracy can be attained
through the integration of several systems. The first system combines a microwave magnetron
with a ferrite circulator to deliver the necessary gain while remaining phase locked. When this
system is then incorporated with a slotted waveguide array, you have an electronically steerable
phased array module, also known as an electronically steerable phased-array module (ESPAM),
to transmit the microwave energy in a focused beam to Earth. While the use of an ESPAM has
proven successful in ground research, the problems that would be encountered in space require
stricter guidelines to be met in order for the system to remain practical. This study was
conducted to assess what orbit altitude would best suit the overall objective of a SPS program
using an ESPAM to direct the energy to Earth.
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Nomenclature
a
Semi Major Axis
km
m/CdA
Ballistic Coefficient
kg/m2
BW required
Required Beamwidth
deg
Change in Velocity
m/s
ΔV
e
Eccentricity
--
Receiving Array Diameter
km
H
Altitude
km
ί
Inclination
deg
Dreciever
μ
Gravitational Parameter
P
Orbital Period
years
ρ
Atmospheric Density
kg/m3
v
Orbital Velocity
km3/sec2
km/s
INTRODUCTION
Background
When the SPS program was first presented to Congress in 1976 as a solution to the
energy crisis, it faced enormous technical and feasibility requirements that Congress deemed
insurmountable in order for such a system to remain economically practical. The rationale for
such a program back then still remains the same today: man will eventually be forced to find an
alternative energy source when fossil fuels become depleted and other sources such as coal
would create too great of an environmental threat in order to produce the level of energy needed.
The amount of energy consumption across the world has more than quadrupled since the 1950s
2
with nearly 90% of that demand being met by the combustion of fossil fuels1 . Increasing energy
consumption, specifically by those countries with high energy demand and those still developing,
will be obligated to search for additional sources that meet consumer specifications of clean,
renewable and reliable standards. These factors have stimulated growth in alternative energy
technology, including the solar power industry and the development of the SPS.
Evaluation of the SPS system shows that its ability to take the inexhaustible, unobstructed energy
from the sun, convert it into a usable source, and then redirect it to Earth makes it a marketable
application as an energy source of the future when comparing technical, economic,
environmental, and political issues and limitations.
The most widespread method of redirecting the DC power produced by the solar arrays is to
convert the energy into radio frequency (RF) energy. This paper’s analysis uses a MDA with a
microwave tube as the source of the RF because of its ability to operate at efficiency levels
approaching 80% and its ability to operate at nearly twice the temperature of other RF sources2.
When this MDA is configured with a simple slotted waveguide array, the RF frequency then
becomes steerable.
Objectives
Altitude Determination
The objective of the altitude determination study was to investigate how varying altitudes would
affect the ESPAM operating requirements. Looking at the results of that study, further objectives
were set to determining factors such as ΔV to remain at varying altitude, ΔV to get to established
3
altitudes and affects of orbital period. While this study may not determine one orbital altitude as
the primary preferred altitude, it will help in determining which altitudes are impractical and
which altitudes can serve as the better option for accomplishing certain SPS goals.
Results And Discussion
Altitude Determination
Determining an operating altitude is needed in order to establish the design of the SPS. A SPS
operation at a higher altitude will need a greater number of ESPAM units in order to get a
required beamwidth than a lower orbiting SPS would need in order to fill a receiving ground
station array. A higher orbit would also put the SPS in the shadow of Earth for decreased extent
of time. For the purpose of this study, it is assumed that an earth-centered orbit is being used
rather than a sun-centered orbit. Using
D

BW required  2 tan 1  reciever 
 2H 
(1)
while keeping Dreciever constant, the relationship between BW required and H is shown in figure 1.
4
4
Beamwidth (deg)
3.5
3
2.5
2
1.5
1
0.5
0
0
5000
10000
15000
20000 25000
30000 35000
40000
Orbital Altitude (km)
Figure 1. Beamwidth to fill a 10 km Receiving Array
It was expected that as the orbital altitude increases, the beamwidth would decrease, but from
this graph, we can see that at around an H of 5000 km, the change in BW required becomes minimal
over a significant increase in H. It is important to note that figure 1 only represents when the
SPS is perpendicular to the receiving array. If it is not directly overhead, the beam becomes
distorted as it hits the ground, changing the size of the receiving array if the same amount if
power needed to be collected
Determining the amount of ΔV needed on a yearly basis in order to maintain altitude can help us
to determine a minimum H below which point station keeping would become too costly and
rigorous. Using
C A
V    D   rv / P
 m 
(2).
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Where the ballistic coefficient is assumed to be 50 kg/m2 , we find the results presented in figure
2.
4000
Delta V ((m/s)/yr)
3500
3000
2500
2000
1500
1000
500
0
0
200
400
600
800
1000
1200
1400
Orbit Altitude (km)
.
Figure 2. Delta V required for orbital maintenance.
From this data, we can conclude that any orbit below 400 km would require so much station
keeping that it would be impracticable. At orbits about 1000 km, the ΔV requirement is nearly
zero.
Station keeping ΔV is not the only requirement though. ΔV to first get the satellite into orbit
must also be taken into consideration. This ΔV requirement can be seen by using
Vtotal  Vorbit  Vlaunch
(3)
where
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Vlaunch  Vtransfer
earth
 Vearth  Vlosses
Vlosses  1000m / s
(4)
Vearth  465.1m / s
and
Vorbit  Vorbit  Vtransfer
Vtransfer
Vorbit 
orbit
orbit
  
   transfer
 2
R
orbit


(5)

Rorbit
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Delta V (km/s)
12
10
8
6
4
2
0
0
5000
10000
15000
20000
25000
30000
35000
40000
orbital altitude (km)
Figure 3. ΔV required to Establish Orbit
From this data we can see that the increase in the amount ΔV needed between launching to a low
orbit as compared to a high orbit is nearly 50% greater.
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Orbital period will not only affect the SPS’s ability to track a ground station, but also the extent
of time that a SPS would be within sight of the sun in order to collect energy. The altitude
directly affects the orbital period and can be calculated with
P  2
a3
(6).

Using the period, we can calculate the angular rate as the satellite moves in orbit. When we
compare this to the angular rate of Earth, we can determine a reasonable number at which a SPS
can track a ground station and steer the RF towards that point even when the receiving array is
difference in rotational speed
(deg/min)
not directly below. This data is represented in figure 4 below.
4
3.5
3
2.5
2
1.5
1
0.5
0
0
5000
10000 15000 20000 25000 30000 35000 40000
Orbital Altitude (km)
Figure 4. Relative angular velocity of a SPS to Earth for Varying Altitudes
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While we may not know the rotational capabilities of a SPS in tracking a ground station, we can
assume that in order to minimize the amount if ESPAM steering needed, which would increase
efficiency, the satellite itself will need to perform some orbital rotations itself. To minimize the
power needed to do so, a higher altitude is required.
The amount of time the SPS will be in the shadow of earth and therefore cannot collect solar
energy can be calculated by
TE 
2
P
360 deg
(7).
This TE measurement only give the eclipse time per orbit though, so to find the total amount of
time per day, the number must be multiplied by the number of revolutions in one day. This data
is shown in figure 5. To further demonstrate these affects, the percent of time that a satellite
would be available to collect energy for a given orbit is shown in figure 6.
Eclipse Time (min/day)
800
700
600
500
400
300
200
100
0
0
5000
10000
15000
20000
25000
30000
Orbital Altitude (km)
Figure 5. Maximum eclipse time per day
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35000
40000
% of daily availability
100
90
80
70
60
50
40
0
5000
10000 15000 20000 25000
30000 35000 40000
Orbital Altitude (km)
Figure 6. Percent availability to solar energy
With a MDA operating at a frequency of 2.45 Hz, the atmospheric attenuation can be calculated
with
Sr 
PA
Pr
 t2 t2 (1  La )
Ar R 
(8).
If the assumption is made that the power transmitted needs to be at least that which could
normally be collected on the ground without the use of a SPS, we can work backwards to
determine the amount of power the SPS needs to produce. With current ground solar arrays
having efficiencies around 30% and being able to collect sunlight for half the day at a rate of
1000 W/m2we find that the SPS must produce 150 W/m2 to be economically viable. Using
equation 7, the total amount of power that must be produced on the ground is 16.83 GW. If we
now take into account that the conversion is currently 70% efficient and the losses due to the
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atmosphere are minimal, the total power transmitted must be 24.04 GW. Assuming each
ESPAM in the transmitting array produces the same amount of power, we can now determine the
Power per ESPAM (kW)
number of ESPAMs needed to produce the necessary amount of power.3
100
90
80
70
60
50
40
30
20
10
0
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
2,000,000
2,200,000
Total number of ESPAM elements
Figure 7. ESPAM elements needed to produce needed power
From the above data collection, a comparison of three orbits was done as shown in table 1.
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Table 1. Comparison of three orbits for possible SPS design
Orbit 1
Orbit 2
Orbit altitude (km)
300
1000
1.9096825
0.572953
Beamwidth (deg)
Number of ESPAM
~25 (5 x 5)
225 (15 x 15)
units needed for
beamwidth
3.72703869
3.17470155
Angular tracking rate
needed (deg/min)
8.632195
9.005282
ΔV to establish orbit
(km/s)
90.52
105.12
Orbital Period (min)
582.09
478.57
Maximum eclipse Time
per day (min)
747
0.151
ΔV for station keeping
(m/s/yr)
Power per ESPAM for
962 MW
107 MW
required power
production on the
ground
Orbit 3
35,768
0.0160187
~284089 (533 x 533)
0.0008454
12.45286
1 day
69.4
~0
84.7 kW
Orbit 1 was picked as a low Earth orbit, orbit 2 as a medium range orbit that would not require
the advancement of heavy lift launch capability (HLLC) technology, and orbit 3 as a
geostationary orbit that would require HLLC.
Recommendations
Three orbital design recommendations were made as a result of the orbital altitude investigation:

While a low Earth orbit would reduce the number of ESPAM units needed and reduce the
ΔV needed to establish orbit, the amount of ΔV needed for station keeping, the decrease
in amount of time available to collect solar energy, and the limitations of a SPS’s ability
to track and send RF to a ground station from such an altitude make such an orbit
impractical for commercial use. An orbit below 400 km should only be used for research
and experimentation of the ESPAM design and not used for full scale production
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
A geosynchronous orbit should be utilized as the first placement for a SPS. Such an orbit
would require minimal station keeping, decreases tracking capabilities, and make the
collection of solar energy nearly continuous.

Heavy Lift Launch Capability is a necessity in order to get a system as large as a SPS into
a geosynchronous orbit. Technological advancement in this area must take place in
parallel with research in the SPS program.
Acknowledgements
The author would like to thank Lt Col Michael Hatfield, Astronautics Professor. Only through
his work was I able to focus this paper enough on one aspect of the SPS program for the purpose
of this paper. I was able to use the process he used and the data he collected to verify my own
data. He has worked closely with me to ensure I’m headed in the right direction throughout my
future study of the SPS program.
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REFERENCES
1. Glaser, P.E., F.P. Davidson, K.I. Csigi, Solar Power Satellites, 1st Ed, 1998, Praxis
Publishing Ltd.
2. Brown, W.C., Solar Power System (SPS) Magnetron Tube Assessment Study, Raytheon
Company, July 1988, Prepared for NASA under contract NASA 8-33157.
3. Hatfield, M.C. Characterization and Optimization of the Magnetron Directional
Amplifier, Doctoral Thesis. University of Alaska Fairbanks: Fairbanks, 1999.
General References
Wertz, James R. and Wiley J Larson (editors). Space Mission Analysis and Design, 3rd
Ed, 1999, Microcosm Press.
Sellers, J.J., Understanding Space: An Introduction to Astronautics, 1st Ed (Revised),
1994, McGraw-Hill, Inc.
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