Method and device for estimating maximum velocity change of asteroid deflected by spacecraft

Abstract

The present invention relates to a method and device for estimating the maximum velocity change of an asteroid deflected by a spacecraft. The method comprises the following steps: obtaining parameters related to a target asteroid; planning an interception mission based on the intersection of the target asteroid's orbit with the Earth, and determining parameters related to the mission spacecraft; obtaining the absolute velocity of the asteroid and the absolute velocity of the spacecraft at the time of impact according to the interception mission plan; and estimating the maximum velocity change of the asteroid deflected by the spacecraft based on a determined momentum transfer coefficient threshold expression, the parameters related to the target asteroid, the parameters related to the mission spacecraft, the absolute velocity of the asteroid, and the absolute velocity of the spacecraft. The momentum transfer coefficient threshold expression is determined by combining the laws of conservation of energy and conservation of momentum. Compared with existing technologies, the present invention has the advantages of high accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of asteroid defense technology, and in particular relates to a method and device for estimating the maximum velocity change of an asteroid deflected by a spacecraft. Background Art

[0002] The frequent occurrence of asteroid hazards has garnered increasing attention from researchers. Consequently, asteroid defense missions are being actively developed both domestically and internationally. Limited by technological maturity and scenario applicability, current asteroid defense missions primarily employ kinetic impact methods, which involve launching a spacecraft into a target asteroid at high velocity to achieve deflection. During a hypervelocity collision between a spacecraft and an asteroid, the change in momentum of the asteroid is the sum of the momentum of the spacecraft and the momentum of the permanently ejected debris generated by the impact. Results from numerous ground-based and simulation experiments indicate that the momentum of the debris is typically many times that of the simulated spacecraft. This results in a momentum change imparted to the asteroid by the impact that is many times greater than the spacecraft's momentum. This factor is typically expressed as the momentum transfer coefficient β.

[0003] Since the velocity change of the target asteroid is affected by the momentum transfer coefficient β, β can be used to evaluate the impact deflection effect. The relationship between β and the velocity change of the target asteroid is deduced as follows:

[0004] m ast v ast +m sc v sc =(m ast +m sc -∑m * )v′ ast +p ej

[0005] ∑m * <<m ast +m sc

[0006] (m ast +m sc )(v ast -v′ ast )=p ej +m sc (v ast -v sc )

[0007] Δv=v ast -v′ ast

[0008] u=v ast -v sc

[0009]

[0010]

[0011] Where m ast is the mass of the target asteroid, m sc is the mission spacecraft mass, v ast is the absolute velocity of the asteroid, v sc is the absolute velocity of the impactor, ∑m * is the mass of the escaped splash produced by the hypervelocity impact, v′ ast is the absolute velocity of the asteroid after impact, p ej is the momentum carried by the escaping splashers, Δv is the change in velocity of the target asteroid before and after the impact, and u is the relative impact velocity between the spacecraft and the asteroid.

[0012] As the above equation shows, the magnitude of β directly affects the change in an asteroid's velocity after being deflected by an impact. Therefore, analyzing the β threshold plays a crucial role in designing asteroid defense mission indicators and evaluating the applicability of kinetic impact methods. Current β analysis methods can be broadly categorized into two main categories: dimensionless analysis based on point source theory and fitting ground-based test data. These methods primarily focus on analyzing the relationship between β and factors such as relative impact velocity and target porosity, while neglecting the study of the β threshold.

[0013] Most current research on the momentum transfer coefficient is based on theoretical analysis and the relationship between β and elements such as relative impact velocity and porosity through fitting ground test data. The literature "mentum transfer in asteroid impacts.i.theory and scaling" (Holsapple KA, Housen K R.Icarus, 2012, 221(2):875-887) established a sputtering scaling law theory of sputtering velocity and mass distribution through point source theory and dimensionless analysis, provided a theoretical description of the sputtering mass, velocity, and position distribution, and gave an expression for β based on this. The paper "Hypervelocity cratering and disruption of the northwest africa 869ordinary chondrite meteorite: Implications for crater production, catastrophic disruption, momentum transfer and dust production on asteroids" (Flynn GJ, Durda DD, Patmore EB, et al. Planetary and Space Science, 2018, 164: 91-105) conducted a hypervelocity impact experiment on an asteroid analogue. The typical evolution of the resplash is shown in the figure below. Figure 1 As shown in the literature, it is found that the plume on the surface of the asteroid analog will form a projectile cone when it collides with the asteroid analog, and the angle between the projectile cone and the surface of the asteroid analog is about 45 degrees. F, Hupfer J, et al. Procedia Engineering, 2015, 103: 197-204) found that the angle between the ejecta cone and the surface of the asteroid analogue decreases with the increase of the porosity of the analogue, which means that the velocity component of the splash parallel to the impact direction decreases, p ejFurthermore, the study "Ejecta velocity distribution for impact cratering experiments on porous and low-strength targets" (Michikami T, Moriguchi K, Hasegawa S, et al. Planetary and Space Science, 2007, 55(1-2):70-88) found that the mass and velocity of the splashed material decrease when impacting asteroid analogs with high porosity. Based on the above derivation and research, it can be concluded that β increases with increasing impact velocity and bulk bond strength, and decreases with increasing asteroid porosity. Unfortunately, the above-mentioned existing technology focuses primarily on the relationship between β and asteroid properties and relative impact velocity when studying and analyzing β, ignoring the qualitative analysis of the β threshold, which affects the accuracy of the determination of asteroid defense missions. Summary of the Invention

[0014] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method and device for estimating the maximum velocity change of asteroid deflected by a spacecraft with high accuracy.

[0015] The purpose of the present invention can be achieved by the following technical solutions:

[0016] A method for estimating the maximum velocity change of an asteroid deflected by a spacecraft comprises the following steps:

[0017] Obtain relevant parameters of the target asteroid;

[0018] Plan the interception mission and determine the relevant parameters of the mission spacecraft based on the intersection of the target asteroid's orbit with the Earth;

[0019] Obtaining the absolute velocity of the asteroid and the absolute velocity of the spacecraft at the time of impact according to the interception mission plan;

[0020] Based on the determined momentum transfer coefficient threshold expression and the target asteroid-related parameters, mission spacecraft-related parameters, the asteroid absolute velocity, and the spacecraft absolute velocity, estimating the maximum velocity change of the asteroid deflected by the spacecraft;

[0021] The momentum transfer coefficient threshold expression is determined by combining the law of conservation of energy and the law of conservation of momentum.

[0022] Furthermore, the target asteroid related parameters include the six orbital numbers of the asteroid and the mass of the target asteroid.

[0023] Furthermore, the relevant parameters of the mission spacecraft include the mass of the mission spacecraft and the number of mission spacecraft.

[0024] Furthermore, the upper limit of the momentum transfer coefficient is determined by the lower limit of twice the kinetic energy E ej carried by the splashes.

[0025] Furthermore, the acquisition of the kinetic energy carried by the splashes includes:

[0026] Estimating the velocity distribution and mass distribution of the splashes generated during the impact of the spacecraft and the asteroid according to the intercept mission plan, and estimating the kinetic energy carried by the splashes.

[0027] Furthermore, the expression of the momentum transfer coefficient threshold is:

[0028]

[0029] In the formula, C is a constant, and 0 < C < 1, u is the relative impact velocity, E ej is twice the kinetic energy carried by the splashes, E ej ∝u n means that E ej is proportional to the nth power of u, β is the momentum transfer coefficient, m ast is the mass of the target asteroid, m sc is the mass of the mission spacecraft, ∑m ej is the mass of the escape splashes generated by the hypervelocity impact, and → means approaching.

[0030] Furthermore, when the power exponent n satisfies n ≤ 2, the estimation formula for the maximum velocity change of the spacecraft deflecting the asteroid is:

[0031]

[0032] In the formula, Δv is the velocity change of the target asteroid before and after the impact, m ast is the mass of the target asteroid, m sc is the mass of the mission spacecraft, C is a constant, and u is the relative impact velocity.

[0033] Furthermore, the method further includes:

[0034] Calculating the deflection distance of the asteroid after the velocity change based on the maximum velocity change of the spacecraft deflecting the asteroid, and determining whether it meets the mission requirements.

[0035] The present invention also provides a computer-readable storage medium, which is characterized in that it includes one or more programs for execution by one or more processors of an electronic device, and the one or more programs include instructions for executing the method for estimating the maximum velocity change of the spacecraft deflecting the asteroid as described above.

[0036] The present invention also provides an electronic device comprising one or more processors, a memory, and one or more programs stored in the memory, wherein the one or more programs include instructions for executing the method for estimating the maximum velocity change of an asteroid deflected by a spacecraft as described above.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] By analyzing the threshold value of the momentum transfer coefficient, the present invention clarifies the relationship between the momentum transfer coefficient and the mass of the spacecraft and the target asteroid, and can accurately estimate the maximum velocity change caused by deflecting the asteroid.

[0039] There is currently no research and analysis on the momentum transfer threshold in the existing technology. This present invention fills a gap in asteroid defense research. The method of the present invention can adapt to complex and changeable planetary defense missions. It can combine the imaging data (estimated asteroid mass) and the spacecraft asteroid velocity data during the mission to more accurately estimate the momentum transfer coefficient after deflection, and then estimate the maximum velocity change caused by the deflected asteroid. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a typical evolution diagram of existing backsplash;

[0041] Figure 2 Schematic diagram showing the effect of the size of β on the final deflection effect when deflecting a target asteroid;

[0042] Figure 3 Flowchart of the method of the present invention. DETAILED DESCRIPTION

[0043] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0044] For a target asteroid of a certain size, the magnitude of the momentum transfer coefficient β will affect the final deflection effect when deflecting it. Figure 2 As shown in the figure, Δv A It refers to the change in the tangential direction of the target asteroid's orbit when β = 1. The B plane is defined as the plane perpendicular to the hyperbolic velocity of the near-Earth asteroid when it enters the Earth's sphere of influence and passing through the Earth's center of mass. It is often used to describe the relative position of the asteroid to the Earth.

[0045] In order to study the threshold of β, it is assumed that there is no energy loss during the hypervelocity collision, that is, the kinetic energy carried by the spacecraft is completely converted into the kinetic energy of the target asteroid and the kinetic energy of the splashing objects. Based on the law of conservation of energy, the formula is listed with the asteroid as the reference system:

[0046]

[0047] Among them, m ast is the mass of the target asteroid, m sc is the mission spacecraft mass, ∑m ej is the mass of the escaped splash produced by the hypervelocity impact, Δv is the velocity change of the target asteroid before and after the impact, u is the relative impact velocity between the spacecraft and the asteroid, and v eji is the relative velocity of the splashing material in the asteroid reference frame.

[0048] Since the mass of the spacecraft is much smaller than the mass of the target asteroid, that is, m ast -∑m ej >>m sc , define twice the kinetic energy carried by the splash as Transforming formula (1) yields formula (2):

[0049]

[0050] According to the conservation of momentum, we can get formula (3):

[0051] m ast v ast +m sc v sc =(m ast +m sc -∑m ej )v′ ast +p ej (3)

[0052] The newly added variable v in the formula ast is the absolute velocity of the asteroid, v′ ast is the absolute velocity of the asteroid after impact, v sc is the absolute velocity of the impactor, u=v ast -v sc , Δv=v ast -v′ ast , p ej is the momentum carried by the escaping splash, considering m sc and ∑m ej are much smaller than m ast , that is, there exists ∑m ej <<m ast +m sc , m sc +∑m ej <<m ast , substituting formula (2) into formula (3) yields:

[0053]

[0054] In the formula, |||| is the norm symbol, which can be understood here as taking the absolute value of a scalar and the modulus of a vector.

[0055] Since the definition formula of β is: Substituting formula (4) into it, we can get:

[0056]

[0057] Assume that β has an upper limit and β 2 < k, then through further derivation of formula (5), we can get:

[0058]

[0059] It can be seen that the lower limit of E ej determines the upper limit of β. It is known that E ej ≥0. When E ej is 0, the upper limit of β is

[0060] It is also known that β generally increases with the increase of the relative impact velocity u. Considering different power-law relationships between E ej and u, when u approaches ∞, the threshold of the momentum transfer coefficient β:

[0061]

[0062] In the formula, n represents the power order, C is a constant, and 0 < C < 1. The above is the threshold expression of β in general cases. → means approaching. When E ej is proportional to various power orders of u, the threshold of the momentum transfer coefficient is discussed in different cases.

[0063] Considering that generally n ≤ 2 in general cases, we can further obtain the estimation formula for the maximum velocity change Δv of the target asteroid:

[0064]

[0065] In summary, it can be found that the threshold of β is positively correlated with the mass ratio of the target asteroid to the impactor. The maximum velocity change brought by deflecting the asteroid can be estimated according to this value. Considering that in actual situations, the relative impact velocity u < 10 km / s, when the target asteroid is too large, the upper limit of β is extremely high. At this time, increasing the value of β will not affect the subsequent deflection effect. This theoretically explains the scenario applicability of the kinetic impact technology in the field of planetary defense. The kinetic impact technology is generally applicable to asteroids with an equivalent diameter of dozens of meters to more than one hundred meters. At the same time, this also means that when conducting ground experiments and digital simulation tests, attention should be paid to the scale ratio between the impactor and the asteroid simulation target material. When formulating the planetary defense mission strategy, the optimization goal should not be only to increase β.

[0066] Through the above-mentioned threshold analysis process of the momentum transfer coefficient, we can more clearly understand the relationship between the momentum transfer coefficient and the mass of the spacecraft and the target asteroid. In practical applications, this can be used to estimate the maximum velocity change caused by deflecting the asteroid, design relevant mission indicators such as deflection distance, mission spacecraft mass, number of mission spacecraft, interception orbit selection, etc., and confirm whether kinetic impact technology is suitable for the defense mission.

[0067] Based on the above-mentioned threshold analysis of the momentum transfer coefficient, the present invention provides a method for estimating the maximum velocity change of asteroids deflected by a spacecraft, obtaining the relevant parameters of the target asteroid, performing interception mission planning based on the orbital intersection of the target asteroid and the Earth, determining the relevant parameters of the mission spacecraft, obtaining the absolute velocity of the asteroid and the absolute velocity of the spacecraft at the time of impact based on the interception mission planning, and estimating the maximum velocity change of asteroids deflected by a spacecraft based on the determined momentum transfer coefficient threshold expression and the relevant parameters of the target asteroid, the relevant parameters of the mission spacecraft, the absolute velocity of the asteroid and the absolute velocity of the spacecraft. The specific steps of this method are as follows: Figure 3 As shown, including:

[0068] Step S1: Obtain relevant parameters of the target asteroid, such as the number of six orbital elements, m ast The six orbital elements are used to describe the six parameters necessary to determine the orbit of a celestial body (including asteroids) under the Newtonian laws of motion and Newton's law of universal gravitation when it moves on its Keplerian orbit, including the semi-major axis, eccentricity, orbital inclination, ecliptic longitude of the ascending node, perihelion angle, and mean anomaly.

[0069] Step S2: Design an interception trajectory based on the intersection of the asteroid and Earth's orbits to obtain a relative impact velocity u interval;

[0070] Step S3: Conduct preliminary planning to determine the mission interception orbit, initial spacecraft mass and quantity, etc.

[0071] Step S4: According to the mission plan, obtain the absolute velocity v of the asteroid at the time of impact ast , spacecraft mass m sc and absolute velocity v sc and other parameters;

[0072] Step S5: Estimate the velocity distribution and mass distribution of splashes generated when the spacecraft collides with the asteroid, and estimate the kinetic energy and E carried by the splashes. ej ;

[0073] Step S6: Estimate the momentum transfer coefficient threshold according to the above-mentioned momentum transfer coefficient threshold estimation method, and estimate the maximum velocity change of the target asteroid after the impact.

[0074] Furthermore, the suitability of the kinetic impact technology for the current defense mission can be determined based on the maximum velocity change of the asteroid deflected by the spacecraft. The method further includes:

[0075] Step S7: further calculate the deflection distance after the asteroid velocity changes, and determine whether it meets the mission requirements. If so, the process ends; if not, the process returns to step S3.

[0076] If the above method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.

[0077] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A method for estimating the maximum velocity change of an asteroid deflected by a spacecraft, characterized in that: The following steps are involved: Obtain relevant parameters of the target asteroid; Plan the interception mission and determine the relevant parameters of the mission spacecraft based on the intersection of the target asteroid's orbit with the Earth; Obtaining the absolute velocity of the asteroid and the absolute velocity of the spacecraft at the time of impact according to the interception mission plan; Based on the determined momentum transfer coefficient threshold expression and the target asteroid-related parameters, mission spacecraft-related parameters, the asteroid absolute velocity, and the spacecraft absolute velocity, estimating the maximum velocity change of the asteroid deflected by the spacecraft; Calculating the deflection distance of the asteroid after the speed change based on the maximum speed change of the asteroid deflected by the spacecraft, and determining whether it meets the mission requirements; The momentum transfer coefficient threshold expression is determined by combining the law of conservation of energy and the law of conservation of momentum; The momentum transfer coefficient threshold expression is: Where, is a constant, and , u is the relative impact velocity, Carrying kinetic energy for twice the splashing objects, express Proportional to u raised to the power of n, is the momentum transfer coefficient, is the target asteroid mass, is the mission spacecraft mass, is the mass of the escaped splash produced by the hypervelocity impact, → indicates approaching; In the power n, When , the estimated formula for the maximum velocity change of the asteroid deflected by the spacecraft is: Where, is the maximum velocity change before and after the target asteroid impact.

2. The method for estimating the maximum velocity change of asteroid deflected by a spacecraft according to claim 1, characterized in that: The target asteroid related parameters include the six orbital numbers of the asteroid and the mass of the target asteroid.

3. The method for estimating the maximum velocity change of asteroid deflected by a spacecraft according to claim 1, characterized in that: The mission spacecraft related parameters include the mission spacecraft mass and the mission spacecraft quantity.

4. The method for estimating the maximum velocity change of asteroid deflected by a spacecraft according to claim 1, characterized in that: The upper limit of the momentum transfer coefficient is twice the kinetic energy carried by the splash The lower limit of .

5. The method for estimating the maximum velocity change of asteroid deflected by a spacecraft according to claim 4, characterized in that: The acquisition of the kinetic energy carried by the splashing objects includes: According to the interception mission plan, the velocity distribution and mass distribution of the splashes generated when the spacecraft collides with the asteroid are estimated, and the kinetic energy carried by the splashes is estimated.

6. A computer-readable storage medium, characterized in that The method comprises one or more programs for execution by one or more processors of an electronic device, wherein the one or more programs include instructions for executing the method for estimating the maximum velocity change of an asteroid deflected by a spacecraft as described in any one of claims 1 to 5.

7. An electronic device, characterized in that: The method comprises one or more processors, a memory and one or more programs stored in the memory, wherein the one or more programs include instructions for executing the method for estimating the maximum velocity change of an asteroid deflected by a spacecraft as claimed in any one of claims 1 to 5.

Images