Method for improving kinetic energy impact asteroid orbit deflection efficiency by utilizing last-stage passivation effect and trajectory calculation system

Abstract

The invention provides a kinetic energy impact asteroid orbit deflection efficiency improvement method and a trajectory calculation system using a final-stage passivation effect, and the method comprises the steps: after an impactor is launched by a carrier rocket, the final stage is not separated from the impactor, and the final stage enters a predetermined orbit and then impacts an asteroid; and passivating treatment is carried out at the last stage, and the speed of the assembly is increased through thrust generated by passivation. Wherein a Lambert problem is utilized to solve an assembly earth departure orbit parameter and an impact moment orbit parameter; solving departure parameters of the parking track by using a gravitational force escape model; utilizing an earth high-precision kinetic model to obtain orbit parameters of an assembly at the boundary of an earth influence ball; utilizing a solar system high-precision orbit dynamics model to solve orbit parameters of the combination before impact and orbit parameters of the asteroid before the impact moment; and solving asteroid perigee parameters by using the earth high-precision kinetic model and the deflection distance calculation model, and calculating the deflection distance. According to the method, the asteroid defense efficiency is effectively improved.

Description

Technical Field

[0001] This application belongs to the fields of asteroid defense and aerospace, and specifically relates to a method and trajectory calculation system for improving the orbital deflection efficiency of kinetic energy impacts on asteroids by utilizing the final stage passivation effect. Background Technology

[0002] Kinetic impact is widely recognized as the most feasible and mature on-orbit disposal technology for planetary defense. In 2022, the United States completed the "Double Asteroid Redirect Test" mission, conducting the first technical experiment of kinetic impact defense against asteroids in space. It successfully shortened the orbital period of the Didymos binary asteroid system by 33 minutes and was named one of the top ten scientific breakthroughs of 2022 by the journal Science.

[0003] Despite the high success of the "Double Asteroid Redirection Test" mission, the test only changed the orbital velocity of the 160-meter-diameter asteroid Demophores by about 2.7 mm / s. At this velocity increment, it would take approximately 25 years to deflect the asteroid's orbit beyond a safe distance of one Earth radius. This demonstrates that even the most feasible kinetic impact technology currently available cannot effectively deflect the orbits of near-Earth asteroids larger than 140 meters in diameter within short- to medium-term warning timeframes. Therefore, existing kinetic impact technologies are limited by payload capacity, making it difficult to effectively improve impact mass, and their orbital deflection capability remains significantly insufficient when dealing with asteroids with limited warning time and large target sizes. Summary of the Invention

[0004] The purpose of this application is to overcome the shortcomings of existing technologies that cannot effectively deflect the orbits of near-Earth asteroids with a diameter greater than 140 meters under short- to medium-term warning conditions.

[0005] To achieve the above objectives, this application proposes a method for improving the orbital deflection efficiency of kinetic energy impacts on asteroids by utilizing the final-stage passivation effect, including: After the impactor is launched by the launch vehicle, the final stage does not separate from the impactor. The combination of the final stage and the impactor enters the predetermined orbit and then impacts the asteroid. Before the combination escapes the Earth parking orbit and reaches the boundary of the Earth's sphere of influence, the final stage is passivated, and the thrust generated by the passivation is used to increase the velocity of the combination. The orbit calculation process for the combined object includes: Set the Earth's departure time, the time of impact with the asteroid, and the initial epoch of the asteroid; based on the Earth's departure time and the time of impact with the asteroid, obtain the positions of the Earth and the asteroid at the two moments, and use them as input to the Lambert problem to solve for the combined Earth's departure orbit parameters and the orbit parameters at the time of impact. Using the Earth's initial orbital parameters as the initial values, the gravity escape model is used to solve for the parking orbit starting parameters, obtaining the orbital parameters of the combined body at the parking orbit when Earth escapes; then, using a high-precision Earth dynamics model considering passivation, the orbit is recursively extrapolated to the boundary of Earth's sphere of influence to obtain the orbital parameters of the combined body at the boundary of Earth's sphere of influence; finally, using a two-body model or a high-precision solar system orbital dynamics model, the orbital parameters of the combined body before the asteroid impact are recursively extrapolated to the moment of asteroid impact. Using the initial epoch and impact time of the asteroid, the asteroid's orbit is recursively derived using a high-precision solar system orbital dynamics model to solve for the asteroid's orbital parameters before the impact. Then, combining the orbital parameters of the combined body before the impact, the asteroid's orbital parameters after the impact are solved using a deflection distance calculation model. Finally, the asteroid's perigee is searched and the geocentric distance is calculated using a high-precision Earth dynamics model and a deflection distance calculation model, and then the deflection distance is calculated.

[0006] As a further description of the above method, the gravitational escape model includes: Solving the Lambert problem yields the escape velocity of the combined Earth. Calculate the right ascension of the escape point. and declination : ; ; In the geocentric inertial frame, declination is the angle between the escape velocity vector and the xoy plane, and right ascension is the angle between the projection of the escape velocity vector onto the xoy plane and the x-axis. , and These represent the projections of the escape velocity onto the x, y, and z axes, respectively. Determine the unit direction vector of the hyperbola asymptote on plane B. : ; The unit vector in the oz direction is The superscript T denotes vector transpose. Therefore, the unit vectors of the other two coordinate axes in plane B are represented as follows: ; ; Angle between plane B By declination and orbital inclination The calculation shows that: ; ; Unit angular momentum of a hyperbola for: ; Unit vectors of position and velocity at perigee of a hyperbolic orbit and It is calculated by the following formula: ; ; in, Let be the true anterior angle as the velocity approaches infinity. Let be the Earth's gravitational constant, whose sine and cosine are calculated by the following formula: ； ; The position and velocity vectors at perigee are calculated from unit vectors: ; ; in, and These represent the perigee position and velocity of the hyperbolic orbit, respectively. and These are scalars representing the position and velocity at perigee of the hyperbolic orbit, respectively.

[0007] As a further description of the above method, the high-precision Earth dynamics model includes: ; in The heliocentric position vector of the composite object; , , These are the gravitational constants of the Earth, the Sun, and the Moon, respectively. This is the geocentric position vector of the Sun; This is the geocentric position vector of the moon; This represents the position vector from the sun to the composite object; This represents the position vector of the moon relative to the composite object; , and These are the accelerations caused by Earth's J2 perturbation, atmospheric drag, and passivation, respectively.

[0008] As a further description of the above method, the high-precision orbital dynamics model of the solar system includes: ; In the formula, This is the heliocentric position vector of the composite object or asteroid; For the first i The gravitational constant of a planet; For the first The heliocentric position vector of a planet; Indicates the first i The position vector from a single planet to a composite or asteroid; The numbers 1 to 9 represent Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto, respectively. and These are accelerations caused by lunar gravity and relativistic effects, respectively.

[0009] As a further description of the above method, the deflection distance calculation model includes: Solve for the velocity of the asteroid after impact using the momentum transfer formula. : ; in, Indicates the moment immediately following the impact; Indicates the moment of impact; and This represents the asteroid's mass and relative impact velocity; Indicates the momentum transfer factor; Indicates the mass of the combined object at the moment of impact; The asteroid's position after the impact remains the same as before. Using the asteroid's post-impact position and velocity as the initial position and velocity, the high-precision solar system model is used to recursively calculate its orbit, searching for the perigee time and calculating the perigee distance. The formula is as follows: ; in, and These are the positions of the asteroid and Earth at their closest points to each other, respectively. Represents the magnitude of a vector.

[0010] This application also provides a trajectory calculation system for improving the orbital deflection efficiency of kinetic energy impacting asteroids by utilizing the final stage passivation effect. Based on the above method, the system includes: The module for solving the Earth's launch orbit parameters and impact orbit parameters of the combined object is used to set the Earth's launch time, the impact time of the asteroid, and the initial epoch of the asteroid; based on the Earth's launch time and the impact time of the asteroid, the positions of the Earth and the asteroid at the two moments are obtained, which are used as inputs to the Lambert problem to solve for the Earth's launch orbit parameters and impact orbit parameters of the combined object. The module for solving the orbital parameters of the combined body at the parking orbit when the Earth escapes is used to solve the parking orbit starting parameters of the combined body using the Earth departure orbit parameters as initial values ​​and the gravitational escape model to obtain the orbital parameters of the combined body at the parking orbit when the Earth escapes. The module for solving the orbital parameters of the pre-impact composite is used to recursively extrapolate the orbit to the boundary of the Earth's sphere of influence using a high-precision dynamics model of the Earth that takes into account passivation, and obtain the orbital parameters of the composite at the boundary of the Earth's sphere of influence. Finally, it uses a two-body model or a high-precision orbital dynamics model of the solar system to recursively extrapolate to the moment of asteroid impact and solve for the orbital parameters of the pre-impact composite. The module for solving the orbital parameters of an asteroid before the impact moment is used to recursively deduce the asteroid's orbit using the asteroid's initial epoch and impact time, and solve for the asteroid's orbital parameters before the impact moment using a high-precision orbital dynamics model of the solar system. The module for solving the orbital parameters of the asteroid after impact is used to combine the orbital parameters of the combined body before impact and use the deflection distance calculation model to solve the orbital parameters of the asteroid after impact. The deflection distance calculation module is used to solve for the perigee parameters of asteroids and calculate the deflection distance using a high-precision Earth dynamics model and a deflection distance calculation model.

[0011] Compared with existing technologies, the advantages of this application are: 1. This application proposes a novel planetary defense method that uses a spacecraft carrying the final stage of a rocket to impact an asteroid, which can effectively improve the asteroid defense performance compared to traditional kinetic impact methods.

[0012] 2. This application proposes a method to improve the speed of the spacecraft and the final stage combination by using final stage passivation, thereby saving launch energy of the launch vehicle and effectively improving the payload mass that the launch vehicle can carry.

[0013] 3. This application proposes a method for optimizing the effectiveness of the final stage impact mission, taking into account engineering constraints such as launch site latitude, launch vehicle gliding time, launch energy, and asteroid impact visibility, which can effectively improve asteroid defense effectiveness. Attached Figure Description

[0014] Figure 1 The image shown is a conceptual diagram of a rocket final stage and spacecraft combination mission to impact an asteroid. Figure 2 The figure shown is a graph of the passivation thrust changing over time; Figure 3 The diagram shown is a schematic of the orbital transfer model; Figure 4 The figure shows the payload capacity curve of a certain type of rocket; where payload mass is the payload capacity and launch energy C3 is the launch energy C3. Figure 5 The image shown is a schematic diagram of the apparent magnitude of an asteroid. Figure 6 The image shows a comparison of the deflection distances between the newly passivated and non-passivated surfaces. Figure 7The image shows a comparison of the orbital insertion quality between newly passivated and unpassivated orbitals. Figure 8 The diagram shows a flowchart of a method to improve the orbital deflection efficiency of asteroids by utilizing the final stage passivation effect. Detailed Implementation

[0015] The technical solution of this application will be described in detail below with reference to the accompanying drawings.

[0016] In current space missions, the final stage of a launch vehicle typically serves to place the spacecraft into a target orbit or a specific energy environment. After completing its orbital insertion mission, the final stage, due to its still high structural mass and residual kinetic energy, often transforms into space debris in orbit. To prevent explosions caused by residual propellant or high-pressure gases, which could generate more uncontrollable debris and threaten the operational safety of other spacecraft, current technologies generally implement passivation treatment for the rocket's final stage. This involves releasing residual propellant and high-pressure gases to reduce the probability of explosion.

[0017] Existing technologies can generate velocity increments during the passivation process of rocket final stages, but these increments have not been used to improve the overall effectiveness of space missions. Furthermore, the high quality and kinetic energy characteristics of the final stage have not been applied to scenarios requiring large kinetic energy or impact mass, such as kinetic impact missions in planetary defense. Therefore, under the current technological framework, the potential energy, mass, and kinetic energy resources of the final stage have not been effectively developed, resulting in limited usable impact energy and making it difficult to meet the mass and velocity requirements of high-energy impact missions.

[0018] This invention proposes a method and trajectory calculation system for enhancing the orbital deflection efficiency of a kinetic energy impact on an asteroid by utilizing the passivation effect of the final stage. Final stage impact refers to a scenario where, after the rocket's final stage carries the spacecraft into space, there is no traditional spacecraft-rocket separation. The spacecraft is responsible for orbit and attitude control, and then it, along with the final stage assembly, impacts an asteroid. The large mass of the rocket's final stage itself enhances the asteroid's orbital deflection efficiency. During this process, the velocity increment generated by the rocket's final stage passivation reduces launch energy, thereby increasing the payload capacity.

[0019] This invention establishes an orbital transfer model encompassing passivation thrust and an asteroid impact deflection model. The optimization process considers engineering constraints such as launch site latitude, rocket coasting time, and asteroid impact visibility. Optimization results show that, compared to traditional kinetic impacts, the deflection efficiency of the final-stage impact can be improved by at least two times, and passivation can save approximately 1 km. 2 / s 2 The launch energy can, on average, increase the payload mass by 180 kg. In summary, considering passivation, the final-stage impact project is highly feasible, can improve the deflection effectiveness of kinetic energy impacts against asteroids, and passivation can increase the payload mass.

[0020] This invention addresses the problem that traditional kinetic impact methods, with their small impactor mass, struggle to cope with asteroids that have limited warning time and large target sizes. By carrying a rocket's final stage, the energy of the impact on the asteroid is increased. Furthermore, by utilizing a new passivation method for the rocket's final stage, the energy required for launch is reduced, thereby increasing the effective payload mass that can be carried.

[0021] Example 1 The method proposed in this application for improving the orbital deflection efficiency of kinetic impacts on asteroids by utilizing the final-stage passivation effect includes: 1. Task Concept After launch by the launch vehicle, the final stage of the impactor does not separate from the impactor. The final stage and the spacecraft combination enter a predetermined orbit and collide with the asteroid. During this process, the final stage undergoes passivation treatment, and the thrust generated by passivation is used to increase the velocity of the combination and reduce the C3 required for launch. Mission concept diagram as follows: Figure 1 As shown.

[0022] 2. Design Methodology The mission trajectory optimization in this invention requires the establishment of an orbital transfer model, an asteroid impact deflection model, and a blunting thrust model. Furthermore, considering the mission's engineering feasibility, engineering constraints such as launch site latitude, rocket coasting time, asteroid impact visibility, and asteroid perigee deflection distance also need to be taken into account. The models and constraints described below are introduced one by one.

[0023] 2.1 Orbital Dynamics Model To ensure that the deflected asteroid does not pose a threat to Earth, its orbit needs to be calculated accurately. This invention establishes a high-precision orbital dynamics model using the DE430 ephemeris, primarily considering a two-body gravitational model centered on the Sun, a third-body gravitational perturbation model including the eight planets, Pluto, and the Moon, as well as relativistic effects. The formulas are as follows:

[0024] In the formula, This is the heliocentric position vector of the spacecraft or asteroid; For the first i The gravitational constant of a planet; For the first The heliocentric position vector of a planet; Indicates the first i The position vector from a planet to a spacecraft or asteroid; The numbers 1 to 9 represent Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto, respectively. and These represent accelerations caused by lunar gravity and relativistic effects, respectively. The ephemeris of the eight planets, Pluto, and the Moon are obtained from the JPL DE430 ephemeris (Folkner et al., 2014). In this invention, the orbital calculations of asteroids and spacecraft outside Earth's sphere of influence all require the use of the aforementioned high-precision solar system orbital dynamics model.

[0025] When asteroids and spacecraft are within Earth's sphere of influence, a high-precision Earth orbit dynamics model can be used for orbital recursion. In this model, Earth is the central gravitational body, and the gravitational perturbations from the Sun and Moon (third bodies) are considered, along with factors such as Earth's non-spherical gravitational perturbations and atmospheric drag.

[0026]

[0027] In the formula, This is the heliocentric position vector of the observer or impactor; , , These are the gravitational constants of the Earth, the Sun, and the Moon, respectively. This is the geocentric position vector of the Sun; This is the geocentric position vector of the Moon; This represents the position vector of the sun relative to the observer or impactor. This represents the position vector from the Moon to the observer or impactor. , and These represent accelerations caused by Earth's J2 perturbation, atmospheric drag, and passivation, respectively. The ephemeris values ​​for Earth, the Sun, and the Moon were obtained from the JPLDE430 ephemeris.

[0028] By adjusting the attitude of the spacecraft and final stage assembly and redesigning the passivation procedure, the new passivation can generate acceleration thrust, thereby increasing the velocity of the assembly. The thrust generated by the passivation changes over time as follows: Figure 2 As shown. Since passivation begins when the spacecraft escapes its Earth parking orbit and ends before reaching the boundary of Earth's sphere of influence, the geocentric high-precision dynamics model will add an acceleration term generated by the passivation thrust when passivation thrust is present. .

[0029] 2.2 Orbit Transfer Model The orbital transfer model of this invention is as follows: Figure 3As shown, the Lambert problem of Earth launching into the final stage assembly colliding with an asteroid is first solved. After obtaining the initial values, the Earth parking orbit parameters are solved using a gravitational escape model. Then, a high-precision Earth orbital dynamics model considering passivation thrust is used to recursively calculate the spacecraft orbit to the boundary of Earth's sphere of influence. After recursively calculating to the asteroid, the velocity increment generated by the asteroid after impact is calculated using an impact deflection model. Finally, a high-precision solar system dynamics model is used to recursively calculate the asteroid orbit, search for its perigee, and calculate the orbital deflection distance to determine the deflection effect.

[0030] 2.2.1 Initial Values ​​for the Lambert Transition Model This invention employs a conic section splicing method for designing the orbital transfer model. Considering both launch cost and launch capacity, this invention selects a mature rocket model as the launch vehicle option. The launch vehicle's capability curve (as shown in the diagram)... Figure 4 As shown, the rocket's carrying capacity and launch capability can be obtained. The relationship between rocket carrying capacity and launch capability can also be obtained from the capability curve of the rocket used in other embodiments. The relationship.

[0031] In the aforementioned mission mode, no maneuvers are performed from orbit insertion to impact, except for minor attitude and orbit adjustments. During the design process, the mass of the spacecraft at the moment of impact can be assumed to be... Equal to the mass of Earth after its escape :

[0032] Based on Earth's position at the time of launch Location of the asteroid at the moment of impact and the transition time from launch to impact Solving the Lambert problem allows us to calculate the heliocentric velocity of the spacecraft during its escape from Earth and during its impact. and :

[0033] From this, we can obtain the escape velocity of the aircraft. ,in and These represent the Earth's heliocentric velocity and launch time, respectively.

[0034] emission can be The calculation yielded:

[0035] in, Represents the magnitude of a vector.

[0036] In addition, the relative velocities of the spacecraft and the asteroid at the moment of impact can be obtained. (here) and (These represent the moments before and after the impact, respectively).

[0037] 2.2.2 Deflection Distance Calculation Model Momentum transfer factor β The momentum transfer factor is a crucial parameter for measuring the impact of a kinetic energy collision on an asteroid's orbit. When an impact occurs, the asteroid's surface ejects a large amount of ejecta. This ejecta generates a reaction force, further enhancing the asteroid's velocity change and causing its total momentum to exceed that of the impactor itself. The momentum transfer factor is typically greater than 1, but its specific value depends on the impact angle, impact velocity, and the asteroid's physical properties. In asteroid defense missions, a higher momentum transfer factor is crucial. A higher value implies a more effective orbital deflection capability.

[0038] This invention conservatively assumes that the collision between the spacecraft and the asteroid is a perfectly elastic collision, with a momentum transfer factor of... The density of an asteroid is 1. A homogeneous sphere. Combined with the mass of an asteroid. relative velocity of impact and momentum transfer factor The velocity of the asteroid after impact can be calculated using the momentum transfer formula. :

[0039] in, Indicates the moment of impact.

[0040] The asteroid's position after impact remains the same as before. Using the post-impact asteroid position and velocity as the initial position and velocity, the aforementioned high-precision solar system model is used for orbit recursion to search for the close-approach (CA) moment. The perigee distance is then calculated. The formula is as follows, where and The positions of the asteroid and Earth at their closest points to each other are shown below:

[0041] 2.2.3 Mooring track splicing Based on the principle of the conic section splicing method, in the design of the geocentric parking orbit parameters, we assume that the spacecraft is only affected by Earth's gravity and use a two-body model to calculate the orbital parameters. We assume that after the impactor is launched from the ground, it first enters a 200km circular parking orbit. After gliding for a period of time, the final stage's secondary ignition causes the impactor to enter a hyperbolic orbit and escape. The escape point is the perigee, and the perigee of the hyperbolic escape orbit is on the parking orbit, with the velocity direction at perigee being the same as the circular orbital trajectory.

[0042] Solving the Lambert problem yields the escape velocity of the spacecraft on Earth, allowing us to calculate the right ascension of the escape point. Declination In a geocentric inertial frame, declination is the angle between the escape velocity vector and the xoy plane, and right ascension is the angle between the projection of the escape velocity vector onto the xoy plane and the x-axis. , and These represent the projections of the escape velocity onto the x, y, and z axes, respectively.

[0043]

[0044]

[0045] Considering carrying capacity, the inclination angle of the parking orbit should not differ too much from the latitude of the launch site. To ensure that multiple escape orbits do not occur when splicing them with the parking orbit, we limit the absolute value of the declination to be less than the latitude of the launch site.

[0046] Next, we determine the unit direction vector of the hyperbola asymptote on the B plane (Kizner, 1961):

[0047] The unit vector in the oz direction is Then the unit vectors of the other two coordinate axes of plane B are expressed as:

[0048]

[0049] The angle between plane B and orbital inclination can be determined by declination and orbital inclination. λ The calculation shows that:

[0050]

[0051] To avoid complex numbers in the above calculations, the absolute value of declination should be less than the given mooring track inclination. The unit angular momentum of the hyperbola is:

[0052] Unit vectors of position and velocity at perigee of a hyperbolic orbit and It can be calculated using the following formula:

[0053]

[0054] In the formula, Let be the true anterior angle as the velocity approaches infinity. Let be the Earth's gravitational constant, and its sine and cosine can be calculated using the following formula:

[0055]

[0056] The position velocity vector at perigee can be calculated from the unit vector, and then the six roots of the hyperbolic orbit can be solved.

[0057]

[0058]

[0059] in, and These represent the perigee position and velocity of the hyperbolic orbit, respectively. and Scalars representing the position and velocity at perigee of the hyperbolic orbit, respectively. The above formulas constitute the gravitational escape model of this application.

[0060] In the conic section splicing method, the boundary between the geocentric and heliocentric segments is the boundary of the Earth's sphere of influence. In the orbit design of the deep space transfer segment, the Earth is considered a point mass, and the distance from the Earth's center to the boundary of the sphere of influence is negligible compared to the distance of the deep space transfer orbit. Therefore, a single escape velocity vector can be determined for each deep space transfer segment orbit. However, in the design of the geocentric segment, a given... and perigee altitude It is possible to find countless lines that affect the magnitude and direction of the velocity at the boundary of the ball. Consistent hyperbolic escape trajectories (Curtis, 2019) form a circle at their perigee, which is called the orbital launch circle.

[0061] The intersection of the parking tracks corresponding to these hyperbolas is: Point, the aircraft passed After reaching the launch circle position, an escape pulse is applied in the velocity direction, and the vehicle enters a hyperbolic orbit. In a geocentric inertial frame, it can be represented as:

[0062] in, This indicates the magnitude of the escape velocity.

[0063] Earth's core Vector of a point The right ascension is Declination is ,

[0064] In addition, the orbital inclination λ and the launch site latitude , firing direction The following relationship must be satisfied:

[0065] Based on the above analysis, the inclination angle of the mooring track surface and the declination of the escape point must satisfy the following formula:

[0066]

[0067] Through the above analysis, we can transform the launch site's geographical latitude engineering constraint into an orbital inclination constraint. To save launch fuel consumption and increase payload mass, the launch trajectory of a carrier rocket is typically close to 90°, and the parking orbit inclination is close to the launch site latitude. Therefore, this invention sets the parking orbit inclination to 19.5°. In the subsequent calculation of the perigee argument, since solutions with a declination absolute value greater than the parking orbit inclination will be complex, only the perigee argument satisfying the declination constraint is calculated.

[0068] The following explains how to translate the engineering constraint of the launch vehicle's coasting time into a limitation on the perigee angle at the Starship separation point. The launch method, in which the launch vehicle coasts to its predetermined position in the near-Earth parking orbit, and then the final stage ignites twice to directly send the probe into deep space orbit, can fully utilize the high specific impulse advantage of the launch vehicle's orbital stage propulsion system. However, the coasting time needs to be within a certain range; this invention assumes it to be 200s to 1000s.

[0069] Glide time between the two launches of the launch vehicle's orbital stage for:

[0070]

[0071] In the formula, and These are the Earth's parking orbit altitude and Earth's radius, respectively; in this invention, we use 200 km and 6378.14 km. and These are the perigee argument and true anomaly in the Earth-fixed coordinate system, respectively. It should be noted that the z-axis in the Earth-fixed coordinate system is affected by the wobble of the Earth's rotation axis, causing the equatorial plane to change over time. Therefore, the perigee argument is converted to the Earth's inertial frame for calculation. This refers to the operational arc from launch vehicle liftoff to entry into parking orbit. This refers to the arc segment from the end of the parking orbit coasting to the separation of the probe. Using the above formula, the launch vehicle's coasting time constraint can be transformed into a perigee argument constraint.

[0072] The calculations in this section transform the launch site latitude constraint into a parking orbit inclination limit, which in turn translates into an escape velocity declination constraint. The launch vehicle's coasting time constraint is transformed into a perigee argument limit at the launch-satellite separation point, a value that can also be derived from parameters at the escape point. Furthermore, the above process allows for the concatenation of the Earth departure time parameters for the deep space transfer segment with the parameters for entering the parking orbit after launch, and the use of these deep space transfer segment parameters to reflect the engineering constraints of the geocentric parking orbit design segment.

[0073] 2.3 Asteroid Impact Visibility Model The size of an asteroid is reflected by its absolute magnitude, while its observability is usually determined by its apparent magnitude. Apparent magnitude represents the brightness level that an observer can see; the observable brightness decreases as the apparent magnitude increases. The conversion between apparent magnitude and absolute magnitude can be achieved using the following formula:

[0074]

[0075]

[0076] In the formula, For apparent magnitude, For absolute magnitude, This represents the distance between the Sun and the asteroid. The distance between the observer (Earth) and the asteroid. for and Phase angle between, The slope parameter of the phase angle curve, when When the phase angle is relatively large, the phase angle curve is steep, and the asteroid's brightness increases rapidly as the phase angle decreases. In actual observations, limited observational data can be used to... and The model is fitted to the data, and the apparent magnitude of the asteroid at different locations can be calculated. The value is 0.15. It should be noted that the sky region near the Sun can affect optical observations; therefore, this invention sets... Figure 5 middle The angle must be greater than 45°.

[0077] Based on the above model design, the method for improving the orbital deflection efficiency of kinetic energy impacting asteroids by utilizing the final stage passivation effect provided in this application includes the following trajectory calculation process for the rocket's final stage and the spacecraft: First, the Earth's departure time, the time of impact with the asteroid, and the asteroid's initial epoch are set. Based on the Earth's departure and impact times, the positions of Earth and the asteroid at these two moments can be read. These positions can be used as input to the Lambert problem to solve for the Earth's departure orbital parameters and the orbital parameters at the time of impact of the final stage assembly (the combination of the rocket's final stage and the spacecraft). This data can then be used as initial values ​​for subsequent operations.

[0078] Using the Earth's initial orbital parameters as the initial values, the orbital elements of the final stage assembly at the parking orbit can be obtained by solving the parking orbit parameters using the gravitational escape model. Then, using a high-precision dynamics model of the Earth that considers passivation, the orbit is recursively extrapolated to the boundary of the Earth's sphere of influence to obtain the orbital parameters of the assembly at the boundary of the Earth's sphere of influence. Finally, using a two-body model (or a high-precision orbital dynamics model of the solar system), the orbital parameters of the assembly before the asteroid impact are solved by extrapolating to the moment of the asteroid impact.

[0079] Using the asteroid's initial epoch and impact time, a high-precision solar system orbital dynamics model is used to recursively deduce the orbit and solve for the asteroid's orbital parameters before impact. Then, combining the orbital parameters of the final stage assembly before impact, a deflection distance calculation model is used to solve for the asteroid's orbital parameters after impact. Finally, the high-precision solar system dynamics model and the deflection distance calculation model are used to solve for the asteroid's perigee parameters, calculate the deflection distance, and evaluate the deflection effectiveness. The process is as follows: Figure 8 As shown.

[0080] Using the method described in this invention, the new passivation and non-passivation task parameters of 10 sets of solutions were optimized respectively. Figure 6 For the comparison of deflection distance, Figure 7 For comparison of orbital mass, dots of the same color in the figure represent the same launch window; solid dots indicate passivation, and hollow dots indicate no passivation. The deflection distance diagram shows that with the same launch transfer window, the impact velocity of the asteroid remains essentially unchanged. Considering the increase in deflection distance after passivation, it is mainly due to the increase in impactor mass. The comparison of orbital mass shows that passivation can save approximately 1 km. 2 / s 2 The C3 can increase the effective payload capacity by an average of 180 kg.

[0081] To verify the deflection effect of the final-stage impactor on different asteroids, this invention randomly selected 10 asteroids from the hazardous asteroids, retaining a, e, and i, and modified them into virtual impactors that would collide with Earth in 2050. These were used as targets for the final-stage impactor mission, taking into account blunting, and their mission trajectories were optimized. We set the time of impact of the virtual impactors on Earth to be within 2050, with a mission warning time of 20 years, meaning the mission could be launched after 2030. All virtual impactors were homogeneous spheres with a diameter of 140m and a density of 2.8. Without considering engineering constraints such as glide time and impact visibility, the mission trajectories of the 10 virtual impactors were optimized. The results show that the final-stage impactor can effectively deflect asteroids impacting Earth, with a minimum deflection distance greater than twice the Earth's radius. Compared to traditional kinetic impact methods, the deflection distance can be increased by 2 to 4 times.

[0082] Table 1 Comparison of deflection distance between final-stage stone impact and classical kinetic energy impact.

[0083] The method for improving the final-stage stone-impact deflection efficiency considering passivation provided in this application has the following advantages: 1. This application proposes a novel planetary defense method that uses a spacecraft carrying the final stage of a rocket to impact an asteroid, which can effectively improve the asteroid defense performance compared to traditional kinetic impact methods.

[0084] 2. This application proposes a method to improve the speed of the spacecraft and the final stage combination by using final stage passivation, thereby saving launch energy of the launch vehicle and effectively improving the payload mass that the launch vehicle can carry.

[0085] 3. This application proposes a method for optimizing the effectiveness of the final stage impact mission, taking into account engineering constraints such as launch site latitude, launch vehicle gliding time, launch energy, and asteroid impact visibility, which can effectively improve asteroid defense effectiveness.

[0086] Example 2 This application also provides a trajectory calculation system for improving the orbital deflection efficiency of kinetic energy impacting asteroids by utilizing the final stage passivation effect. Based on the above method, the system includes: The module for solving the Earth's launch orbit parameters and impact orbit parameters of the combined object is used to set the Earth's launch time, the impact time of the asteroid, and the initial epoch of the asteroid; based on the Earth's launch time and the impact time of the asteroid, the positions of the Earth and the asteroid at the two moments are obtained, which are used as inputs to the Lambert problem to solve for the Earth's launch orbit parameters and impact orbit parameters of the combined object. The module for solving the orbital parameters of the combined body at the parking orbit when the Earth escapes is used to solve the parking orbit starting parameters of the combined body using the Earth departure orbit parameters as initial values ​​and the gravitational escape model to obtain the orbital parameters of the combined body at the parking orbit when the Earth escapes. The module for solving the orbital parameters of the pre-impact composite is used to recursively extrapolate the orbit to the boundary of the Earth's sphere of influence using a high-precision dynamics model of the Earth that takes into account passivation, and obtain the orbital parameters of the composite at the boundary of the Earth's sphere of influence. Finally, it uses a two-body model or a high-precision orbital dynamics model of the solar system to recursively extrapolate to the moment of asteroid impact and solve for the orbital parameters of the pre-impact composite. The module for solving the orbital parameters of an asteroid before the impact moment is used to recursively deduce the asteroid's orbit using the asteroid's initial epoch and impact time, and solve for the asteroid's orbital parameters before the impact moment using a high-precision orbital dynamics model of the solar system. The module for solving the orbital parameters of the asteroid after impact is used to combine the orbital parameters of the combined body before impact and use the deflection distance calculation model to solve the orbital parameters of the asteroid after impact. The deflection distance calculation module is used to solve for the perigee parameters of asteroids and calculate the deflection distance using a high-precision Earth dynamics model and a deflection distance calculation model.

[0087] This application may also provide a computer device, including: at least one processor, memory, at least one network interface, and a user interface. The various components in this device are coupled together via a bus system. It is understood that the bus system is used to implement communication between these components. In addition to a data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0088] The user interface can include a display, keyboard, or clicking device. Examples include a mouse, trackball, touchpad, or touchscreen.

[0089] It is understood that the memory in the embodiments disclosed in this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced Synchronous DRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memories described herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0090] In some implementations, the memory stores elements such as executable modules or data structures, or subsets thereof, or extended sets thereof: operating systems and applications.

[0091] The operating system includes various system programs, such as the framework layer, core library layer, and driver layer, used to implement various basic business functions and handle hardware-based tasks. The application programs include various applications, such as media players and browsers, used to implement various application functions. Programs implementing the methods of the embodiments of this disclosure can be included in the application programs.

[0092] In the above embodiments, the processor can also invoke programs or instructions stored in memory, specifically programs or instructions stored in an application program, for the following purposes: Follow the steps described above.

[0093] The above methods can be applied to or implemented by a processor. The processor may be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above methods can be completed by integrated logic circuits in the processor's hardware or by software instructions. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic diagrams disclosed above. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the disclosed methods can be directly implemented by a hardware decoding processor, or by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0094] It is understood that the embodiments described in this application can be implemented using hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0095] For software implementation, the technology of this application can be implemented by executing the functional modules (e.g., procedures, functions, etc.) of this application. The software code can be stored in memory and executed by a processor. The memory can be implemented in the processor or outside the processor.

[0096] This application may also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, it can implement the steps in the above method embodiments.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and are not intended to limit it. Although this application has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of this application do not depart from the spirit and scope of the technical solutions of this application, and should all be covered within the scope of the claims of this application.

Claims

1. A method for improving the orbital deflection efficiency of kinetic energy impacts on asteroids by utilizing the final-stage passivation effect, comprising: After the impactor is launched by the launch vehicle, the final stage does not separate from the impactor. The combination of the final stage and the impactor enters the predetermined orbit and then impacts the asteroid. From the moment the combined object escapes Earth's parking orbit until it reaches the boundary of Earth's sphere of influence, the final stage undergoes passivation treatment, and the thrust generated by passivation is used to increase the combined object's speed. The orbit calculation process for the combined object includes: Set the Earth's departure time, the time of impact with the asteroid, and the initial epoch of the asteroid; based on the Earth's departure time and the time of impact with the asteroid, obtain the positions of the Earth and the asteroid at the two moments, and use them as input to the Lambert problem to solve for the combined Earth's departure orbit parameters and the orbit parameters at the time of impact. Using the Earth's initial orbital parameters as the initial values, the gravity escape model is used to solve for the parking orbit starting parameters, obtaining the orbital parameters of the combined body at the parking orbit when Earth escapes; then, using a high-precision Earth dynamics model considering passivation, the orbit is recursively extrapolated to the boundary of Earth's sphere of influence to obtain the orbital parameters of the combined body at the boundary of Earth's sphere of influence; finally, using a two-body model or a high-precision solar system orbital dynamics model, the orbital parameters of the combined body before the asteroid impact are recursively extrapolated to the moment of asteroid impact. Using the initial epoch and impact time of the asteroid, the asteroid's orbit is recursively derived using a high-precision solar system orbital dynamics model to solve for the asteroid's orbital parameters before the impact. Then, combining the orbital parameters of the combined body before impact, the asteroid's orbital parameters after impact are solved using a deflection distance calculation model. Finally, the asteroid's perigee is searched using the high-precision solar system dynamics model and the deflection distance calculation model, and the geocentric distance is solved to calculate the deflection distance.

2. The method for improving the orbital deflection efficiency of kinetic energy impacts on asteroids using the final-stage passivation effect as described in claim 1, characterized in that, The gravitational escape model includes: Solving the Lambert problem yields the escape velocity of the combined Earth. Calculate the right ascension of the escape point. and declination : ； ； In the geocentric inertial frame, declination is the angle between the escape velocity vector and the xoy plane, and right ascension is the angle between the projection of the escape velocity vector onto the xoy plane and the x-axis. , and These represent the projections of the escape velocity onto the x, y, and z axes, respectively. Determine the unit direction vector of the hyperbola asymptote on plane B. : ； The unit vector in the oz direction is The superscript T denotes vector transpose. Therefore, the unit vectors along the other two coordinate axes of plane B are expressed as: ； ； Angle between plane B By declination and orbital inclination The calculation shows that: ； ； Unit angular momentum of a hyperbola for: ； Unit vectors of position and velocity at perigee of a hyperbolic orbit and It is calculated by the following formula: ； ； in, Let be the true anterior angle as the velocity approaches infinity. Let be the Earth's gravitational constant, whose sine and cosine are calculated by the following formula: ； ； The position and velocity vectors at perigee are calculated from unit vectors: ； ； in, and These represent the perigee position and velocity of the hyperbolic orbit, respectively. and These are scalars representing the position and velocity at perigee of the hyperbolic orbit, respectively.

3. The method for improving the orbital deflection efficiency of kinetic energy impacts on asteroids using the final-stage passivation effect as described in claim 1, characterized in that, The high-precision dynamic model of the Earth includes: ； in The heliocentric position vector of the composite object; , , These are the gravitational constants of the Earth, the Sun, and the Moon, respectively. This is the geocentric position vector of the Sun; This is the geocentric position vector of the moon; This represents the position vector from the sun to the composite object; This represents the position vector of the moon relative to the composite object; , and These are the accelerations caused by Earth's J2 perturbation, atmospheric drag, and passivation, respectively.

4. The method for improving the orbital deflection efficiency of kinetic energy impacts on asteroids using the final-stage passivation effect as described in claim 1, characterized in that, The high-precision orbital dynamics model of the solar system includes: ； In the formula, This is the heliocentric position vector of the composite object or asteroid; For the first i The gravitational constant of a planet; For the first The heliocentric position vector of a planet; Indicates the first i The position vector from a single planet to a composite or asteroid; The numbers 1 to 9 represent Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto, respectively. and These are accelerations caused by lunar gravity and relativistic effects, respectively.

5. The method for improving the orbital deflection efficiency of kinetic energy impacts on asteroids using the final-stage passivation effect as described in claim 1, characterized in that, The deflection distance calculation model includes: Solve for the velocity of the asteroid after impact using the momentum transfer formula. : ； in, Indicates the moment immediately following the impact; Indicates the moment of impact; and This represents the asteroid's mass and relative impact velocity; Indicates the momentum transfer factor; Indicates the mass of the combined object at the moment of impact; The asteroid's position after the impact remains the same as before. Using the asteroid's post-impact position and velocity as the initial position and velocity, the high-precision solar system model is used to recursively calculate its orbit, searching for the perigee time and calculating the perigee distance. The formula is as follows: ； in, and These are the positions of the asteroid and Earth at their closest points to each other, respectively. Represents the magnitude of a vector.

6. A trajectory calculation system for improving the orbital deflection efficiency of kinetic energy impacting asteroids using the final-stage passivation effect, implemented based on the method described in any one of claims 1-5, characterized in that, The system includes: The module for solving the Earth's launch orbit parameters and impact orbit parameters of the combined object is used to set the Earth's launch time, the impact time of the asteroid, and the initial epoch of the asteroid; based on the Earth's launch time and the impact time of the asteroid, the positions of the Earth and the asteroid at the two moments are obtained, which are used as inputs to the Lambert problem to solve for the Earth's launch orbit parameters and impact orbit parameters of the combined object. The module for solving the orbital parameters of the combined body at the parking orbit when the Earth escapes is used to solve the parking orbit starting parameters of the combined body using the Earth departure orbit parameters as initial values ​​and the gravitational escape model to obtain the orbital parameters of the combined body at the parking orbit when the Earth escapes. The module for solving the orbital parameters of the pre-impact composite is used to recursively extrapolate the orbit to the boundary of the Earth's sphere of influence using a high-precision dynamics model of the Earth that takes into account passivation, and obtain the orbital parameters of the composite at the boundary of the Earth's sphere of influence. Finally, it uses a two-body model or a high-precision orbital dynamics model of the solar system to recursively extrapolate to the moment of asteroid impact and solve for the orbital parameters of the pre-impact composite. The module for solving the orbital parameters of an asteroid before the impact moment is used to recursively deduce the asteroid's orbit using the asteroid's initial epoch and impact time, and solve for the asteroid's orbital parameters before the impact moment using a high-precision orbital dynamics model of the solar system. The module for solving the post-impact asteroid orbital parameters is used to combine the orbital parameters of the pre-impact assembly with a deflection distance calculation model to solve for the post-impact asteroid orbital parameters; and The deflection distance calculation module is used to determine the perigee of a searched asteroid using a high-precision dynamic model of the solar system and a deflection distance calculation model, and to calculate the Earth-center distance, thereby calculating the deflection distance.

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