Note: Descriptions are shown in the official language in which they were submitted.
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$ FIXED SATELLITE CONSTELLATION SYSTEM EMPLOYING
NON-GEOSTATIONARY SATELLITES IN
SUB-GEOSYNCHRONOUS ELLIPTICAL ORBITS
WITH COI~iON GROUND TRACKS
Cross-Referenced to Related Applications
This applications claims benefit of U.S. Provisional
application no. 60/153,289 filed September 10, 1999
Background
Satellite communications systems often require that
a station on the ground communicate with a satellite.
The satellite tracking is simplified when the satellite
appears to be maintained stationary relative to the
Earth. Geosynchronous ("geo") satellites have this
characteristic. However, geo-satellites require high
altitude orbits. These high altitude orbits require
large payloads and launches, and also can have relatively
long propagation delays during communication.
Summary
The present disclosure describes an array of non-
geostationary satellites in sub-geosynchronous, inclined
elliptical orbits. Each of the satellites communicates
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with a point on the earth. At least a plurality of the
satellites is in an elliptical orbit with the earth at
one focus of the ellipse.
At and near their apogee points, the satellites move
slowly relative to the Earth. These satellites appear
virtually geostationary to users within at least part of
the desired coverage area.
The disclosed embodiments use three sub-
constellations, each with 5 satellites. Three total sub-
constellations are used. Two of these sub-constellations
are used for Northern Hemisphere operation. A third
constellation is for Southern Hemisphere operation. The
satellites are active over only part of their total time
of their orbits. The active time of the orbit is when
the satellites are closest to their apogees.
These active times can occur when the satellites are
at latitudes above 45°. These satellites are hence seen
at high elevations over much of their primary service
areas.
This system is also effectively transparent to the
geostationary fixed satellite services and can be
separated from the geostationary arc preferably by at
least 40° at all times within the service area of the
system.
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Brief Description of the Drawings
Fig. 1 shows a basic layout of the multiple
elliptical orbits of the present invention;
Fig. 1A shows a graphical depiction of the
satellite's angular motion along its orbit as a function
of the semi-major axis of the elliptical orbit.
Figs. 2A and 2B show a block diagram of the
satellite communication equipment used according to the
present invention;
Fig. 2C shows a flowchart of operation of the
satellites of the present invention;
Fig. 3 shows the characteristics of a basic ellipse;
Figs. 4A-4F show characteristics of the three-
satellite orbit of the present invention;
Fig. 4G shows characteristics of this orbit which
prevent interference with geosynchronous satellites in an
inclined orbit;
Fig. 4H shows characteristics of this orbit which
prevent interference with geosynchronous satellites in an
equatorial orbit;
Figs. SA-5E show characteristics of the five
satellite orbit of the present invention;
Fig. 6 shows an overall view of the ten satellite
orbit of the present invention;
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Figs. 7A-7G show the positions of the satellites of
the ten satellite embodiment within their repeating
ground tracks;
Fig. 8 shows the operating elevation angles for the
ten satellite orbit, and their angular isolation from geo
satellites; and
Fig. 9 shows ground tracks of the preferred orbits.
Description of the Preferred Embodiments
The disclosed system defines a communication system
including ground communication equipment and a special
constellation of satellites in elliptical orbits at lower
altitudes than those necessary for geosynchronous, which
simulate the characteristics of a geosynchronous orbit
from the viewpoint of the ground communication equipment
on the earth. The inventors recognized that satellites
which orbit in certain elliptical orbits spend most of
their time near the apogees of their orbits: the time
when they are most distant from the earth. These
satellites spend only a minority of their time near their
perigee. For example, an elliptical satellite in a 12-
hour orbit spends eight of those hours near its apogee.
By appropriately choosing characteristics of the
satellite orbit, the satellite can be made to orbit,
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during that time, at a velocity that approximates the
rotational velocity of the earth. The disclosed system
defines a communication system using a constellation of
satellites chosen and operating such that a desired point
on the earth always tracks and communicates with a
satellite at or near apogee.
Another important feature of the disclosed system is
the recognition of how this mode of operation of the
satellite changes its power characteristics.
Geosynchronous satellites are used virtually 1000 of the
time (except when in eclipse) and hence their power
supplies must be capable of full-time powering. This
means, for example, if the satellite requires 5 Kw to
operate, then the power supply and solar cells must be
capable of supplying a continuous 5 Kw of power. The
satellites of the disclosed system, however, are not used
1000 of the time. During the perigee portions of the
satellite orbit, the satellites are typically not using
most of their transmit and receive capability and hence,
the inventors recognized, do not use a large part of
their power capability.
The inventors of the disclosed system recognized
this feature of the satellites, and realized that the
satellites could be storing the power that is being
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produced during this time of non-use. Therefore, the
inventors realized that the size of the power supply
could be reduced by a factor of the percentage of time
that the satellite is not used.
The power sources can be any known means, including
solar cells, nuclear reactors, or the like. If the
satellite is used half the time, then the power source
need only be sized to provide half the power. At times
when the satellite is not being used, the power source
provides power to a battery storage cell, which holds the
power in reserve for times when the satellite is being
used.
Like geo systems, the satellite of the disclosed
system is virtually continuously in the same location.
Unlike geo-based systems, however, the ground
communication equipment of the disclosed system does not
always communicate with the same satellite. The
satellites move slightly relative to the earth, i.e. they
are not always precisely at the same point in their
apogees. One important advantage of the disclosed system
is that the one satellite at apogee later moves to
perigee, and still later to apogees at other locations
overlying other continents and areas. Hence, that same
satellite can later communicate with those other areas.
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Therefore, this system allows a store-and-dump type
system. The information can be stored on board the
satellite and later re-transmitted when the satellite
overlies those other areas. This system also allows all
the satellites in the array to communicate with the other
satellites in the constellation, through intersatellite
links. This feature is desirable for real time
communications .
This system has a number of other distinct
advantages. Importantly, the system operation allows
selecting specific geographic locations to be
preferentially covered; for example, continents can be
followed by the constellation to the exclusion of other
areas, e.g. ocean areas between the continents. The
communication equipment on the continent always
communicates with one satellite at apogee, although not
always the same satellite. From the point of view of the
ground station, the satellite appears to hover over the
ground.
This satellite system operates virtually like a
geosynchronous satellite system. Importantly, these
satellites according to the disclosed system orbit at
about half the altitude of the geo systems. A geo orbit
orbits at 36,000 miles altitude: the virtual geo
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satellite orbits at average altitudes of 16-18,000 miles.
Also, geo satellites require "apogee motors", to boost
them from their original orbits into the final geo orbit.
These apogee motors can double the weight of the
satellite.
This yields a communications system which costs less
dollars per launch capability because of the reduced
weight to boost and less size. Also, since the geo
satellites orbit at a higher altitude, they operate at a
higher power, and use a larger illuminating antenna, all
other conditions on the ground being equal. These
satellites also have a much larger overall size. This
size of the satellites increases as the square of the
distance. Therefore, the geo satellite needs to be at
least twice as large and twice as powerful as a low
altitude satellite. The power supply conservation
techniques of the disclosed system allow the satellite to
be made even smaller.
The system also provides satellites with very high
elevation angles. Maximizing the elevation angle
prevents interference with existing satellites such as
true geosynchronous satellites.
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This is another feature of the disclosed system
which allows these satellites to operate in ways which
avoid any possibility of interference with the geo band.
Another objective and important feature of the
disclosed system is its ability to re-use satellite
communication channels. Regulatory agencies such as the
FCC allocate frequency bands by allocating a specific
frequency band for a specific purpose. The geo
satellites, for example, receive an assignment of a
frequency band. Thereafter, the regulatory agency will
consider that other satellites located in the same
orbital position can not use this frequency because of
possibility of interference. Hence, frequencies in
adjacent bands which might interfere with that assigned
band will not be allocated for new satellite use. With
the disclosed system, there is a large angular separation
between the geo-sats and those covered by the invention.
Thus, the same frequencies ca be allocated anew. Another
feature of the disclosed system is the location of the
earth stations and satellites in a way which prevents
interference with the geo bands. Specifically, the
disclosed system defines embodiments using both inclined
orbits and non-inclined (equatorial) orbits. The
inclined orbit embodiment of the disclosed system only
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communicates with the ground stations when a line drawn
between the ground station and current position of the
satellite will not intersect any point within x° of the
ring of geosynchronous satellites, where x is the
required separation between the communication for geo
satellites and the communication for the satellites of
the disclosed system. During other times, the equatorial
component of the communication is shut off. The
satellite only communicates when it is near apogee.
During those times, the rotational velocity of the
satellite approximates the rotational velocity of the
earth, and hence the satellite tends to hang overhead
relative to the earth.
For non-inclined (equatorial) orbits, the ground
stations are placed in a position such that the
communication does not intersect the ring of equatorial
orbits, by ensuring that satellite apogees are at lower
altitidues than apogees of geostationary satellites.
The system is controlled by on-board processor 280,
which determines the position in the orbit and the
steering of the antenna from various parameters.
Processor 280 carries out the flowchart shown in Figure
2a which will be described herein.
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The overall system is powered by power supply 290
which supplies power to all of the various components and
circuitry which require such power. Power supply 290
includes a source of power, here shown as a solar array
292, and an energy storage element here shown as a
battery array 294. Importantly, according to the
disclosed system, the solar array 292 is sized to provide
only some amount of power less than that required to
power the satellite communication. The amount by which
the solar array can be less is called herein the power
ratio of the device. The power ratio depends on the kind
of orbit that the satellite will have, and how long the
satellite will be transmitting during each elliptical
orbit. The preferred power ratio is 0.5: this will
power a satellite which is communicating half the time,
and the other half the transmitter and receiver on board
the satellite is off and the solar array is providing
power to charge battery 294.
The flowchart of operation is shown in Figure 2a.
Step 350 represents controlling the antenna. This
requires that the processor keep track of the satellite's
position in the orbit. Step 352 determines if the
satellite is in a position in its orbit where it is
active (transmitting and/or receiving). If so, flow
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passes to step 354 where power is drawn from power supply
and the battery. If the satellite is not powered, then
power is used to charge the battery at step 356.
The system also allows selective expansion of the
communications coverage by adding additional satellites
into additional elliptical orbits.
The virtual geo satellite system of the disclosed
system also enables complete communications coverage of
the earth without requiring a ground network. The same
satellite services all different portions of the earth at
different times of day. The coverage of the earth
repeats over a 24 hour period. A preferred embodiment
receives information relayed from the ground, relays it
to the earth area below it, then stores the information,
and later reads back the stored information to re-
transmit that same information to other areas of the
earth. The system of the disclosed system increases the
satellite coverage at high density geographic locations
using fewer satellites than was possible with previous
constellations by fixing the satellite apogee passages
over given geographic regions defined by both longitude
and latitude.
Integral values for mean motion of the satellites in
the array ensures that the ground track repeats on a
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daily basis. The ground tracks preferably repeat each
day so that the orbit apogee passes in the same location
relative to the geographic target area. This system
maximizes the time of coverage and elevation angles for
that pass.
Before describing the minimum satellite arrangement
according to the disclosed system, the nomenclature used
herein to describe the characteristics of satellite
orbits will be first described. The "mean motion" is a
value indicating the number of complete revolutions per
day that a satellite makes. If this number is an
integer, then the number of revolutions each day is
uniform. This means that the ground tracks of the
satellites repeat each day: each ground track for each
day overrides previous tracks from the preceding day.
Mean motion (n) is conventionally defined as the
hours in a day (24) divided by the hours that it takes a
satellite to complete a single orbit. For example, a
satellite that completes an orbit every three hours ("a
3-hour satellite") has a mean motion of 8.
The "elevation angle" S is the angle from the
observer's horizon up to the satellite. A satellite on
the horizon would have 0° elevation while a satellite
directly overhead would have 90° elevation. Geo
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satellites orbit near the equator, and usually have a 20-
30° elevation angle from points in the United States.
The "inclination" I is the angle between the orbital
plane of the satellite and the equatorial plane.
Prograde orbit satellites orbit in the same orbital sense
(clockwise or counter-clockwise) as the earth. For
prograde orbits, inclination lies between 0° and 90°.
Satellites in retrograde orbits rotate in the opposite
orbital sense relative to the earth, so for retrograde
orbits the inclination lies between 90° and 180°.
The "critical inclination" for an elliptical orbit
is the planar inclination that results in zero apsidal
rotation rate. This results in a stable elliptical orbit
whose apogee always stays at the same latitude in the
same hemisphere. Two inclination values satisfy this
condition: 63.435° for prograde orbits or its supplement
116.565° for retrograde orbits.
The "ascending node" is the point on the equator
where the satellite passes from the southern hemisphere
into the northern hemisphere. The right ascension of the
ascending node ("RAAN") is the angle measured eastward in
the plane of the equator from a fixed inertial axis in
space (the vernal equinox) to the ascending node.
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The "argument of perigee" is a value that indicates
the position where orbital perigee occurs. When using
equatorial orbits, 0° argument of perigee is used for all
the orbits. Inclined orbit arrays use non-zero arguments
of perigee. Arguments of perigee between 0° and 180°
locate the position of perigee in the northern hemisphere
and hence concentrate the coverage in the southern
hemisphere. Conversely, arguments of perigee between
180° and 360° locate the perigees to the southern
hemisphere and hence concentrate the coverage on the
northern hemisphere.
An embodiment of the disclosed system evenly spaces
the axes of the ellipses. The spacing between RAANs is
called "S" and calculated by S= 360/n = 120°.
The disclosed system positions the satellite
coverage based on both longitude and latitude of the
desired continental area to be covered by the orbit.
This is done, first, by synchronizing the orbit apogee to
pass over the targeted geographical region for each
successive satellite. We select a suitable value for the
mean anomaly, which is a fictitious angle relating to the
elapsed time in orbit. 360° represents the completion of
the orbit. In this example, the mean anomalies are also
S = 120° apart.
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This "mean anomaly" M relates the amount of time it
takes the satellite to rotate S° around the earth (here
120°). The mean anomaly required for the 12-hour
satellites to rotate to S° is 8 hours; two-thirds of a
S period. This corresponds roughly to the amount of time
the satellite remains in apogee.
Taking the initial satellite near apogee, therefore,
(180° mean anomaly) the next satellite should be backed
up by 240°. This means that after 8 hours that satellite
will be at 180°. Since 180° minus 240° is negative
60°
which equals 300°, this is the value of mean anomaly M
for satellite number 2. This system is used to select
values for the constellation in a similar manner for each
succeeding satellite.
Arrays with more satellites ("higher order arrays")
can also be made using the same rules as those discussed
above. Successively larger numbers of satellites can be
used to provide more coverage, more overlapping coverage,
or smaller integral mean motion values. As the values of
M get larger, the eccentricity of the ellipses become
smaller. This is because the perigee altitude is fixed
at about 500 km to avoid re-entry and decay into the
earth's atmosphere; longer periods have higher apogee
altitudes greater supportable eccentricities.
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Figure 1A shows how the satellite ellipse is
selected to have an angular rate in the plane of the
equator, at apogee, which approximates the angular rate
of the earth. The dotted line in Figure 1A represents
the angular rate of a geo satellite, and hence at this
angular rate a satellite would approximate the angular
speed of the earth. The ellipse is selected to have a
semi-major axis length to set the minimum angular rate of
the satellite at apogee. At apogee, the satellite
angular rate should approximate the rotational velocity
of the earth. In reality, this rotational velocity will
be either a little faster or a little slower than the
earth. At this time, therefore, the satellite appears to
hang relative to the earth.
All elliptical orbits, including those described
herein, are also subject to effects of long-term
perturbations. If effects of these long term
perturbations are not compensated, this could cause
continental coverage to drift with the passage of time.
These perturbation effects are mainly effects from
the Earth's J2 rotation harmonic. The earth is not a
perfect sphere; it actually bulges at the equator. This
causes gravitational effects on objects which orbit the
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earth. For posigrade orbits (i > 90°) the line of nodes
will regress. For inclinations greater than critical
(63.4° > i > 116.6), the line between the perigee and
apogee (line of apsides) will regress; for other
inclinations,
I < 63.4° or I > 116.6, the line of apsides will
progress. Exactly at the critical angles I = 63.4 or I =
116.6, the line of apsides will remain stable a very
desirable feature in maintaining apogee at a certain
latitude. In the equatorial plane, the combined effect
of these two major perturbations cause the apogee to
advance or move counter-clockwise from the sense of
looking down from the celestial north pole. All of the
satellites in a given array design would be affected
similarly. Fortunately, this effect could be compensated
by slightly increasing the period of each satellite in
the array by an amount which offsets the J2 perturbation.
This affects the system by causing a point on the earth
to take a slightly longer time to reach the satellite's
next apogee arrival point. This effect is compensated by
slightly increasing the satellite's period. The advance
of perigee is suppressed by setting the inclination at
one of the critical values.
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A first embodiment of the invention uses N=3
satellites, where N is the total number of satellites,
preferably in the equatorial plane, to cover N - 1 = 2
continents. The rules for spacing and phasing the
satellites will be given in the general form that can be
used later for more complicated constellations or arrays.
The mean motion integer sets the minimum number of
satellites in the array and nc the number of continents
that are followed. Here nc = 2 provides a satellite
period equal to 12 sidereal hours. N (the minimum number
of elliptic satellites in the array) is determined by
using the relationship N = nc + 1. Thus, N = 3. This is
the minimum number of satellites that need to be in the
array; we can also set the number of satellites in the
array N to be any integer greater than n+1.
The apogee passage is synchronized over the targeted
geographical region, for each successive satellite,
moving counterclockwise as viewed from the celestial
North Pole. This is accomplished by selecting a suitable
value for the mean anomaly.
Refinements: Additional features augmenting the
usefulness of the above simpler version include:
1) Inclining the elliptical orbital planes at the
critical inclination angles (63.435 or 116.535°), with
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phasing to maintain a single repeating ground track. The
single repeating ground track for the simplified non-
inclined example above is simply the line of the equator.
2) Taking advantage of the higher apogees in
allowing more direct cross-linking between satellites
than with present low-altitude circular arrays. Usually,
a single cross-link suffices, even when the longitude
difference between end points is 180° (on the opposite
side of the earth).
3) Placement of apogees over a selected latitude and
longitude for optimal coverage of a potential market
area. This is done through proper selection of all the
orbital parameters, with particular attention given to
selection of argument of perigee, c~.
First Embodiment
The orbits of the disclosed system are shown in
Figure 1. The satellite 100 is shown in an elliptical
orbit 102 around the earth. The communication equipment
on the satellite 100 communicates with earth ground
station 104, and also beams the information to earth
ground station 106. Satellite 110 is shown in a separate
independent elliptical orbit communicating with ground
stations 112 and 114 on the earth. Note also that the
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satellite 100 can communicate directly to the satellite
110 via communication link 120.
The preferred characteristics of these orbits are
described in Table I.
TASr~ i
Satellite No. P1 P2 P3
Semi-Major Axis, a 26553.98km 26553.98km26553.98km
=
Inclination, I = 0 deg 0 deg 0 deg
Arg. Perigee, w = 270 deg 270 deg 270 deg
Eccentricity, a 0.51 0.51 0.51
=
Rt. Ascension, RAAN= 0 deg 120 deg 240 deg
Mean Anomaly, MA = 180 deg 300 deg 60 deg
Satellite 100 also includes store and dump hardware
thereon as described herein. This allows the satellite
to obtain program information so that later in its orbit,
when at the position 130, it can send its same
information to ground station 132.
A detailed block diagram of the electronics in the
satellite is shown in Figure 2. This block diagram shows
elements which carry out communication between the ground
station 104, the satellite 100, and the remote user
station 106. The inter-satellite links 120 are shown
from the satellite 100 to the satellite 110.
The video input to be distributed is received as
video input 200, and input to a video coder 202 which
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produces digital coded video information. This digital
coded video is multiplexed with a number of other
channels of video information by video multiplexes 204.
The resultant multiplexed video 206 is modulated and
appropriately coded by element 208 and then up-converted
by transmitter element 210. The up-converted signal is
transmitted in the Ku band, at around 14 GHz, by antenna
212. Antenna 212 is pointed at the satellite 100 and
received by the satellite's receive phased array antenna
214. Antenna 212 is controlled by pointing servos 213.
The received signal is detected by receiver 216,
from which it is input to multiplexes 218. Multiplexes
218 also receives information from the inter-satellite
transponders 240.
The output of multiplexes 218 feeds the direct
transponders 250, which through a power amplifier 252 and
multiplexes 254 feeds beam former 256. Beam former 256
drives a transmit, steerable phased-array antenna 260
which transmits a signal in a current geo frequency band
to antenna 262 in the remote user terminal 106. This
signal preferably uses the same frequency that is used by
current geo satellites. The phased array antenna is
steered by an on-board computer which follows a pre-set
and repeating path, or from the ground. This information
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is received by receiver 264, demodulated at 266, and
decoded at 268 to produce the video output 270.
The satellite includes another input to the
multiplexes from the steerable antenna, via the
intersatellite link 120 and receiver 240. Transmit
information for the the intersatellite link is
multiplexed at 242 and amplified at 246 prior to being
multiplexed.
Output 222 of input multiplexes represents a storage
output. The satellite electronics include the capability
to store one hour of TV program information. The TV
channels typically produce information at the rate of 6
megabytes per second. The channels are typically
digitally multiplexed to produce information on 4-6
channels at a time. Therefore, the disclosed system
preferably uses 22 gigabytes of storage to store over 1
hour of information at about 4.7 megabytes per second.
The information stored will be broadcast over the next
continent.
The storage unit 224, accordingly, is a wide SCSI-2
device capable of receiving 4.7 megabytes per second and
storing 22 GB.
Upon appropriate satellite command, the output of
the storage unit is modulated and up-converted at 226.
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This basic system shown in Fig. 2 can be used in one
of the preferred satellite arrays of the disclosed
system. These arrays will be discussed herein with
reference to the accompanying drawings which show the
characteristics of these satellite arrays.
This first embodiment uses a simplified 12-hour
equatorial plane satellite array n=2, N=3. The mean
motion n of 2 means that each satellite completes an
orbit around the earth twice per day.
An important enhancement of an N=3 case is obtained
by modifying the characteristics of the orbits so that
the satellites coalesce over the covered areas at the
moments when satellite coverage changes. The term
coalesce as used herein means that as one satellite moves
out of range of the ground tracking, the next satellite
moves into range at that same position. In fact, the two
satellites come very close to one another at that point -
- within 1° from the view of the satellite. This
simplifies the ground tracking, since the switchover
between satellites does not require much antenna
movement.
Figures 4A-4F show the basic three-satellite
"rosette" formed by the three elliptical orbits. The
earth 300 is located at one of the foci of each of the
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three ellipses of the respective satellites. Satellite
302 communicates with point 304 on the earth. Satellite
302 orbits the earth in ellipse 306. The satellites l, 2
and 3 respectively have ascending nodes of 0, 120 and
240, and respectively have mean anomalies of 180, 300,
and 60.
Similarly, satellite 310 orbits the earth in ellipse
312, and satellite 320 orbits the earth in ellipse 322.
Satellites 310 and 320 are both in a position to provide
coverage to the second covered continent area 314. Note
that satellites 310 and 320 are in their coalesced
position -- they are very close positionally, to one
another. Satellite 320 is moving away from apogee while
satellite 310 is moving toward apogee. The tracking
antenna is hence commanded to switch between tracked
satellites at the time when satellites 310 and 320 are
positionally very close, but having adequate angular
separation to avoid self-interference. According to the
disclosed system, this switchover occurs when the
satellites are within 5° of each other.
The satellites all orbit in a counter-clockwise
direction relative to the sense shown in Figure 4. The
earth also orbits in the counter-clockwise direction.
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The semi-major axes of the ellipses in Figure 4 are shown
as axes 308, 314, and 316, respectively.
In order to describe these orbits, first the
characteristics of an ellipse will be described. Figure
3 shows ellipse 400, having a focus 402. The satellite
orbits along the path of the ellipse 400, with the center
of the earth being at the focus position 402 ("the
occupied focus").
The apogee 404 and the perigee 406 of the orbits are
defined by the points on the ellipse which are farthest
from and closest to the focus of the ellipse,
respectively. The amount of difference between these
distances define the eccentricity of the ellipse. The
semi-major axis 408 is defined as half of the long axis
of the ellipse. This semi-major axis runs through the
two foci of the ellipse, to split the ellipse into two
halves. The two lengths along the semi-major axis, from
one edge of the ellipse to the occupied focus of the
ellipse are called the "radius of perigee" and the
"radius of apogee"; the latter being the longer.
As the eccentricity of an ellipse approaches zero,
the ellipse becomes less elliptical, eventually
approaching a circle (e=0) when the eccentricity is zero.
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The semi-major axis of a circle is the radius of the
circle.
The characteristics of the ellipse/ object in
elliptical orbit are calculated as follows.
The apogee, ra = a ~ (1 + ECC).
Perigee rP = a ~ ( 1 - ECC ) .
A more eccentric ellipse (higher value of eccentricity
ECC) has a greater difference between the values P and R.
Hence, such an ellipse is less like a circle. The
characteristics of the ellipse are therefore determined
as a function of its eccentricity.
The position of a satellite in orbit follows
Kepler's laws of motion which states that the orbiting
element will sweep out equal areas of the orbit in equal
times. This results in the satellite moving very rapidly
when it is at an approaching perigee, but very slowly
when it reaches apogee. For a twelve hour elliptical
orbit, therefore, it can be seen that the satellite will
spend most of its time near apogee. The numbers on the
ellipse of figure 3 represent time indications of hours
passed in a 12 hour orbit, e.g., they indicate the number
of hours since zero that have elapsed in a 12 hour orbit.
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The preferred ellipse for the 3-satellite elliptical
orbit has an eccentricity of about 0.51. This value best
allows the satellites to coalesce.
The earth rotates once in every 24 hour period, and
hence takes eight hours to rotate between the major axes
of the three equally spaced ellipses (120° spacing).
Figure 4A shows the point to be covered 304 is initially
pointing directly towards satellite 302 which is at
apogee at time 0:00. As time passes, both the satellite
302 and the earth will rotate.
As time passes, the satellites move from the
position shown in Fig. 4A. Fig. 4B shows the position
one hour later at time 1:00. Satellite P1 has moved away
from apogee, although it has moved relatively little.
Satellite P2, on the other hand, is now moving much more
rapidly at this time, since it is approaching perigee,
while P3 is still near the apogee position.
An observer on or near the equator sees the nearest
satellite appear to climb in altitude from almost
directly overhead, towards apogee, all the while staying
almost directly overhead at an elevation angle of 80-90°.
The satellite is actually rotating more slowly than the
earth during this time: it is appearing to move from east
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to west, rather than west to east as most low or medium
altitude satellites move in the sky.
Fig. 4C shows a view of the satellites one hour
later at time 2:00. The tracked locations 304 and 314
each still view a satellite near its apogee position.
Satellite P3 continues to move towards apogee and hence
appears to hang overhead. P1 is still around apogee and
thus also appears to hover.
Fig. 4D shows yet another hour later at time 3:00.
P3 is still at apogee, but P1 is approaching perigee.
Notice that P2 is coming out of perigee and approaching
the coalescence point at which P1 and P3 will cross
paths. That crossing of paths is shown in Figure 4E,
time 4:00, when P1 and P2 have coalesced in their
positions at the time when point 304 switches over
between coverage by satellite P1 and P2. At that time,
the satellites are within 1° of one another as viewed
from the ground.
The above has described the satellite Pl moving from
directly overhead the point to be covered, to the point
where satellite P1 no longer covers the point to be
covered. Therefore, the satellite is transmitting for
eight of the twelve hours of its orbit; 2/3 of the time.
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This cycle repeats. As the satellites continue to
orbit, different satellites take similar positions to
those shown in Figs. 4A-4E. Fig. 4F shows the cycle
starting to repeat with satellite P2 moving toward
apogee, satellite Pl moving toward perigee, and P3
hovering relative to the earth near its apogee.
Figures 4A-4F demonstrate the important features
recognized by the inventors of the disclosed system,
whereby the satellites spend most of their time at
apogee. At the highest points of apogee, the velocity of
the satellite very nearly matches that of the earth, and
so the satellite appears to hang overhead. The satellite
is preferably tracked while its angular velocity differs
from the earth's angular velocity by 200 or less.
Importantly, the covered areas on the earth always
see either a satellite directly overhead or two
satellites which are very nearly directly overhead.
Figures 4A-4F show how this system actually appears to
the communications point 304 to be virtually
geosynchronous. The communications point communicates
with different satellites at different times in the
satellite orbit. The communications point is always
communicating with one satellite.
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The satellites follow repeating ground tracks, since
the cycle of satellite movement shown in Figures 4A-4F
continually repeats. Importantly, this allows the ground
tracking antenna 212 to continually follow the same path,
starting at a beginning point, tracking the satellite,
and ending at the coalesce point. After the satellites
coalesce as shown in Figure 4A, the antenna begins its
tracking cycle.
The inventors of the disclosed system have optimized
this system for preventing interference with geo
satellites.
Specifically, consider Figure 4G which shows a
multiplicity of satellites in inclined elliptical orbits.
The disclosed system preferably operates to monitor
satellites at and near their apogee positions. The
satellites near perigee are moving too rapidly, and hence
are not tracked. More generally, the system of the
disclosed system operates such that the satellites are
only being used at certain times during their orbits. In
this embodiment, those certain times are when the
satellites are at apogee. Non geosynchronous circular
arrays are commonly used at present; they are actually
much less efficient, since with zero eccentricity they
spend a significantly greater time on the side of the
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earth away from the populated continents. The arrays of
the disclosed system, on the other hand, spend most of
the time at or near apogee over the populated continents
of interest, and a relatively small time (at high angular
velocities) passing through perigee in regions of no
commercial interest.
The satellites are only used when their geometry is
such that there is no possibility of the line of sight
between the ground station and the satellite interfering
with the geosynchronous band of satellites. This allows
the satellite communication to take place on the same
communication frequency band normally assigned to
geosynchronous satellites.
Moreover, the disclosed system teaches that when the
satellites are not communicating, either because the
satellites are no longer at their tracked apogee portion
and/or when the satellites are in a region where they
might interfere with geosynchronous satellites, the main
transmission is turned off. During this time, the power
supply is used to charge the battery. This means that
the power supply can be made smaller by some factor
related to the duty cycle of the satellite.
Another consideration is since the satellites only
communicate while near apogee, they are never eclipsed by
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the earth. The satellites can always receive sunlight
for solar operation while transmitting and receiving.
For example, Figure 4G shows satellites in orbit.
In the example given in Figure 4G, the satellites are
only tracked when they are in the position of the orbit
above the line 450. The only possibility of interference
with geo satellites comes when the tracking beam is
within 10° to 30° of the geo band. So long as an angular
separation greater than this amount is maintained, there
can be no interference. Therefore, the disclosed system
allows re-using the frequency bands which are usually
assigned to geosynchronous satellites in a position where
interference with the existing satellites can not occur.
The same rules are used to construct higher order
arrays with successively larger integer mean motions and
hence shorter periods. These arrays require a larger
number of satellites, but provide somewhat better
coverage of the earth.
Since more satellites are used in these higher order
arrays, each satellite need spend a lesser amount of its
time at apogee. This allows orbits to be formed wherein
the values of eccentricity are allowed to become smaller
as the mean motion increases. The ultimate limit is
atmospheric drag, which limits perigee altitudes to about
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500 kilometers. This would correspond to a 1500
kilometer apogee elliptical orbit with a resulting
eccentricity of (rd - rp) / (ra + rP) which is
approximately 0.067. This described orbit is not
practical since its period is about 1 hour and 45 minutes
which is not an integral value for the mean motion. The
next nearest value for mean motion would be n=14. The
n=14 orbit, however, would be so slightly elliptic that
it would not offer much advantage over the circular
orbits.
Practically, those arrays having mean motions of 3,
4, 5, 6, 7 and 8 are most preferred according to the
disclosed system. The most preferred orbits according
to this invention include the three-satellite orbits, the
four-satellite orbits, and the five-satellite orbits. A
particularly advantageous embodiment uses two arrays of
five satellite orbits.
As discussed above, all of these orbits include
long-term perturbations which would, if not compensated,
cause the desired continental coverage to drift off with
the passage of time. The two major perturbation effects
are due to the earth's J2 harmonic; and include:
- Regression of the line of nodes (for posigrade
orbits), and
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- Advance of perigee.
- For inclined orbits, the advance of perigee can be
suppressed by setting the inclination, i, at either
63.435 or 116.565°.
The combined effect of these two major perturbations
in the equatorial plane, due to the J2 harmonic term has
the net effect of causing the apogee to advance in a
counter-clockwise direction looking down from the
celestial North Pole.). All the satellites in a given
array design would be affected alike. Fortunately, this
effect can be compensated by increasing slightly the
period of each satellite in the array in a way such that
the earth takes a slightly longer time to reach the next
satellite's apogee arrival point. This is compensated by
adding this extra time to the satellites' periods. The
exact amount will vary, and is a function of a number of
variables, including the orbital periods, inclinations,
and eccentricities.
For inclined elliptic orbits (at critical
inclination angles), there will be no rotation of perigee
in either direction. However, there will be a regression
of the line of nodes which must be compensated by a small
adjustment in orbital period. This will cause the plane
of the orbit to rotate clockwise in the sense looking
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down from the North Pole. If that happens, the satellite
would pass over a selected meridian at a slightly earlier
time each day (or each repeat cycle), unless we adjust
the period of the satellite. In this case, we would
shorten the period of the satellite, which effectively
'stretches' out the trajectory ground trace and causes
the ground track to repeat exactly over the life of the
satellite.
As described above, third order effects due to
tesseral terms may need to be compensated by small orbit
maintenance maneuvers using minuscule amount of fuel.
The preferred four-satellite array is shown in
Figures 5A-5E. This array shows four satellites used to
track three continents. These satellites orbit in
elliptical orbits having an eccentricity of 0.6. Figures
5B and 5D show the satellite coalescing which occurs
according to this embodiment.
Figure 6 shows an overall view of the 10 satellite
array; and Figures 7A-7E show the ground tracks for a
satellite array with 5 satellites having a period, T,
equal to 6 hours. This array is preferably used with
two sets of five satellites, yielding a ten-satellite,
six hour constellation.
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The preferred communications system uses a ten
satellite system, each having six hour orbits, and each
optimized for users in the Washington, DC area. This
still, however, provides coverage throughout the rest of
the continental United States, and the entire northern
hemisphere as well as that part of the southern
hemisphere down to about 10 deg South latitude.
The system uses ten equally-spaced prograde
satellite orbit planes. All satellite orbits are at the
'critical' inclination angle of 63.435° to prevent
rotation of the line of apsides.
The ground track is adjusted so as to pass directly
over Washington, DC by adjusting the right ascensions of
all the orbits while maintaining their equal spacing.
The argument of perigee is adjusted to obtain apogees
over or nearly over the targeted latitude and longitude.
Fig. 6 shows an overview of the orbital
constellation. It can readily be seen that the
satellites favor the Northern Hemisphere by spending more
time, and reaching a higher altitude in the Northern
Hemisphere. Figure 6 shows a snapshot of time at 0:00
hours, and it should be seen that all satellites except
for satellites P5 and Pl are over the Northern Hemisphere
at that time.
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Figs. 7A-7G show a Cartesian, or Mercator, plot of
the world showing the repeating ground tracks. The
satellite array has a repeating ground track that repeats
every 24 hours. The satellites appear to 'hover' or
dwell along four equally-spaced meridians, one of which
is at the longitude of Washington, DC; the others being
spaced at 90° intervals from Washington.
Fig. 8 shows the minimum elevation angle to the
highest satellite over Washington, DC, as a function of
time. Every 24 hour period has ten elevation angle peaks
of satellites on a descending (from north proceeding
towards the equator) at or near the observer's zenith (90
deg). The lower, sharper peaks in the figure represent
other satellites on ascending passes; they are at lower
altitudes and thus going faster. These ascending
satellites are not actively transmitting to users on the
ground at the times when they are on ascending passes.
The preferred system uses a total of ten (10)
satellites in critically-inclined (i=63.4 deg) 6-hour
orbits, phased and oriented to provide optimal earth
coverage. As will be seen, this geometry also provides a
very high elevation angle, and hence avoids interference
with the existing geo communications satellite band. The
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preferred orbits have apogee and perigee altitudes of
20074 and 654 kilometers, respectively.
From a user's viewpoint, the satellites are accessed
sequentially at nominal 2 hour and 24 minute intervals at
exactly the same point in the northwestern sky (the
'start point' of the tracking segment), and are tracked
in a roughly northwest to southeast trajectory to a point
in the sky well short of intersecting the geo band of
satellites. The satellites remain at apogee during the
time while they are being tracked from the ground.
Hence, these satellites are only tracked, and
communicated with, while their velocity closely matches
the velocity of the earth. When the satellites begin to
approach the perigee stage, and hence their velocity
increases relative to the earth's rotation to differ
therefrom by more than 250, for example, they are no
longer being tracked by the communication equipment on
the earth. At this end point of the tracking segment,
the ground communications antenna is directed back to
tracking its start point to repeat the sequence as the
next-appearing satellite is acquired. Tracking along the
active arc segment is accomplished at less than 2
deg/min. For the present array, this results in every
ground communications antenna effecting ten switchovers
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per day. As explained above with reference to Figure 1,
the steering operation of the disclosed system preferably
uses phased array steering of the antenna. However,
more-conventional antenna steering is also contemplated.
Importantly, the trajectory segments appear exactly
the same to the user for every satellite, since the
azimuth-elevation trace is repeated for each satellite.
This system defines significant advantages. Its
operating altitudes are half that of existing geo
systems. This greatly reduces link margins and emitted
power requirements for the satellites.
Apogees are placed on the meridians of longitude of
the heavily-populated areas for which the constellation
is optimized. Apogee points may also be adjusted to
approximate the targeted area latitudes as well. The
satellite tracking arcs over the targeted areas remain
roughly overhead (within 30-40° of zenith), with slow
angular movement during periods when the satellite is
active. The trajectories for mid-latitude (20-50° North
latitude) observers located directly under the apogee
points in the high-population targeted areas are
approximately north-south oriented.
All ten ground tracks are identical, and only the
satellite that is currently covering the repeating ground
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tracks change. The repeat cycle is 24 hours. Since the
satellites move from one geographic area to another,
information once transmitted can be re-broadcast at
another location.
The Mercator plot of Figures 7A-7E show that the
entire system actually follows one ground track,
repeating after 24 hours. It actually 'folds over' from
the left edge of the world map to the right edge, giving
it the appearance of multiple traces.
Table II gives the orbital parameters, or
ephemerides, of the entire array of ten satellites:
TABLE II
SYSTEM ORBITAL PARAMETERS
IS
Sat # a(km) i(deg) e,(ecc.)w,(deg)RAAN deg)MA (deg)
1 16742 63.435 0.58 315 0 0
2 16742 63.435 0.58 315 072 072
3 16742 63.435 0.58 315 144 144
4 16742 63.435 0.58 315 216 216
5 16742 63.435 0.58 315 288 288
6 16742 63.435 0.58 315 180 0
7 16742 63.435 0.58 315 252 072
8 16742 63.435 0.58 315 324 144
9 16742 63.435 0.58 315 036 216
10 16742 63.435 0.58 315 108 288
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Some adjustments will be required to account for
long term orbital perturbations as described above. This
adjustment is common in satellites requiring precise
repeat cycles such as Topex-Poseidon, or the Canadian
Radarsat.
Similar views to those from the above can be drawn
for the preferred ten-satellite array. An important
point of the ten-satellite array, moreover, is that there
is good inter-satellite connectivity for cross-linking.
Fig. 7A shows the position of the satellites at time
00:00. Compare this with Fig. 7B, which shows the same
satellites twenty-four minutes later. The satellite P4,
which is substantially over Washington, D.C., has moved
very little, albeit P5 will be picking up speed as it
approaches perigee. P4 appears to hang over Washington,
D.C., since it is near the apogee portion of its orbit
and its velocity very closely matches the velocity of the
earth.
In contrast, during the same short period of time,
the satellite P1, at perigee, has moved very quickly and
very far along its orbit. Similarly, satellite P8 (over
Europe), P5 (over Southern Africa) and P9 have moved very
little. Twenty-four minutes later, Fig. 7C shows that
satellite P4 has started to move away from the United
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States, but satellite P7 is now in place, very close to
its apogee. This is evident from its position twenty-
four minutes after that, shown in Fig. 7D, where
satellite P7 has moved only very little, and is still
well-covering the United States. At time 1:36 shown in
Fig. 7E, the satellite P7 is over Washington, D.C.
The satellite P7 is still over Washington D.C. at
time 2:00 hours, shown in Fig. 7F. The satellite starts
to move at time 2:24, shown in Fig. 7G.
The disclosed system intends that the satellites be
used for communication during only some part of the time
while they are in orbit. During other times in orbits,
the satellites are not being used for communication, but
instead are charging their energy storage. This feature
of the invention has been described above, but will be
described in more detail herein with reference to Figures
2A, 4G and 4H.
Figure 4G shows a view of the earth from, for
example, the view of the satellite from the sun. This
figure shows all of the satellite orbits, and their
elliptical orbital paths. The geosynchronous satellites
are in equatorial planes shown as the geo ring 800.
Communications equipment on the earth communicates with
this geo ring 800. Moreover, sometimes the geo
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satellites are perturbed by the earth's oblateness, hence
effectively forming orbits which are slightly inclined.
The geo rings should therefore be considered at occupying
a 5° position bordering their nominal position.
Ground communications equipment on the earth
communicates with this geo ring. The cone of
communications to the geo ring is shown as 802.
When the ground communication equipment on the earth
communicates with the satellites P1-P5, it should be seen
that they are aimed at a position of the sky, 804, which
is completely separated from the geo ring 802. According
to the disclosed system, a distance is maintained between
the satellites and the geo ring 800. The angular
separation 8 is the minimum acceptable angular separation
which can ensure no interference between the geo ring and
the satellites of the disclosed system. An embodiment
uses an angular separation of 30°, which is an amount
which will obviate any possibility of interference
problem. More generally, however, any angular separation
greater than 15° would be acceptable.
Taking the satellite P3 as an example, therefore,
the satellite can only be used according to the disclosed
system when it is in its orbit between the points
labelled 808 and 810. However, the virtual geo system
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which is preferably used according to the disclosed
system uses these satellites during even less of their
orbit, only between the points 812 and 814. When the
satellite is in the other positions of its orbit, the
satellite is not consuming power or transmitting.
Therefore, this prevents any possibility of interference
with the geo satellite systems.
The operation of the equatorial satellites is
similar. The equatorial satellite array is shown in
Figure 4h. The equatorial satellite is shown as
satellite ring 850. If the ground station is on the
equator, shown as ground station 852, then it would, at
least at some times, interfere with satellites in the geo
ring shown as 854. However, if the ground station is
separated from the equator by at least 30°, such as shown
as position 856, then at least part of the satellite ring
has no chance of interference with the ring 854.
Therefore, the satellite calculates geometries such as to
obviate interference with the satellite ring.
Therefore, more generally, the disclosed system
operates as shown in Figure 2a. The antenna is
controlled at step 350, and from the antenna control the
position of the satellite relative to geo are determined
at step 870. This can be determined, for example, from
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the pointing angle of the antenna. Step 872 determines
if there is any possibility of interference between the
two. This is determined from a numerical difference
between the pointing angle and the position of the geo
ring. If there is any possibility of interference,
control passes to step 874 where the satellite
communications is disabled. If interference is not
possible at step 872, then the satellite is enabled at
step 874. An enabled satellite can be, but is not
necessarily, turned on. For example, in the virtual geo
embodiments, the enabled satellite will be maintained in
the "off" position during some of the time when it is
enabled. Therefore, step 352 determines if the satellite
is powered. This may be determined from the repeating
ground track, or other information. If the satellite is
not powered at step 352, the battery is charged at step
356. If the satellite is powered, then power is drawn
from both the supply and the battery at step 354.
Second Embodiment
Another embodiment, also referred to herein as the
"VIRGO" embodiment, uses satellite sub-constellations
with prograde elliptical orbits of approximately 8 hour
periods. Each of the satellites within a sub-
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constellation has the same ground tracks as the other
satellites within the subconstellation, or repeating
ground tracks.
Each sub-constellation includes several satellites
in each of the individual ground tracks. The satellites
are spaced such that as one satellite leaves a service
area, another satellite replaces it in the same ground
track.
As will be established herein, each satellite is in
communication with the ground station during a portion of
the trajectory where the satellite is at or near its
apogee. During this time, the relative motion of the
satellite, i.e. the perceived motion of the satellite
relative to the Earth, is slow. The satellite travels
through a relatively small angular arc, e.g., 400, during
its active phase.
As the one satellite departs from its active phase
in the descending direction, the ground user can switch
to the next-appearing satellite in the ascending portion
of the active phase of this next satellite. Continuity
of coverage is thus provided by this switch-over.
During its active phase, each satellite is virtually
geostationary. That means that it appears relatively
stationary to a user on the earth.
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The concept behind the virtual geostationary orbit
can be illustrated with analogy to the walking juggler.
A juggler's clubs cluster together and move very slowly
at the highest point in their trajectories. At the low
point of the trajectories, the juggler is catching and
transferring the clubs hand-to-hand rapidly. At the
high point of the trajectory, however, the clubs move
much slower.
The satellites in a virtually geostationary
constellation are intentionally placed in stable
elliptical orbits with their apogees over the intended
users. Like the juggler, these portions rise over the
service area and appear to hang there. Additionally,
each satellite is active for only a predetermined portion
of its orbiting time, closest to its apogee portion. The
satellites are spaced such that when one satellite in the
subconstellation reaches its inactive portion, another
satellite in the subconstellation becomes active. Hence,
the satellites are spaced such that one ascending
satellite replaces another descending satellite leaving
the service area.
Since the satellites are in 8 hour orbits, each
satellite peaks three times in each 24-hour day. Each of
the peaks is located to follow a populated region. Using
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a Northern Hemisphere apogee orbit as an example, each
satellite ascends, reaches its turn on point and begins
operating, goes through its peak ("apogee")and then
descends. The satellite eventually reaches its turn off
point. The satellite is then replaced, after its time of
"hanging", by the next satellite in the array. The first
satellite then falls rapidly into the Southern Hemisphere
and quickly rises into the next Northern Hemisphere peak.
Each satellite's peak is placed over one of the three
Northern Hemisphere Continental masses each day.
In order to provide coverage to countries in the
Southern Hemisphere, the embodiment employs another
grouping of 5 satellites having their apogees in the
Southern Hemisphere.
Each of the subconstellations is a mean motion 3
array. Each of the satellite peaks is separated from
other satellite peaks by 120° of longitude (360°/3).
The longitudes selected for apogee placement of this
array are 79°W, 41°E, and 161°E longitude. These five
satellites serve the populated areas of South America,
South Africa, Australia and New Zealand.
Each satellite, in a single day, appears at apogee
three times. This requires three satellites out of a
total of five to be active at any time. Overall, each
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satellite must then be active 3/5 of the time over a full
day, or 14.4 hours. Since this represents one day's total
active time, and the satellite has been active over three
geographic region, each region will be covered by a
single satellite for 4.8 hours. In other words, each 8-
hour satellite period, the satellite will be active for a
4.8 hour period - or 2.4 hours on either side of the
apogee.
The satellites in this array have a duty cycle of
600; that is, they are actively communicating 60% of the
time. Their on/off switching times occur 2.4 hours on
either side of the apogee. This corresponds to a latitude
of 46°, and an altitude of 18044 km. The active phase
for each satellite occurs at latitudes greater than 46°
and altitudes greater than 18044 (up to and including
apogee at 27288 km). The satellites remain well clear of
the GEO band, while active, so there is no possibility
for electronic interference with GEO communication
satellites.
Because of the operating features discussed above,
VIRGO satellites operate only when the satellites are at
least 40° separated from the line of sight of geo
satellites. Hence, existing Ku and C frequency equipment
can be used without interfering with other communciation.
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The elliptical planes in the two Northern Hemisphere
sub-constellations are inclined at 63.4° with respect to
the plane of the equator. This means that the apogees
will always appear to be roughly at 63.4° North latitude.
The two 5-satellite sub-constellations are called
Aurora 1 and Aurora 2. These are used to provide
continuous coverage of this type. The third
subconstellation is called Australia. Two or three spare
satellites are placed into "parking" orbits where they
can be boosted into different orbits if necessary.
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The VIRGOTM orbital characteristics are as follows.
TABLE 1
VIRGO''" ORBITAL
CHARACTERISTICS
Aurora Aurora AustralisTMSpare
IT" IITM
$ Sats n=1-5Sats n=1-5Sats n=1-5Satellites
Semimajor Axis 20281 20281 20281 7285
Eccentricity 0.66 0.66 0.66 0.05346
Inclination 63.435 63.435 63.435 63.435
Right Ascension
of the
1$Ascending Node 341.5 255.3 52.2 0
53.5 327.3 124.5
125.5 39.3 196.5 180
197.5 111.3 268.5
269.5 183.3 340.5 30
Argument of
Perigee
270 270 90 270
270 270 90 270
270 270 90 90
270 270 90
270 270 90
Mean Anomaly
0 108.2 0 0
144 252.2 144 0
288 36.2 288 0
72 182.2 72
216 324.2 216
The apogee of these VIRGOTM satellites is at 27,300
kilometers. This is approximately three-quarters the
altitude of geostationary satellites. This lower
altitude provides less propagation delay to orbit.
The ground tracks of this embodiment are shown in
FIG. 9. These produce the following locations of VIRGO''
active arcs.
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TABLE 2
LOCATIONS OF THE VIRGD'~ ACTIVE ARCS
(Sub-Satellite Longitudes in Degrees East)
AURORA I~ AURORAS AUSTRALIS~
NORTHERN NORTHERN SOUTHERN
HEMISPHERE HEMISHPHERE HEMISPHERE
8 - 53 78 - 123 19 - 64
Europe India - China Africa
128 - 173 198 - 243 139 - 184
Japan Alaska - Hawaii Australia - NZ
248 - 293 318 - 3 259 - 304
Con. US N. Atlantic South America
Further information on the ground track is shown in
the following.
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TABLE 3
VIRTUAL-GEOORBITAL EMBODIMENT
ELEMENTS,
PREFERRED
All Satellites: or (a) = 20381km; ntricity,
Semi-Maj Axis Ecce e, _
0.6 6; 63.435
Inclination,
I,
=
Ground Sat. RAAN _o _MA
Track
No.
#1 (West.US) Vela 350 270 0
1~#1 (West.US) VG2a 62 270 144
#1 (West.US) VG3a 134 270 288
#1 (West.US) VG4a 206 270 72
#1 (West.US) VGSa 278 270 216
#2 (East.US) VGlb 263.8 270 108.2
1$#2 (East.US) VG2b 335.8 270 252.2
#2 (East.US) VG3b 47.8 270 36.2
#2 (East.US) VG4b 119.8 270 180.2
#2 (East.US) VGSb 191.8 270 324.2
#3 (S.A.,Australia) VGlc 61 90 0
2~#3 (S.A.,Australia) VG2c 133 90 144
#3 (S.A.,Australia) VG3c 205 90 288
#3 (S.A.,Australia) VG4c 277 90 72
#3 (S.A.,Australia) VGSc 349 90 216
25 Although only a few embodiments have been described
in detail above, other embodiments are contemplated by
the inventor and are intended to be encompassed within
the following claims. In addition, other modifications
are contemplated and are also intended to be covered.
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