Method for transferring a spacecraft from geosynchronous transfer orbit to lunar orbit

Abstract

Method for placing a spacecraft into a lunar orbit, either by standard (i.e., impulsive) or ballistic (i.e., non-impulsive) capture, from an Earth orbit that is significantly inclined relative to the lunar orbit plane, with no constraint on the local time of perigee for the starting orbit.

Claims

1. A method for placing a spacecraft into a selected orbit, the select orbit comprising a lunar resonance orbit, in the lunar orbit plane, the method comprising: placing a spacecraft into a selected geosynchronous transfer orbit (GTO), or orbit associated with a plane having a significant inclination relative to the Moon's orbit plane, with no constraint on the local time of perigee so that launch time of day is compatible; for each of two or more spaced apart positions of perigee of a spacecraft trajectory, adding a selected velocity increment, V1, oriented in a present direction of spacecraft velocity vector, in order to increase an apogee height, h1, to a value greater than the Earth-Moon distance and to adjust a phase of the spacecraft to a selected phase value relative to a phase value of the Moon; at an apogee position of the spacecraft, adding a selected velocity increment, V2 or V6, oriented in a first selected direction relative to present direction of spacecraft velocity vector, so that a subsequent spacecraft trajectory will execute a lunar flyby and will intersect the Moon's orbit, where the selected velocity increment, V2 or V6, has at least one of a contra-velocity component and a normal-velocity component; executing the lunar flyby on at least one of the Moon's leading edge or the Moon's trailing edge so that the spacecraft enters the lunar orbit plane; and after the spacecraft has executed the lunar flyby, executing contra-velocity maneuver with a selected velocity increment, V3 or V7, at spacecraft perigee to yield a lunar resonance orbit in the lunar orbit plane.

2. The method of claim 1, further comprising selecting said apogee height, h1, for said spacecraft trajectory to lie beyond lunar distance.

3. The method of claim 1, further comprising selecting at least one of said velocity increments to have a value V1=730 m/sec, V2=277 m/sec, V3=45 m/sec, V6=40 m/sec, and V7=340 m/sec.

4. The method of claim 1, further comprising after the spacecraft has executed the lunar flyby, executing contra-velocity maneuver with a selected velocity increment, V3, at spacecraft perigee to yield a lunar resonance orbit that, in turn, yields a subsequent lunar encounter possibility; after the spacecraft executes a final perigee in the lunar resonance orbit, executing a selected velocity maneuver, V4, to yield a selected inclination, relative to a lunar equatorial plane, and a selected perilune altitude above Moon surface; and executing a contra-velocity maneuver with a selected velocity increment, V5, at a selected low perilune altitude in order to produce a lunar orbit insertion and thus yield a lunar orbit.

5. The method of claim 4, further comprising selecting said apogee height, h1, for said spacecraft trajectory to lie beyond lunar distance.

6. The method of claim 4, further comprising selecting said perilune altitude to have a value of 500 km.

7. The method of claim 1, wherein the step of executing the lunar flyby is on the Moon's trailing edge; after the spacecraft has executed the lunar flyby, executing contra-velocity maneuver with a selected velocity increment, V7, at spacecraft perigee to yield a lunar resonance orbit; and entering into lunar orbit by ballistic capture after entering the lunar resonance orbit without need for an insertion maneuver.

8. The method of claim 7, further comprising selecting said apogee height, h1, for said spacecraft trajectory to lie beyond lunar distance.

9. The method of claim 7, further comprising selecting the final perigee altitude, before lunar capture, to have a value of at least 50,000 km in order to yield subsequent ballistic lunar capture.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIGS. 1L, 1TR, and 1BR illustrate a trajectory with an initial GTO right ascension of ascending node (RAAN) of 270 degrees (which corresponds to a GTO perigee with local time of 07:00 hours), viewed in Earth-centered, Earth inertial frames, oriented normal to (1L) and edge-on (1TR) relative to the lunar orbit plane, and in a Moon-centered, Moon inertial frame with view in the lunar equatorial plane (1BR).

(2) FIG. 2L illustrates a trajectory with initial GTO RAAN of 180 degrees (which corresponds to a GTO perigee with local time of 01:00 hours), viewed in an Earth-centered, Earth inertial frame, viewed normal to the lunar orbit plane; FIG. 2R illustrates the trajectory in a Moon-centered, Moon inertial frame, viewed normal to a lunar orbit plane.

(3) FIG. 3 illustrates multiple trajectory solutions (designed for the DARE spacecraft), with local time of the GTO perigee varied in 2-hour increments throughout a 24-hour period (analogous to varying RAAN from 0 to 360 degrees). The view is normal to the lunar orbit plane in an Earth-centered, Earth inertial frame.

(4) FIG. 4 illustrates multiple trajectory solutions (designed for the DARE spacecraft), with local time of the GTO perigee varied in 2-hour increments throughout a 24-hour period (analogous to varying RAAN from 0 to 360 degrees). The view is edge-on to the lunar orbit plane in an Earth-centered, Earth inertial frame.

(5) FIG. 5 displays a graph of the total deterministic V required for DARE spacecraft trajectory solutions with varying local time of GTO perigee (i.e., the same trajectory solutions shown in FIGS. 3 and 4). The x-axis displays both local time of perigee and corresponding RAAN values.

(6) FIG. 6 illustrates a trajectory in a Moon-centered, Moon inertial frame, viewed normal to the lunar orbit plane, including a 100 m/sec V preform at a time of ballistic capture, to strengthen the orbit by a reduction of C3 value.

(7) FIG. 7 illustrates a low-thrust maneuver (assuming 2 millinewton (mN) of thrust, with spacecraft wet mass of 10 kg), performed to strengthen a lunar orbit by change of C3; trajectory is shown in a Moon-centered, Moon inertial frame, viewed normal to the Moon's orbit plane.

(8) FIG. 8 is a Flow Chart generally illustrating six Steps to implement the invention.

DESCRIPTION OF THE INVENTION

(9) To demonstrate the proposed method, a geosynchronous transfer orbit (GTO), inclined at a specified inclination (here, 28.5 degrees) to the Earth's equatorial plane is connected to a lunar orbit either by standard orbit insertion (i.e., impulsive, or thrust needed for initial capture into lunar orbit, FIGS. 2L and 2R).

(10) Although this method is applicable to GTOs with any local time of perigee, two specific GTOs are chosen for presentation since they represent boundary cases among all similar lunar flyby solutions analyzed (local time of perigee is solved in 2-hour increments throughout a 24-hour period; see FIGS. 3, 4, and 5). The first GTO requires the largest magnitude total V and is the most inclined to the lunar orbit plane; its corresponding local time of perigee is 07:00 hours, which corresponds to a RAAN of 270 degrees. The second GTO presented requires the least total V and is the least inclined to the lunar orbit plane; the corresponding local time of perigee is 01:00 hours (corresponding to a RAAN of 180 degrees).

(11) All velocity maneuvers are modeled as instantaneous delivery, unless noted otherwise. All trajectory segments were modeled in Systems Tool Kit (STK) Astrogator using an 8.sup.th/9.sup.th order Runge-Kutta integrator within a force model that included gravity fields for the Sun, Earth, Moon and all remaining planets.

(12) Step 1: Spacecraft Maneuvers at Perigee to Increase Apogee Distance and Adjust Phase with Moon (8-1 on FIG. 8 Flow Chart)

(13) After separation from the primary payload in GTO (FIG. 1L, site A or FIG. 2L, site A), the spacecraft will increase the apogee altitude to well beyond lunar distance (e.g., 800,000 kin from Earth) by executing a velocity maneuver at perigee (FIG. 1L, site A or FIG. 2L, site A) totaling V1 (e.g., 730 m/sec). In the presented case, this velocity maneuver is divided into two or more separate maneuvers, which act as lunar phasing orbits with the benefit of also reducing gravity losses experienced by a spacecraft on this trajectory. These maneuvers are executed in the direction of the spacecraft's orbit velocity (with respect to its central body, the Earth in this phase).

(14) Justification for choosing an apogee altitude beyond lunar distant, approximately 800,000 kin in the presented method, is as follows. Most geosynchronous transfer orbits do not intersect the lunar orbit plane. By extending apogee to beyond lunar distance, an out-of-plane maneuver (normal to the velocity vector direction) can be executed far from Earth's gravity well (and thus at relatively low V cost) to yield an intersection with the Moon's orbit (and the Moon itself) on the return leg. Although this V cost is more than that flown when apogee is farther from the Earth (e.g., 1.5 million km) the solution is simpler, more consistent, and yields a lower transfer duration. Proceed to Step 2.

(15) Step 2: Maneuver at Apogee to Achieve Lunar Flyby (8-2 on FIG. 8 Flow Chart)

(16) A velocity maneuver V2 (e.g., 277 m/sec) is executed at apogee, FIG. 1L, site B or V6 (e.g., 40 m/sec), FIG. 2L, site B), which allows the trajectory to intersect the Moon's orbit to set up a lunar flyby and enter the Moon's orbit plane; this decreases the lunar approach speed at a subsequent lunar encounter. This maneuver is executed in a direction normal to the velocity vector direction, with some of the component also in the contra-velocity or velocity direction. Proceed to Step 3.

(17) Step 3: Perform Lunar Flyby (8-3 on FIG. 8 Flow Chart)

(18) Execute the lunar flyby, either on the Moon's leading edge or trailing edge above its equator (targeted in Step 2L). No deterministic V is needed to perform the lunar flyby. If a ballistic lunar capture is needed, the flyby occurs on the Moon's trailing edge; either a leading or trailing edge lunar flyby is compatible with a standard/direct lunar capture. Proceed to Step 4.

(19) Step 4-1: Maneuver at Perigee to Enter Lunar Resonance Orbit LRO (8-4 on FIG. 8 Flow Chart)

(20) A lunar resonance orbit is set up that yields a standard lunar capture opportunity (i.e., thrust is needed for initial capture into lunar orbit). After a leading (or trailing) edge lunar flyby (FIG. 1L, site C), execute a perigee contra-velocity maneuver with V345 m/sec near FIG. 1L, site A, to yield a lunar resonance orbit (FIG. 1L, site D). Proceed to Step 5.

(21) Step 4-2: (Alternative to Step 4-1)

(22) To set up a lunar resonance orbit that yields a ballistic lunar capture (i.e., no thrust is needed for initial capture into lunar orbit). After performing a trailing-edge lunar flyby (FIG. 2L or FIG. 2R, site C), execute a velocity maneuver at the subsequent perigee with V7 (e.g., 340 m/sec) contra-velocity (FIG. 2L, site D) to yield a lunar resonance orbit (FIG. 2L, site E). The resulting orbit is now compatible with ballistic lunar capture about one month later, near perilune altitude (FIG. 2L or FIG. 2R, site F), given that the perigee altitude above 50,000 kin and apogee altitude near lunar distance. The resulting capture will yield a lunar orbit with C3=0.063 km.sup.2/sec.sup.2. Lunar orbit is achieved.

(23) Since a lunar ballistic capture does not provide long-term orbit stability, one or more contra-velocity maneuver(s) can be executed to strengthen (i.e. decrease the C3) of the lunar orbit. For example, a 100 m/sec contra-velocity maneuver is executed at perilune altitude (FIG. 6, site F) to reduce the C3 to approximately 0.166 km.sup.2/sec.sup.t. Alternatively, a contra-velocity, low-thrust (and finite) maneuver can be executed beginning before the ballistic capture (FIG. 7, site F-0) and continuing for 12.5 days until a velocity increment V5 (e.g., 265 m/sec; not instantaneous) is delivered (FIG. 4, site F-1); a C3 of 0.258 km.sup.2/sec.sup.t is attained assuming the use of a 10 kg spacecraft (wet mass) with 2 millinewton thrust capability (FIG. 7). The corresponding lunar orbit period is 61 hours. End of procedure.

(24) Step 5: Post-Perigee Maneuver to Achieve Lunar Orbit Insertion Conditions (8-5 on FIG. 8 Flow Chart)

(25) Execute a velocity maneuver V4 (e.g., 46 m/sec) in the contra-velocity and/or normal-velocity direction of the orbit about 24 hours after the final perigee (near site A in FIG. 1L or FIG. 1TR) to select the specified inclination and perilune altitude conditions desired for the lunar orbit insertion maneuver. Proceed to Step 6.

(26) Step 6: Lunar Orbit Insertion Maneuver at Perilune Altitude (8-6 on FIG. 8 Flow Chart)

(27) Execute a contra-velocity maneuver of V5 (e.g., 265 m/sec) at a low perilune altitude (500 km perilune altitude chosen for the presented case) near position site E of either FIG. 1L, FIG. 1TR, or FIG. 1BR. This will result in a 24-hour period elliptical lunar orbit (C30.5 km.sup.2/sec.sup.2), about 2.5 months after separation in GTO as seen in FIG. 1BR. Lunar orbit achieved, end of procedure. Each of Steps 1-6 is covered generally in a Flow Chart in FIG. 8.

(28) From GTO as the starting orbit, the preceding ordered sequence of actions, taken or allowed to develop, will allow a spacecraft to be launched at any time from this orbit, to travel to and enter a lunar orbit having arbitrary inclination and arbitrary perilune altitude. The energy expended to transfer to this new orbit is represented by a sequence of v(m/sec) velocity perturbations and lunar gravitational assistance (e.g., lunar flyby) relative to the originally contemplated trajectory path, such that the desired final goal of lunar orbit is achieved. Application of the preceding sequence(s) to the DARE mission is one among many possible applications of the presented method.