Data processing: vehicles – navigation – and relative location – Vehicle control – guidance – operation – or indication – Aeronautical vehicle
Reexamination Certificate
2000-01-27
2001-03-06
Zanelli, Michael J. (Department: 3661)
Data processing: vehicles, navigation, and relative location
Vehicle control, guidance, operation, or indication
Aeronautical vehicle
C701S226000
Reexamination Certificate
active
06198990
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to satellites and more particularly to satellite orbits.
2. Description of the Related Art
The orbit diagram
20
of
FIG. 1
illustrates relationships between movements of a satellite, the earth, the sun and the moon. In the diagram, a satellite
22
orbits the earth
24
in an orbit plane
26
. An orbit axis that is orthogonal to and centered in the orbit plane is typically referred to as an orbit normal
28
. Similarly, the earth rotates about an equatorial pole
32
which is normal to an equatorial plane
30
.
The sun appears to move about the earth
24
in an ecliptic plane
36
which has an ecliptic pole
38
that is tilted ~23.44 degrees from the equatorial pole
32
. The sun
34
is shown at two exemplary positions, a winter solstice position
34
W and a summer solstice position
34
S. Similarly, the moon
40
is shown at two positions
40
A and
40
B which respectively represent its farthest and closest approach to the equatorial plane
30
.
The moon orbits the earth in a lunar orbit plane
42
which has a lunar orbit normal
44
. The lunar orbit normal
44
is canted ~5.14 degrees from the ecliptic pole
38
and regresses (i.e., rotates clockwise as viewed from north of the ecliptic plane
36
) about that pole with a period of ~18.6 years. This regression is indicated by movement arrow
45
and the lunar orbit normal
44
is shown in two extreme positions
44
A and
44
B that correspond to extreme orientations
42
A and
42
B of the lunar orbit plane
42
.
The celestial diagram
48
of
FIG. 2
relates the orbit plane
26
and the equatorial plane
30
to an equatorial coordinate system
50
(the plane
26
is shown at a greater angle in
FIG. 2
for clarity of illustration). The system
50
has 3 orthogonal axes; an e
3
axis coaxial with the equatorial pole (
32
in FIG.
1
), an axis e
1
that is oriented through the vernal equinox (and points generally to Aries) and a third orthogonal axis e
2
. The right ascension of a celestial body is its angle (taken counterclockwise from above the e
1
-e
2
plane) from the axis e
1
and the declination of a celestial body is its angle from the e
1
-e
2
plane (alternatively, the body's codeclination is its angle from the e
3
axis).
In reference to the equatorial plane
30
, the orbit plane
26
has an ascending node
52
where the satellite
22
crosses to the upper side of the equatorial plane and a descending node
54
where it crosses to the lower side (satellite motion is indicated by movement arrow
55
). With respect to the coordinate system
50
, an orbit plane's inertial position is typically specified by its inclination I and its right ascension of the ascending node (RAAN). In
FIG. 2
, the inclination I is the angle
56
between the equatorial plane
30
and the orbit plane
26
and the RAAN is the angle
58
.
The earth, the sun and the moon all perturb a satellite's orbit plane. The dominant sources of these orbit-plane perturbations are the oblateness (i.e., polar flattening) of the earth and the gravitational-gradients generated by the sun and the moon. Various references (e.g., R. R. Allan and G. E. Cook, “The long-period motion of the plane of a distant circular orbit”,
Proceedings Royal Society,
1964, vol 280, pp. 97-109) have shown that these perturbations cause an orbit normal to regress about a theoretical vector that is hereinafter referred to as a Q vector.
The orbit normal
28
and a Q vector
60
are shown in the diagram
61
of
FIG. 3
with reference to the equatorial coordinate system
50
of FIG.
2
. The Q vector
60
has three vector components; a first fixed vector
62
associated with earth-induced perturbations and oriented coaxially with the e
3
axis, a second fixed vector
64
associated with sun-induced perturbations and oriented parallel to the ecliptic pole (
38
in
FIG. 1
) and a rotating vector
66
associated with moon-induced perturbations. The latter vector is parallel to the lunar orbit normal (
44
in
FIG. 1
) and, accordingly, it cones about the vector component
64
at an angle of ~5.14 degrees and with a period of ~18.6 years (for clarity of illustration, the angle is considerably increased in FIG.
3
). As shown in
FIG. 3
, the resultant Q vector
60
tilts by an offset angle &phgr; from the e
3
axis and the equatorial pole (
32
in FIG.
1
).
If the orbit normal
28
is initially tilted from the Q vector
60
by an angle &thgr;, the combined perturbations cause the orbit normal to regress, as illustrated by the motion arrow
67
, about the Q vector
60
with a constant angle &thgr; and at an angular rate equal to cosine &thgr; times the magnitude of the Q vector (this rate is also shown in FIG.
3
). As indicated by the motion arrow
68
, the Q vector
60
repetitively traces a path with an ~18.6 period and, accordingly, its magnitude and direction vary over that period. The magnitudes of the vector components
62
,
64
and
66
are functions of the semimajor axis of the satellite's orbit and the satellite's mean motion (i.e., a function of the satellite's altitude).
Because of the offset angle &phgr; regression of the orbit normal
28
about the Q vector
60
effects changes in the orbit plane's inclination (
56
in FIG.
2
). Satellite missions generally require that the inclination be controlled within a specified band. If correction is required, inclination control is typically effected through the application of corrective thruster forces to the satellite. In particular, inclination corrections are accomplished with thruster forces that are directed normal to the orbit plane and inclination corrections are the dominant users of thruster fuel. Because reduction of fuel usage permits an increase of satellite payload and revenue, extensive efforts have been directed to the reduction or elimination of thruster fuel use in control of orbit plane inclination.
Inclination control is particularly important in systems (e.g., communication systems) that require a constellation of satellites to occupy a single orbit plane. Significant savings in thruster fuel and operational complexity can be realized in these systems if the satellites can be inserted into orbit so that the need for inclination control is reduced over the system's lifetime.
SUMMARY OF THE INVENTION
The present invention is directed to methods for accurately inserting a constellation of satellites into a common orbit plane with a mean inclination &thgr;. This accurate insertion can reduce the need for thruster corrections of orbit inclination. Because the accuracy of the methods increases as the period of the common orbit is reduced, they may even eliminate the need for thruster corrections in some satellite constellations.
The methods are practiced with an operational inertial position of the Q vector. In different method embodiments, this operational position may be the instantaneous position at each satellite's insertion date or various averages of the Q vector's position.
In one method embodiment, a respective orbit insertion date and a respective RAAN are selected for an initial satellite. For each subsequent one of the satellites, a respective orbit insertion date is selected that is delayed from the orbit insertion date of the first satellite by a respective elapsed time. For each subsequent one of the satellites, the RAAN of the first satellite is updated with its respective regression rate and the subsequent satellite's respective elapsed time to realize a respective RAAN for the subsequent satellite.
With reference to the operational inertial position of the Q vector, an instantaneous orbit inclination is then derived for each of the satellites that corresponds to the mean inclination &thgr; and that satellite's respective RAAN. Each of the satellites is then inserted on its respective orbit insertion date into a respective orbit with that satellite's respective instantaneous inclination and respective RAAN.
The novel features of the invent
Croom Christopher Allen
Snyder William Allen
Gibson Eric M.
Hughes Electronics Corporation
Terje Gudmestad
Zanelli Michael J.
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