Aeronautics and astronautics – Spacecraft – Spacecraft formation – orbit – or interplanetary path
Reexamination Certificate
2000-03-10
2002-04-02
Carone, Michael J. (Department: 3644)
Aeronautics and astronautics
Spacecraft
Spacecraft formation, orbit, or interplanetary path
Reexamination Certificate
active
06364252
ABSTRACT:
BACKGROUND OF THE INVENTION
The present invention relates to orbital operations involving Earth satellites in general, and more particularly to an improved method and apparatus for rendezvousing with and/or servicing orbital platforms and satellites, or transporting material from one orbit to another.
There are many satellites in the range of altitudes generally referred to as Low Earth Orbit (LEO), particularly proximal to the lower reaches of the Van Allen belts. One preferred band of altitudes above the Earth's surface for LEO satellite operation is between 200 km (kilometers) and 1500 km in mid inclinations, or 200 km to 1000 km in polar inclinations.
LEO satellites may malfunction for a variety of reasons including, but not limited to, failure of booms or panels to deploy, computer or transponder failure, upper stage rocket failure, loss of orientation in relation to the sun and subsequent power loss, fundamental design flaws such as optical systems that can not focus properly or running out of fuel required for orbital station keeping or maneuvering. Currently, in most cases, a malfunctioning satellite is declared a complete loss and is replaced by a new satellite. This costs many tens of millions of dollars for commercial LEO satellites, hundreds of millions of dollars for commercial Geostationary Earth Orbit (GEO) satellites, and upwards of a billion dollars for many defense-related satellites. In addition to the cost of replacement there is also a delay caused by the need to build a replacement satellite.
In a few cases, the failure of some satellites has been remedied by in-orbit repair of the satellite or recapture of the satellite to Earth-bound repair and re-launch. In 1995, NASA used the Space Shuttle to repair faulty optics on the $1.5 billion Hubble Space Telescope. Using the Shuttle's robotic arm to grapple the Hubble telescope in its 600 kilometer altitude orbit, astronauts put on spacesuits, went out into space and replaced major sub-components of the Hubble system. Then, in 1997, NASA used the Shuttle to perform additional in-orbit repairs on the Hubble Space Telescope to fix failed inertial navigation sub-systems and to upgrade the Hubble Space Telescope with improved optics.
The use of the Space Shuttle for a repair mission, at an estimated mission cost of $500 million, is only practical and cost-effective for satellites with an existing value of at least half a billion dollars, and then only for satellites in orbits accessible by the Shuttle—from about 28.6 degrees inclination to 57 degrees inclination under normal circumstances, and under 650 kilometers altitude. With the current mix and positions of satellites in orbit today, that limits this repair scenario to less than one percent of the satellites in Earth orbit.
Direct launch from the Earth of satellite servicing apparatus, using space transportation vehicles other than the Shuttle, to the orbit occupied by a malfunctioning satellite has been proposed—but not implemented—by numerous parties. Direct launch from Earth of an apparatus that can recover or service a satellite is technically feasible, but expensive. Such a servicing approach might be useful in some cases, but the cost of launching the apparatus from Earth might well be more than the replacement cost of a satellite.
One issue for operations rendezvous in orbit is minimizing the cost and time of rendezvous. One factor that complicates rendezvous is the fact that orbits “precess” around the Earth (or other planetary bodies). A brief inspection of orbital mechanics shows why this is a problem. The path that an object takes in a closed-circuit orbit around a more massive body (such as a satellite around the Earth) is in the shape of an ellipse. If we consider a satellite's orbit around the Earth, the ellipse can be defined by its semimajor axis (a) given by Equation 1,
a
=
h
A
+
h
P
+
2
R
2
(
Equ
.
1
)
and eccentricity (e) given by Equation 2,
e
=
h
A
-
h
P
h
A
+
h
P
+
2
R
(
Equ
.
2
)
where R is the equatorial radius of the Earth, and h
A
and h
P
are the highest and lowest altitudes of the satellite above the Earth's surface, or “apogee” and “perigee”, respectively. In the special case of a circular obit, h
A
=h
P
. The location of this ellipse in space relative to the Earth can be given by its inclination (i) relative to the equatorial plane, its right ascension of the ascending node (RAAN, or &OHgr;) which is measured counterclockwise in the equator plane from the direction of the vernal equinox to the point where the satellite makes its south-to-north crossing of the equatorial plane, and argument of perigee (&ohgr;) which is measured in the orbit plane in the direction of the satellites motion from the ascending node to perigee. These relationships are shown in FIG.
1
.
Westward precession of an orbit, taken herein to mean changes in the orbit's RAAN, will occur over time due to perturbations caused by J
2
zonal harmonics in the central attractive body's gravitational field (“oblateness”). Orbits of differing altitudes, inclinations, and eccentricity will exhibit different “precession rates” (&OHgr;), which for an Earth orbit can be approximated by Equation 3.
Ω
.
=
-
9.9639
(
1
-
e
2
)
2
×
(
R
R
+
h
A
+
h
P
2
)
3.5
cos
i
[
degrees
mean
solar
day
]
(
Equ
.
3
)
Orbital rendezvous, such as changing from one orbit to another of a different altitude, requires a change in velocity (&Dgr;V). The &Dgr;V that can be achieved by expending a predetermined amount of energy, e.g., burning a predetermined amount of propellant in a rocket engine, where the predetermined amount can be calculated using Equation 4,
Δ
V
=
g
0
I
sp
ln
m
f
+
m
fuel
m
f
(
Equ
.
4
)
where g
0
is the Earth's gravitational constant at sea level, I
SP
is the rocket engine's specific impulse, mf is the final mass of the space vehicle, and m
fuel
is the mass of the fuel used in the maneuver. Since &Dgr;V is related to the amount propellant used, it thus affects the cost of the transfer.
Precession affects the cost of orbit transfer because changing from one orbit to another one in a different plane, i.e., one with a different inclination and/or RAAN, requires a certain &Dgr;V even if those orbits are otherwise identical. For example, changing a circular orbit with velocity V
C
and inclination i from a RAAN of &OHgr;
1
to &OHgr;
2
will require a &Dgr;V given by Equation 5,
&Dgr;
V=
2
V
C
sin &thgr;/2 (Equ. 5)
where the equivalent plane change angle &thgr; is given by Equation 6.
cos &thgr;=cos
2
i
+sin
2
cos(&OHgr;
2
−&OHgr;
1
) (Equ. 6)
By waiting for a specific orbit to precess to the same RAAN of another orbit, a minimum energy trip between the two orbits is available since no plane change is required. Conversely, reducing the waiting time needed to transfer from one orbit to another can be achieved by performing a transfer with some plane change, at the expense of extra &Dgr;V required.
For missions launched from Earth into LEO, the relative precession rate between the launch site and the plane of an orbit in LEO is large (since the launch site on the Earth's surface rotates through 360 degrees in about one day) and hence the period between launch opportunities, or “windows”, that can be made given the &Dgr;V capability of the booster is measured in hours to a few days. For example, if a Delta rocket launch designed to emplace an Iridium satellite in a particular orbital plane is not launched on schedule, the next opportunity for launch presents itself within 24 hours. Therefore, precession rates have not presented a significant problem when traveling from Earth to LEO.
However, the relative precession rate between any two independent orbits in LEO is much smaller, and the corresponding periods between minimum energy windows is often in months or even years. For example, the relative precession rate
Albert Philip H.
Carone Michael J.
Constellation Services International, Inc.
Dinh Tien
Townsend and Townsend / and Crew LLP
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