Orbit Design Method for Kinetic Impact Mission of Near-Earth Asteroids with Optimal Deflection Effect

Abstract

The present invention discloses a method for designing an orbit of a kinetic impact mission on a near-Earth asteroid with the optimal deflection effect, comprising the following steps: S1, selecting the initial parameters of the spacecraft, including the departure and arrival times of the spacecraft; S2, designing the spacecraft orbit as a splicing of three segments, namely a large elliptical Earth parking orbit, an Earth escape orbit starting from the large elliptical orbit, and an interplanetary transfer orbit, and calculating the orbit parameters; S3, evaluating the deflection effect of the target near-Earth asteroid; S4, traversing all possible departure and arrival times of the spacecraft, repeating steps S1 to S3, drawing a contour map of the deflection distance versus the departure and arrival times of the spacecraft, and determining the optimal spacecraft launch window from it after eliminating unreasonable times. By adopting a large elliptical Earth parking orbit and screening the spacecraft launch window, the present invention enables the mass and relative velocity of the spacecraft to be relatively large when impacting the asteroid, thereby achieving the optimal asteroid deflection effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of deep space exploration, and particularly relates to a method for designing an orbit for a kinetic impact mission on a near-Earth asteroid with the optimal deflection effect. Background Art

[0002] There is a possibility that near-Earth asteroids will impact the Earth, and they have brought disasters to the Earth's organisms and human society in history. All along, the Earth has been facing a huge threat of impact from extraterrestrial celestial bodies. The impact of near-Earth asteroids on the Earth may induce drastic catastrophes in the climate, ecology, and environment on a global scale.

[0003] In order to cope with the threat of near-Earth object impacts to humans and the Earth, a large amount of work has been carried out in recent years on how to detect in time and effectively reduce the risk of near-Earth asteroids impacting the Earth, and in-depth research has been conducted on aspects such as on-orbit disposal technologies and damage assessment methods. Among many technologies, the principle and implementation approach of kinetic impact are relatively simple, and it is the only technology verified by on-orbit experiments. However, for kinetic impact on asteroids, the effect of the impact on the orbit deflection of the asteroid is closely related to various factors such as the mass of the spacecraft reaching the target and the impact orbit, and parameters such as the launch time and arrival time of the spacecraft affect factors such as the mass of the spacecraft reaching the target, the relative velocity, and the impact angle. Therefore, the optimal design of the kinetic impact orbit of the spacecraft is of great significance and value for the kinetic impact mission on near-Earth asteroids.

[0004] Most existing studies assume that the spacecraft is directly launched by a rocket into an Earth escape orbit and then impacts the target near-Earth asteroid, or the spacecraft departs from a circular Earth parking orbit and realizes the impact on the target near-Earth asteroid through one or more pulsed orbit maneuvers, which have the disadvantages of being greatly restricted by rocket performance and having a large velocity increment required for orbit maneuver. Moreover, most current studies specify the mass of the spacecraft when it impacts the target asteroid, rather than considering the spacecraft mass as a dependent variable that changes with the launch window and the velocity increment of orbit maneuver. Therefore, the optimal kinetic impact orbit cannot be obtained. Summary of the Invention

[0005] The main object of the present invention is to provide a method for designing an orbit for a kinetic impact mission on a near-Earth asteroid with the optimal deflection effect, aiming at the deflection mission of near-Earth asteroids, taking the optimal deflection effect as the goal, proposing a method and process for designing the orbit of the spacecraft starting from the Earth's large elliptical orbit, obtaining parameters such as the departure time and velocity increment of the spacecraft, and solving the problem of designing and optimizing the orbit parameters of the spacecraft for the kinetic impact mission on near-Earth asteroids.

[0006] To achieve the above object, the present invention proposes a method for designing an orbit for a kinetic impact mission on a near-Earth asteroid with the optimal deflection effect, and the steps include:

[0007] S1, select the initial parameters of the spacecraft:

[0008] According to the time when the target near-Earth asteroid may hit the Earth, given the departure time and arrival time of any spacecraft, the flight time is obtained. Then, based on the position of the Earth at the departure time and the position of the target near-Earth asteroid at the arrival time, the starting point and ending point of the interplanetary transfer orbit are obtained respectively;

[0009] S2. Using the conic section splicing method, the orbit of the spacecraft is designed as three segments: a large elliptical Earth parking orbit, an Earth escape orbit starting from the large elliptical orbit, and an interplanetary transfer orbit. And the calculation of the spacecraft orbit parameters is carried out, including the interplanetary transfer orbit parameters, the Earth escape orbit parameters starting from the large elliptical orbit, and the large elliptical Earth parking orbit parameters;

[0010] S3. Conduct the deflection effect evaluation of the target near-Earth asteroid: successively calculate the mass of the spacecraft when it arrives at the near-Earth asteroid, the velocity change of the target near-Earth asteroid, and the deflection distance of the target near-Earth asteroid;

[0011] S4. Traverse all possible departure times and arrival times of the spacecraft, repeat the above steps S1 - S3, and draw a contour map of the deflection distance of the target near-Earth asteroid versus the departure time and arrival time of the spacecraft; from the maximum fuel ratio of the spacecraft, calculate the maximum allowable velocity increment of the spacecraft, and eliminate the departure times and arrival times corresponding to those exceeding the maximum allowable velocity increment in the contour map; finally, determine the optimal launch window with the best deflection effect from the said contour map.

[0012] Furthermore, when using the conic section splicing method in step S2, the spacecraft starts from the large elliptical Earth parking orbit, and then passes through the Earth escape orbit starting from the large elliptical orbit and the interplanetary transfer orbit to achieve an impact with the target near-Earth asteroid; the large elliptical Earth parking orbit is a large elliptical orbit with the Earth as a focus; the Earth escape orbit is a hyperbolic orbit with the Earth as a focus; the interplanetary transfer orbit is an elliptical orbit with the Sun as a focus.

[0013] Furthermore, in step S2, the orbit parameters of the interplanetary transfer orbit include the semi-major axis a, the orbital inclination i, the eccentricity e, the right ascension of the ascending node Ω, the argument of periapsis ω, and the mean anomaly M;

[0014] The orbit parameters of the Earth escape orbit are calculated based on the hyperbolic residual velocity v of the interplanetary transfer orbit ∞ 、the velocity components of the spacecraft in the geocentric inertial system (v x , v y , v z ) and the perigee distance H of the Earth escape orbit;

[0015] The orbit parameters of the large elliptical Earth parking orbit are calculated according to the two-body problem formed by the spacecraft and the Earth.

[0016] Furthermore, in step S2, the velocity increment Δv required to enter the Earth escape orbit from the large elliptical Earth parking orbit is as follows:

[0017] Δv = v p - v p0 ,

[0018] wherein, v p is the velocity of the spacecraft at the perigee of the Earth escape orbit, and there is

[0019]

[0020] wherein, μ e is the Earth's gravitational constant, H is the perigee distance of the Earth escape orbit, and v ∞ is the hyperbolic excess velocity calculated from the orbital parameters of the interplanetary transfer orbit;

[0021] v p0 is the velocity of the spacecraft at the perigee of the large elliptical Earth parking orbit, and there is

[0022]

[0023] wherein, r p0 is the perigee distance of the large elliptical Earth parking orbit, a p is the semi-major axis of the large elliptical Earth parking orbit, and e p is the eccentricity of the large elliptical Earth parking orbit.

[0024] Furthermore, in step S3, the mass m sc of the spacecraft when it reaches the near-Earth asteroid is:

[0025]

[0026] wherein, g0 is the gravitational acceleration on the Earth's surface, M sc is the initial mass of the spacecraft, Δv is the velocity increment, I sp is the specific impulse of the propulsion system, and the symbol exp represents the exponential function with base e.

[0027] Furthermore, in step S3, the velocity change of the asteroid after the collision is:

[0028]

[0029] wherein, V sc and V ast respectively represent the velocities of the spacecraft and the target near-Earth asteroid at the time of impact, m sc and m astrespectively represent the masses of the spacecraft and the target near-Earth asteroid during impact, and β represents the impact efficiency factor, which is used to measure the impact of the sputtered matter generated by the impact on momentum.

[0030] Furthermore, in step S3, the deflection distance of the target near-Earth asteroid is:

[0031] L deflect = d′ - d0,

[0032] where d′ is the perigee distance of the asteroid after deflection, and d0 is the perigee distance of the asteroid in its original orbit.

[0033] Furthermore, the velocity increment Δv applied by the spacecraft in the large elliptical Earth parking orbit cannot exceed the maximum allowable velocity increment Δv of the spacecraft max ; the maximum allowable velocity increment Δv of the spacecraft max The calculation formula is:

[0034]

[0035] where δ is the maximum fuel ratio of the spacecraft, g0 is the acceleration due to gravity on the Earth's surface, and I sp is the specific impulse of the propulsion system.

[0036] Compared with the prior art, the beneficial technical effects of the technical solution of the present invention mainly include:

[0037] 1) By adopting a large elliptical Earth parking orbit instead of the conventional direct departure from the ground or a circular Earth parking orbit, and screening the spacecraft launch window, including the departure time and flight time, the present invention enables the mass and relative velocity of the spacecraft during impact on the target near-Earth asteroid to be relatively large, thereby achieving an optimal deflection effect;

[0038] 2) The present invention provides a feasible method for the orbital design of a spacecraft for a near-Earth asteroid kinetic impact mission. The orbit of the spacecraft calculated by this method can enable the near-Earth asteroid to achieve an optimal deflection effect, laying a theoretical foundation for the engineering implementation of the near-Earth asteroid kinetic impact mission. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on the structures shown in these drawings without creative efforts.

[0040] Figure 1Flowchart for implementing the orbital design method for the near-Earth asteroid kinetic impact mission with the optimal deflection effect in the embodiments of the present invention;

[0041] Figure 2 Schematic diagram of the deflection distance contour obtained in the specific application embodiment of the present invention;

[0042] Figure 3 Two-dimensional schematic diagram of the 2019 PDC kinetic impact mission orbit obtained in the specific application embodiment of the present invention;

[0043] Figure 4 Schematic diagram of the Earth parking orbit and escape orbit for the mission of impacting the 2019 PDC asteroid obtained in the specific application embodiment of the present invention. Specific implementation manner

[0044] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are not all the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0045] The object of the present invention is to design a spacecraft orbit with the optimal deflection effect for the near-Earth asteroid kinetic impact mission, and this method solves the problem of the orbital design of the kinetic impactor.

[0046] The object of the present invention is achieved through the following technical solutions:

[0047] For the orbital design method of the near-Earth asteroid kinetic impact mission with the optimal deflection effect in the present invention, in the initial state, the spacecraft orbits on a large elliptical orbit with the Earth as a focus. The spacecraft applies a certain velocity pulse at a certain moment and enters the Earth escape orbit, and its running trajectory is a hyperbolic orbit with the Earth as a focus. When the spacecraft reaches the boundary of the Earth's gravitational field, its velocity is equal to the hyperbolic residual velocity. Then the spacecraft enters the interplanetary transfer orbit, and its running trajectory is an elliptical orbit with the Sun as a focus. After a certain flight time, the spacecraft impacts the target near-Earth asteroid. The velocity of the near-Earth asteroid changes, its running trajectory changes, and the distance (minimum orbit intersection distance) from the Earth when crossing the ecliptic plane where the Earth is located changes. In order to make the deflection effect of the near-Earth asteroid the best, that is, the change amount of the minimum orbit intersection distance is the largest, it is necessary to optimize parameters such as the departure time and transfer time of the spacecraft.

[0048] As Figure 1 shown, the orbital design method of the near-Earth asteroid kinetic impact mission with the optimal deflection effect in this embodiment includes the following steps:

[0049] S1, Selection of initial parameters of the spacecraft:

[0050] According to the time when the target near-Earth asteroid may hit the Earth, given the departure time and arrival time of any spacecraft, the flight time of the spacecraft is obtained. Then, based on the position of the Earth at the departure time and the position of the target near-Earth asteroid at the arrival time, the starting point and ending point of the interplanetary transfer orbit are obtained respectively.

[0051] S2. Calculation of spacecraft orbit parameters:

[0052] Classified according to the trajectory characteristics during the spacecraft flight, the spacecraft trajectory can be divided into three segments: the Earth parking orbit, the Earth escape orbit, and the interplanetary transfer orbit.

[0053] The present invention adopts the conic curve splicing method for the orbit design of the impact spacecraft. The orbit of the spacecraft is designed as three segments: a large elliptical Earth parking orbit, an Earth escape orbit starting from the large elliptical orbit, and an interplanetary transfer orbit. Then, the calculation of the spacecraft orbit parameters is carried out, including the interplanetary transfer orbit parameters, the Earth escape orbit parameters starting from the large elliptical orbit, and the large elliptical Earth parking orbit parameters.

[0054] The spacecraft starts from the large elliptical Earth parking orbit, and then passes through the Earth escape orbit starting from the large elliptical orbit and the interplanetary transfer orbit to achieve the impact on the target near-Earth asteroid, which has the advantage of fuel saving.

[0055] 1) Calculation of interplanetary transfer orbit parameters

[0056] According to Lambert's theorem, when the position vectors of the initial and final states of the interplanetary transfer orbit are determined, for a certain fixed transfer time Δt, the orbital elements of the transfer orbit can be solved, and then the velocity vectors of the starting and ending points can be obtained.

[0057] The velocities of the starting and ending points of the transfer orbit are obtained by solving the Lambert problem, and the position vector r0 and velocity vector v of the spacecraft in the heliocentric coordinate system are known L , let i, j, k be the unit vectors of the three coordinate axes of the heliocentric coordinate system respectively. The method for calculating the interplanetary transfer orbit elements based on the known position and velocity vectors is as follows:

[0058] According to the vis-viva equation The semi-major axis a can be obtained as:

[0059]

[0060] where, μ s is the solar gravitational constant, with a magnitude of 1.32712×10 20 m 3 ·s -2 .

[0061] From the angular momentum vector h = r0×vL = h x i + h y j + h z k gives the orbital inclination i as:

[0062]

[0063] The right ascension of the ascending node Ω can be obtained from the following formula

[0064]

[0065] Introduce the eccentricity vector e:

[0066]

[0067] where, e x , e y , e z are the components of the eccentricity vector e on the x, y, and z coordinate axes of the heliocentric coordinate system, respectively.

[0068] The eccentricity e can be obtained as:

[0069] e = ||e||

[0070] The direction of the ascending node is from the heliocenter to the direction of the ascending node, and the unit vector n in this direction is

[0071]

[0072] Then the argument of latitude θ and the argument of perigee ω satisfy

[0073]

[0074] When e z > 0, the perihelion is above the ecliptic plane, and vice versa.

[0075] According to the relationship between the argument of latitude θ and the argument of perigee ω, calculate the true anomaly f as:

[0076] f = θ - ω (6)

[0077] The eccentric anomaly E can be calculated from the following formula

[0078]

[0079] From the Kepler equation, the mean anomaly M is

[0080] M = E - e sin E (8)

[0081] 2) Calculation of the Earth escape orbit parameters starting from the large elliptical orbit

[0082] The hyperbolic excess velocity v can be calculated based on the parameters of the interplanetary transfer orbit ∞ (The velocity of the spacecraft at the initial moment of the interplanetary transfer orbit can be obtained by solving the Lambert problem. The difference between the velocity of the spacecraft at the initial moment in the heliocentric coordinate system and the velocity of the Earth is the hyperbolic excess velocity), and based on the velocity components (v x , v y , v z ) of the spacecraft in the geocentric inertial coordinate system and the perigee distance H of the escape orbit, the orbital parameters of the Earth escape orbit starting from the large elliptical orbit can be calculated. The method is as follows:

[0083] The semi-major axis a of the Earth escape orbit e is

[0084]

[0085] where μ e is the Earth's gravitational constant, with a magnitude of 3.986005×10 14 m 3 ·s -2 ;

[0086] The eccentricity e of the Earth escape orbit e is

[0087]

[0088] When the velocity increment is applied at the perigee of the Earth's large elliptical parking orbit, the direction of the velocity increment is the same as the flight direction of the spacecraft. Therefore, the orbital inclination i e of the Earth escape orbit is the same as that of the Earth's large elliptical parking orbit, and the orbital inclination of the Earth's large elliptical parking orbit is known at the beginning of the design. According to the conversion relationship between the geocentric inertial coordinate system and the asymptote coordinate system, and the orbital inclination of the parking orbit, the right ascension of the ascending node Ω e is

[0089]

[0090] In the formula, u is the angle between the hyperbolic excess velocity v ∞ and the direction of the ascending node.

[0091] The asymptote characteristic angle β is the angle between the asymptote of the hyperbolic orbit and v ∞ , and can be calculated by the following formula

[0092]

[0093] The argument of perigee ω e is

[0094] ω e = u + β + 180° (13)

[0095] Typically, a spacecraft applies a velocity increment at the perigee of a large elliptical orbit to escape into a hyperbolic orbit. At this position, the true anomaly f of the escape orbit e = 0. Then, according to the boundary conditions of the interplanetary transfer orbit, the orbital parameters of the Earth escape orbit can be calculated, and further, the velocity of the spacecraft at the perigee of the escape orbit can be obtained as

[0096]

[0097] 3) Calculation of parameters and velocity increment of the large elliptical Earth parking orbit

[0098] The parameters of the large elliptical Earth parking orbit can be calculated based on the two-body problem between the spacecraft and the Earth. Set the perigee distance r of the large elliptical orbit p0 and the apogee distance r a0 . According to

[0099]

[0100] the eccentricity e p and the semi-major axis a p can be calculated. The right ascension of the ascending node Ω and the argument of latitude ω of the large elliptical parking orbit satisfy

[0101]

[0102] where e e is the eccentricity of the hyperbolic escape orbit and can be calculated by Equation (10); RLA is the right ascension and can be calculated by the following formula:

[0103]

[0104]

[0105] From Equation (18) and Equation (16), the right ascension of the ascending node Ω and the argument of latitude ω of the parking orbit can be calculated.

[0106] The spacecraft has the maximum operating velocity at the perigee of the large elliptical parking orbit, with the true anomaly f = 0°, and the velocity is

[0107]

[0108] The velocity increment required for escape at the perigee is the smallest, and the energy required is the smallest. Therefore, the velocity increment for escape is

[0109] Δv = v p - v p0 (20)

[0110] The energy C3 of the escape orbit is:

[0111] C3 = |v∞ | 2 (21)

[0112] According to the above formula, the parameters of the Earth escape orbit can be obtained.

[0113] S3. Evaluate the deflection effect of the target near-Earth asteroid:

[0114] Calculate successively the mass of the spacecraft when it reaches the near-Earth asteroid, the velocity change of the target near-Earth asteroid, and the deflection distance of the target near-Earth asteroid;

[0115] Evaluate the deflection effect based on the relationship between the deflection distance of the target near-Earth asteroid obtained by calculation and the Earth's diameter. To deflect the target near-Earth asteroid away from the Earth, the larger the deflection distance, the better. It should be at least greater than 1 times the Earth's diameter to prevent the near-Earth asteroid that would otherwise hit the Earth from hitting the Earth.

[0116] 1) The mass of the spacecraft when it reaches the near-Earth asteroid

[0117] It is known that the initial mass of the spacecraft (i.e., the wet weight when operating in the large elliptical Earth parking orbit) is M sc , from the velocity increment Δv and the specific impulse I of the propulsion system sp , the mass of the spacecraft when it reaches the near-Earth asteroid can be obtained, that is, the mass m of the spacecraft before hitting the asteroid sc is

[0118]

[0119] In the formula, g0 is the acceleration due to gravity on the Earth's surface, and the symbol exp represents the exponential function with base e.

[0120] 2) The velocity change of the target near-Earth asteroid

[0121] According to the law of conservation of momentum, the velocity change of the target near-Earth asteroid after the collision is calculated as

[0122]

[0123] where, V sc and V ast represent the velocities of the spacecraft and the target near-Earth asteroid at the time of impact respectively, m sc and m ast represent the masses of the spacecraft and the target near-Earth asteroid at the time of impact respectively, and β represents the impact efficiency factor, which is used to measure the influence of the sputtered matter generated by the impact on momentum.

[0124] The value range of β is between 1 and 5. β = 1 corresponds to a perfectly plastic collision, in which the spacecraft and the asteroid combine into a whole and move at the same speed; β = 2 corresponds to a perfectly elastic collision, where the momentum of the impactor is equal in magnitude and opposite in direction to the momentum of the asteroid; β > 2 corresponds to a super-elastic collision.

[0125] Then the velocity of the asteroid after the collision is

[0126] V′ ast = V ast + ΔV ast (24)

[0127] 3) Deflection distance of the target near-Earth asteroid

[0128] According to the conversion relationship between orbital elements and motion state parameters, the orbital elements σ′ of the asteroid after deflection can be obtained, and then it is recursively deduced to the perigee using the two-body orbit initial value theory. Calculate the distance to the Earth at this position. The deflection distance of the target near-Earth asteroid is the change in the distance to the Earth, and the expression is:

[0129] L deflect = d′ - d0 (25)

[0130] In the formula, d′ is the distance to the Earth of the asteroid after deflection, and d0 is the distance to the Earth of the asteroid on the original orbit.

[0131] S4. Determination of the spacecraft launch window:

[0132] Traverse all possible departure times and arrival times of the spacecraft, repeat the above steps S1 to S3, and draw a contour map of the deflection distance of the target near-Earth asteroid versus the departure time and arrival time of the spacecraft, that is, the Pork-chop plot;

[0133] Based on the maximum fuel ratio of the spacecraft, calculate the maximum allowable velocity increment of the spacecraft from the formula. The velocity increment Δv applied by the spacecraft on the large elliptical parking orbit cannot exceed the maximum allowable velocity increment of the spacecraft. Eliminate the departure times and arrival times corresponding to the maximum allowable velocity increment in the contour map. The calculation formula for the maximum allowable velocity increment of the spacecraft is:

[0134]

[0135] In the formula, δ is the maximum fuel ratio of the spacecraft.

[0136] Finally, determine the launch window with the optimal deflection effect from the contour map.

[0137] Figure 1 This is a specific embodiment of the present invention, but it is not limited to this embodiment. Figure 1The flowchart of the present invention is shown. First, the 2019 PDC asteroid is selected as the impact target. 2019 PDC is an asteroid hypothesized by the International Academy of Astronautics during the Near-Earth Asteroid Defense Exercise mission as a kinetic impact mission target at the Planetary Defense Conference in 2019. Classified as an Apollo-type according to its orbital characteristics, it is expected to impact the Earth on April 29, 2027.

[0138] According to the known information given by the conference, the detailed orbital characteristics of 2019 PDC are shown in Table 1.

[0139] Table 1 Orbital characteristics of the 2019 PDC asteroid

[0140]

[0141] In order to conduct a kinetic impact on the asteroid and evaluate the deflection effect, the launch window is selected according to the flowchart below.

[0142] The specific implementation process of the program is as follows: First, the parameters of the spacecraft are set. The initial mass M of the impact spacecraft at the large elliptical orbit is set sc to be 14 t, the specific impulse I of the engine sp is 450 s. The launch time of the spacecraft from the Earth is traversed from January 1, 2020 to January 1, 2027. The transfer orbit flight time is taken as 6 months to 36 months. The launch time takes 2 days as a step, and the transfer time takes 10 days as a step. The launch C3 in all launch cases is traversed, and the velocity change amount generated by the impact on the asteroid is calculated according to Equation (23). Thus, the orbit of the deflected asteroid is obtained by solving the two-body orbit initial value problem, and the change amount of the distance between the asteroid and the Earth caused by the impact is calculated.

[0143] Due to the limitation of the spacecraft's carrying capacity and its own weight, the ratio of fuel to the total mass of the spacecraft is always less than 1. Therefore, for a spacecraft launched with a certain fuel ratio, the maximum velocity increment obtained is certain. In this example, assuming that the mass ratio of fuel is 80%, then the maximum velocity increment Δv obtained by the spacecraft can be obtained according to Equation (26) max is 7.0976×10 3 km / s. When the velocity increment required to escape from the elliptical parking orbit is greater than Δv max , it exceeds the velocity increment capacity that the spacecraft propulsion system can provide, that is, this set of launch window data is discarded.

[0144] In order to achieve the optimal deflection effect, that is, to maximize the change amount of the perigee distance of the 2019 PDC asteroid in April 2027 after the impact, the relevant parameters of the launch window corresponding to the maximum deflection distance are screened and shown in Table 2.

[0145] Table 2 Launch Windows for the 2019 PDC Asteroid Impact Mission

[0146]

[0147] The Earth, the 2019 PDC asteroid, and the transfer orbit of the kinetic impact mission plotted in the same coordinate system are as Figure 3 shown.

[0148] Based on the calculation method of the parameters of the starting point of the escape orbit and combined with the parameters of the launch window, the parameters of the starting point of the escape orbit can be calculated, and the results are shown in Table 3.

[0149] Table 3 Parameters of the Starting Point of the Spacecraft's Earth Escape Orbit

[0150]

[0151] Next, a large elliptical parking orbit is designed according to the conditions of the starting point of the escape orbit. The design of the parking orbit is regarded as a two-body problem between the Earth and the spacecraft, and the true anomaly at the escape point and the velocity increment required for escape are determined according to the boundary conditions at the starting point of escape. In this example, the perigee altitude of the large elliptical orbit is set to 200 km, and the apogee altitude is 36,000 km. The parameters at the perigee of the large elliptical Earth parking orbit calculated are shown in Table 4.

[0152] Table 4 Parameters of the Starting Point of the Earth Parking Orbit

[0153]

[0154] It can be seen that when using a circular orbit with the same perigee altitude as the large elliptical parking orbit, a larger velocity increment is required to enter the escape orbit. Therefore, using a large elliptical parking orbit can achieve escape with lower energy.

[0155] According to the above calculation results, the three-dimensional schematic diagrams of each orbit and the positions where the impulses are applied are plotted, as Figure 4 shown.

[0156] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention. Any method for designing the orbit of the kinetic impact mission of near-Earth asteroids with the optimal deflection effect under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields, is included in the patent protection scope of the present invention.

Claims

1. A method for designing an orbit of a kinetic impact mission on a near-Earth asteroid with optimal deflection effect, characterized in that, It includes the following steps: S1. Select the initial parameters of the spacecraft: According to the time when the target near-Earth asteroid may hit the Earth, arbitrarily specify the departure time and arrival time of the spacecraft to obtain the flight time of the spacecraft. Then, based on the position of the Earth at the departure time and the position of the target near-Earth asteroid at the arrival time, respectively obtain the starting point and ending point of the interplanetary transfer orbit; S2. Adopt the conic curve splicing method to design the orbit of the spacecraft into three segments: a large elliptical Earth parking orbit, an Earth escape orbit starting from the large elliptical orbit, and an interplanetary transfer orbit, and calculate the orbit parameters of the spacecraft, including the interplanetary transfer orbit parameters, the Earth escape orbit parameters starting from the large elliptical orbit, and the large elliptical Earth parking orbit parameters; S3. Evaluate the deflection effect of the target near-Earth asteroid: successively calculate the mass of the spacecraft when it reaches the near-Earth asteroid, the velocity change of the target near-Earth asteroid, and the deflection distance of the target near-Earth asteroid; S4. Traverse all possible departure times and arrival times of the spacecraft, repeat the above steps S1 to S3, and draw a contour map of the deflection distance of the target near-Earth asteroid versus the departure time and arrival time of the spacecraft; then, based on the maximum fuel ratio of the spacecraft, calculate the maximum allowable velocity increment of the spacecraft, and eliminate the departure times and arrival times corresponding to those exceeding the maximum allowable velocity increment in the contour map; finally, determine the launch window with the optimal deflection effect from the contour map; In the step S2, the velocity increment Δv required to enter the Earth escape orbit from the large elliptical Earth parking orbit is: Δv = v p -v p0 , where v p is the velocity of the spacecraft at the perigee of the Earth escape orbit; v p0 is the velocity of the spacecraft at the perigee of the large elliptical Earth parking orbit, and there is where r p0 is the perigee distance of the large elliptical Earth parking orbit, a p is the semi-major axis of the large elliptical Earth parking orbit, e p is the eccentricity of the large elliptical Earth parking orbit, μ e is the Earth's gravitational constant; The velocity increment Δv applied by the spacecraft in the large elliptical Earth parking orbit cannot exceed the maximum allowable velocity increment Δv of the spacecraft max ; the maximum allowable velocity increment Δv of the spacecraft max is calculated by the formula: where δ is the maximum fuel fraction of the spacecraft, g0 is the acceleration due to gravity at the Earth's surface, and I sp is the specific impulse of the propulsion system.

2. The method for designing an orbit of a near-Earth asteroid kinetic impact mission with optimal deflection effect according to claim 1, characterized in that, In the step S2 when adopting the conic curve splicing method, the spacecraft starts from the large elliptical Earth parking orbit, and then passes through the Earth escape orbit starting from the large elliptical orbit and the interplanetary transfer orbit to achieve an impact with the target near-Earth asteroid; The large elliptical Earth parking orbit is a large elliptical orbit with the Earth as a focus; The Earth escape orbit is a hyperbolic orbit with the Earth as a focus; The interplanetary transfer orbit is an elliptical orbit with the Sun as a focus.

3. The orbital design method for a near-Earth asteroid kinetic impact mission with optimal deflection effect according to claim 1, characterized in that, In the step S2, the orbit parameters of the interplanetary transfer orbit include the semi-major axis a, the orbital inclination i, the eccentricity e, the right ascension of the ascending node Ω, the argument of periapsis ω, and the mean anomaly M; The orbital parameters of the Earth escape orbit are calculated based on the hyperbolic excess velocity v obtained from the orbital parameters of the interplanetary transfer orbit ∞ , the velocity components of the spacecraft in the geocentric inertial system (v x , v y , v z ) and the perigee distance H of the Earth escape orbit; The orbit parameters of the large elliptical Earth parking orbit are calculated according to the two-body problem formed by the spacecraft and the Earth.

4. The method for designing the orbit of a near-Earth asteroid kinetic impact mission with the optimal deflection effect according to claim 1, characterized in that In step S2, the velocity v of the spacecraft at the perigee of the Earth escape orbit p is as follows: where μ e is the Earth's gravitational constant, H is the perigee distance of the Earth escape orbit, and v ∞ is the hyperbolic excess velocity calculated from the orbital parameters of the interplanetary transfer orbit.

5. The method for designing an orbit of a near-Earth asteroid kinetic impact mission with the optimal deflection effect according to claim 1, characterized in that, In step S3, the mass m of the spacecraft when it reaches the near-Earth asteroid sc is as follows: where \(g_0\) is the acceleration due to gravity at the Earth's surface, \(M\) sc is the initial mass of the spacecraft, \(\Delta v\) is the velocity increment, \(I\) sp is the specific impulse of the propulsion system, and the symbol exp represents the exponential function with base \(e\).

6. The orbital design method for the near-Earth asteroid kinetic impact mission with the optimal deflection effect according to claim 1, characterized in that, In the step S3, the velocity change of the asteroid after the collision is: Where, V sc and V ast respectively represent the velocities of the spacecraft and the target near-Earth asteroid at the time of impact, m sc and m ast respectively represent the masses of the spacecraft and the target near-Earth asteroid at the time of impact, and β represents the impact efficiency factor, which is used to measure the impact of the spallation produced by the impact on the momentum.

7. The method for designing the orbit of a near-Earth asteroid kinetic impact mission with the optimal deflection effect according to claim 1, wherein In the step S3, the deflection distance of the target near-Earth asteroid is: L deflect = d′ - d0, In the formula, d′ is the distance of the asteroid from the Earth after deflection, and d0 is the distance of the asteroid from the Earth in the original orbit.

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