Direct estimation method for optimal monthly abortion orbit

Abstract

The method comprises the following steps: according to transfer time Tn, a perilune inclination angle in, a perilune height rpn and pause time t0 of a nominal orbit, solving optimal perilune transfer time # imgabs0 #, searching a lower bound rpmin of the perilune height of the orbital around the moon in a feasible region F 'corresponding to the optimal perilune transfer time # imgabs1 #, and calculating the lower bound rpmin of the perilune height of the orbital around the moon according to the lower bound rpmin of the perilune height of the orbital around the moon; and recording the optimal perilune transfer time # imgabs3 # and the optimal perilune height # imgabs4 # as the perilune height # imgabs2 # of the optimal perilune abortion orbit, establishing constraint conditions of the perilune abortion orbit, solving injection speed solutions of the perilune abortion orbit corresponding to the optimal perilune transfer time # imgabs3 # and the optimal perilune height # imgabs4 # of the optimal perilune abortion orbit, and further obtaining the optimal perilune abortion orbit.

Description

Technical Field

[0001] The invention provides an optimal direct estimation method for abort orbit around the moon, which is applicable to the design of manned emergency return mission for lunar landing, and belongs to the fields of aerospace, mission and orbit design technology, and orbit optimization. Background Art

[0002] The lunar abort orbit is an important way of emergency return in manned lunar missions, especially in the second half of the Earth-Moon transfer flight close to the Moon. In actual engineering, fuel constraints are a relatively strict basic constraint on emergency return missions. Therefore, the design of the lunar abort orbit considering the optimal fuel is an important part of the design of the manned lunar emergency return orbit.

[0003] The optimization of the lunar abort orbit is essentially a trajectory optimization problem, which has high nonlinearity and sensitivity, a complex solution process, and a long optimization time. This is acceptable in academic research, but it is rarely recognized in the field of actual engineering applications. On the one hand, the continuous iteration of engineering constraints and mission design processes requires that the optimization design process cannot be too long; on the other hand, engineering often does not require the optimization result to be a strict global optimum in mathematical problems. Therefore, a method that can quickly and directly estimate the optimal lunar abort orbit has become a key and difficult problem in the emergency return research in the field of manned lunar landing engineering. Summary of the invention

[0004] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art and provide a method for directly estimating the optimal lunar abort orbit, which can quickly give the optimal orbit design using the lunar abort orbit in the current situation based on the information of the nominal orbit and the abort point.

[0005] The solution to the technical problem of the present invention is: a method for directly estimating an optimal lunar abort orbit, the method comprising the following steps:

[0006] Transfer time T according to the nominal orbit n 、Perimenal inclination i n 、perilun point height r pn And the termination time t0, solve the optimal perigee transfer time

[0007] Searching for the best perigee transfer time The lower bound r of the perigee height of the corresponding feasible region F is pmin , denoted as the perigee height of the optimal lunar abort orbit

[0008] Establish the constraints of the lunar abort orbit and solve the optimal perigee transfer time and the perigee height of the optimal lunar abort orbit The corresponding lunar abort orbit is injected into the velocity solution to obtain the optimal lunar abort orbit.

[0009] Preferably, the nominal orbit refers to the Earth-Moon transfer orbit.

[0010] Preferably, the stop time t0 refers to the transfer time from the perigee end on the nominal orbit to the stop point, wherein the stop point is a position point on the nominal orbit for stop and return, and the stop time t0 is used to characterize the position of the stop point on the nominal orbit.

[0011] Preferably, the optimal perigee transfer time for:

[0012]

[0013] Preferably, the feasible domain F is defined as:

[0014] F={{r p ,t p}|V=H(r p ,t p ,G)}

[0015] The function H is obtained by taking the feasible parameters {r p ,t p} and the reentry constraint G determine the function of the initial velocity of the abort orbit around the moon. The feasible domain is the feasible parameters {r p ,t p}, r p is the perigee height of the lunar termination orbit, t p This is the time for the perigee transfer.

[0016] Preferably, the reentry constraint G is:

[0017]

[0018] in,

[0019] h E is the reentry point altitude;

[0020] is the constraint target value of the reentry point height;

[0021] γ E is the flight path angle of the spacecraft at the reentry point;

[0022] is the constraint target value of the flight path angle of the spacecraft at the re-entry point.

[0023] Preferably, a binary search is used to find the optimal perigee transfer time. The lower bound r of the perigee height of the corresponding feasible region F is pmin , that is, the perigee height of the optimal lunar abort orbit The specific steps are:

[0024] Find the parameters that make the termination trajectory converge and the parameter that stops the trajectory from converging is the optimal perigee transfer time, r p1 is the height of the perigee of the convergent orbit around the moon, r p2 It is recorded as the perigee height of the non-convergent orbit around the moon;

[0025] In r p1 and r p2 Use the binary search method to obtain a certain convergence accuracy | r p1 -r p2 |<εSearch parameters The boundary between the convergence and non-convergence of the termination orbit is the lower bound r of the perigee height of the termination orbit around the moon in the feasible domain F. pmin , ε is the accuracy requirement of the perigee height value.

[0026] Preferably, the accuracy requirement ε of the perigee height value does not exceed 1 m.

[0027] Preferably, the parameter perigee height and perigee time The constraints for determining an abort orbit around the moon are:

[0028]

[0029] in:

[0030] r p is the lunar center position vector of the perigee of the lunar termination orbit;

[0031] v p is the lunar center velocity vector at the perigee of the lunar termination orbit;

[0032] r p is the perigee height of the termination orbit around the moon;

[0033] R Lunar is the radius of the moon;

[0034] R E ,V E are the position and velocity vector of the reentry point relative to the center of the earth respectively;

[0035] γ E is the flight path angle at the reentry point;

[0036] Rearth is the radius of the Earth;

[0037] h E is the reentry point altitude.

[0038] Preferably, the parameter perigee height is solved and perigee time The corresponding solution for the injection velocity of the lunar abort orbit is:

[0039] First, the pseudo-state two-body splicing method is used to obtain the estimated value of the injection velocity solution of the lunar abort orbit, and then the differential correction method is used under the high-precision dynamic model to obtain the accurate solution of the injection velocity of the lunar abort orbit. Compared with the prior art, the beneficial effects of the present invention are:

[0040] (1) The optimal direct estimation method for the lunar abort orbit proposed in the present invention utilizes orbital characteristics and avoids the traditional complex optimization solution process. It can quickly provide the optimal estimate of the lunar abort orbit for the top-level mission design without complex optimization calculations. It is simple, scientific, and highly practical. It solves the problems of complex optimization process, low solution efficiency, and poor application of engineering iterative design in the optimal design of the lunar abort orbit in engineering, and provides an efficient and convenient tool for the optimization design of the emergency return orbit for manned lunar landing.

[0041] (2) In order to solve the problem of rapid estimation of the optimal lunar abort orbit, the present invention provides a direct estimation method of the optimal lunar abort orbit based on the parametric optimization design of the lunar abort orbit and with the help of the orbital characteristics of the optimal lunar abort orbit, thereby realizing rapid estimation of the optimal lunar abort orbit and having a certain degree of originality.

[0042] (3) The optimal lunar abort orbit characteristics discovered by the present invention have important theoretical value, and the present invention realizes the engineering application and implementation of the theoretical characteristics;

[0043] (4) The present invention is a method that uses the invariant characteristics of the optimal lunar abort orbit to quickly estimate the key design parameters corresponding to the optimal lunar abort orbit based on the two-parameter design of the lunar abort orbit, thereby quickly obtaining the optimal solution of the lunar abort orbit. While quickly solving the problem, it meets the accuracy requirements of the engineering task design and achieves practicality in the engineering field.

[0044] (5) The two-parameter design method used in the process of proposing the present invention is aimed at the common problems of track design. The ideas and perspectives of this solution have broad application value in such related problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Schematic diagram of the lunar abort orbit according to an embodiment of the present invention;

[0046] Figure 2is a flow chart of the method described in an embodiment of the present invention;

[0047] Figure 3 It is a flow chart of the process of solving the optimal lunar abort orbit according to an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The present invention will be further described below in conjunction with the embodiments.

[0049] The present invention provides a method for directly estimating an optimal lunar abort orbit, the flow chart of which is as follows: Figure 2 As shown, it includes the following steps:

[0050] (1) According to the transfer time T of the nominal orbit n 、Perimenal inclination i n 、perilun point height r pn And the termination time t0, solve the optimal perigee transfer time

[0051] The nominal orbit refers to the Earth-Moon transfer orbit. In a specific embodiment of the present invention, the nominal orbit refers to the Earth-Moon transfer orbit in a manned lunar mission, and its orbit type can be a general transfer orbit, a free return orbit, or a hybrid orbit that combines the two. As an emergency return orbit in the Earth-Moon transfer process of a manned lunar landing, the lunar abort orbit refers to an emergency return orbit that no longer requires a large orbital maneuver after a maneuver at the abort point of the Earth-Moon transfer nominal orbit and returns to the Earth side after flying over the moon, such as Figure 1 As shown. The position point on the nominal orbit where the abort return is performed is called the abort point. The transfer time from the perigee end of the nominal orbit of the Earth-Moon transfer nominal orbit to the abort point is used to characterize the position of the abort point on the nominal orbit, which is recorded as the abort time t0. Given the position of the abort point on the nominal orbit, the reentry constraints are the reentry point altitude and the flight path angle.

[0052] The optimal perigee transfer time for:

[0053]

[0054] Solving for the optimal perigee transfer time The derivation process of formula (1) is as follows: a. Establish the optimization model of the lunar abort orbit

[0055] At the end point of the nominal orbit, the spacecraft's relative geocentric state is (R0, V0). The original optimization model for the fuel optimization of the lunar end-of-terminate orbit is as follows:

[0056]

[0057] The design variable V is the injection velocity of the lunar abort orbit after the maneuver at the abort point. The target F(V, V0) represents the magnitude of the velocity increment Δv. (R E ,V E ) is the flight state of the spacecraft relative to the earth at the reentry point. The flight state includes the position R of the spacecraft at the reentry point relative to the earth. E and speed V E .

[0058] F is the feasible domain of the design variable V, and in a specific embodiment of the present invention, it is defined as G={h E =120km,γ E =-6deg}, where h E is the reentry point altitude; the flight path angle γ E It can be equivalently converted into the flight direction angle γ of the aircraft at the reentry point E_RV In this embodiment, the relationship between the two angles is:

[0059]

[0060] In the above optimization model, the design variables are three-dimensional vectors and their three components are highly coupled, which is difficult to decouple without other information.

[0061] Therefore, two new design parameters are proposed: p is the perigee height of the lunar termination orbit, t p is the perigee transfer time, which indicates the transfer time from the perigee end of the nominal orbit to the perigee. Therefore, the transfer time from the stop point to the perigee of the lunar stop orbit is t p -t0. The relative geocentric state (R0, V0) of the spacecraft before the maneuver at the abort point is determined by the nominal orbit and the abort point.

[0062] After the ΔV maneuver, the geocentric velocity at the end point of the lunar end orbit is recorded as V, ΔV = V-V0. Since V0 is known, to determine ΔV, V must be determined. Based on the given design parameters {r p ,t p}, V can be determined by the following constraints,

[0063]

[0064] Among them, (r p ,v p ) is the relative lunar center state of the spacecraft at the perigee on the termination orbit, R Earth is the radius of the Earth. Based on the three constraints in the above formula, the initial velocity V of the corresponding lunar termination orbit can be solved by numerical methods. Therefore, the parameter {r p ,t p} corresponds to a certain lunar abort orbit. All feasible lunar abort orbits at this abort point can be determined by the feasible parameters {r p ,t p} collection to describe.

[0065] The above two design parameters are used as new design variables to replace the speed variable in the original optimization model. Using these two parameters as design variables, the original optimization model of formula (2) is transformed to obtain a new optimization model:

[0066]

[0067] Different from formula (2), the feasible region F′ here is defined as:

[0068] F′={{r p ,t p}|V=H(r p ,t p ,G)}

[0069] The function H is obtained by taking the feasible parameters {r p ,t p} and the reentry constraint G determine the function of the initial velocity of the abort orbit around the moon. The feasible domain is the feasible parameters {r p ,t p}. The determination process is to combine the constraints of formula (3) and use the pseudo-state two-body splicing method and differential correction method to obtain the initial velocity solution of the lunar abort orbit under the precise orbit model. The method and solution process can be found in the document "Two-Parameter Design of Lunar Emergency Return Orbit", which will not be repeated here.

[0070] b. Secondary conversion of lunar abort orbit optimization model based on design parameter characteristics

[0071] Numerical simulations show that when the perigee transfer time t p When fixed, the velocity increment Δv and the perigee height r p It is a positive monotonic relationship; when the height of the perigee r p When fixed, the velocity increment Δv and the perigee transfer time t p It presents a single valley nonlinear function relationship. When the parameter variable near-moon point transfer time t p Fixed, another variable is the height of the perigee r p When the minimum value is reached within the feasible range, the target speed increment is fixed to t p Therefore, the optimal perigee transfer time and the The corresponding minimum perigee height r pmin The minimum velocity increment Δv can be obtained minTherefore, the two-dimensional optimization problem can be further simplified to a one-dimensional optimization problem, where the only design variable is the perigee transfer time t p , the new optimization model is shown in formula (5). After the above two-stage model conversion method, the original three-dimensional optimization model is equivalently converted into a one-dimensional optimization model.

[0072]

[0073] c. Solve the converted optimization model

[0074] The converted one-dimensional optimization model is solved using the Bayesian optimization method, that is, the non-parametric proxy model based on Gaussian process regression is used for optimization. The kernel function directly affects the approximation degree of the Gaussian process to the real data and the proxy effect, and needs to be set in combination with the characteristics of the objective function itself. Here, according to the velocity increment Δv and the perigee transfer time t p The characteristics of a single-valley nonlinear function relationship, the Bayesian optimization kernel function selects the square exponential kernel:

[0075]

[0076] In the formula, the hyperparameter σ l is the characteristic length scale, σ f is the signal standard deviation, which is usually determined by optimization during the calculation process; θ is the hyperparameter of the kernel function, x i is the sample point of the kernel function. j is another sample point of the kernel function. k(x i ,x j |θ) is the kernel function, i.e., the covariance function.

[0077] The acquisition function a(x) selects LCB (Lower Confidence Bound) based on the confidence boundary strategy, where the hyperparameter "β" is taken as 0.5.

[0078] a LCB (x)=μ(x)-βσ(x) (7)

[0079] μ(x) is the mean function, σ(x) is the variance function

[0080] After setting up the important structures of Bayesian optimization, Bayesian optimization can be performed to solve the optimization problem. According to the above optimization model and optimization method, the system framework and solution process of the fuel optimization of the lunar abort orbit at a given abort point are as follows:

[0081] Step 1: Given the nominal orbit of the spacecraft and the abort time t0 used to represent the abort point;

[0082] Step 2: Solve the initial state at the corresponding stop point on the nominal orbit;

[0083] Step 3: Determine the variable near-month transfer time t p Range, Bayesian algorithm initialization;

[0084] Step 4: Find the variable near-moon transfer time t by maximizing the LCB acquisition function p ;

[0085] Step 5: Find the corresponding perigee transfer time t p The minimum perigee distance r p ;

[0086] Step 6: Use the two-stage method to calculate the feasible parameters {r p ,t p}The corresponding target speed increment Δv;

[0087] Step 7: Calculate the current mean μ and variance σ of all data points;

[0088] Step 8: Check whether the number of iterations has reached the maximum. If so, stop all calculations; otherwise, initialize all parameters and go to step 4.

[0089] The implementation diagram of the entire optimization system is shown in Figure 3 shown.

[0090] d. Extract the optimal lunar abort orbit features

[0091] A large number of optimization simulation results show that the parameters corresponding to the optimal fuel orbit around the moon are the perigee transfer time t p It always appears near the transfer time of the nominal orbit and is also affected by the transfer time T of the nominal orbit. n 、Perimenal inclination i n 、perilun point height r pn The position of the stop point, i.e. the stop time t0, is affected. The simulation results of a large number of examples show that the stop time t0 and the transfer time T of the nominal track n 、Perimenal inclination i n 、perilun point height r pn The mutual influence between them is weak and can be regarded as independent. n With r pn 、i n It can also be regarded as approximately independent, r pn and i n Optimal t p There is a certain coupling relationship.

[0092] e. Quantify the influencing features to obtain the optimal parameter estimation formula

[0093] Based on the discussion of the relationship between the influencing factors in the previous section, the following relationship can be approximated:

[0094]

[0095] The function value of the first term f1 is much larger than the function values ​​of the latter two f2 and f3, and there is a difference in magnitude. For the first term f1, when other conditions are the same, the optimal parameter t p and the transfer time T of the nominal orbit n is linearly related, and the ratio is close to 1, so there is

[0096]

[0097] Among them, Δ is the parameter t0, i n 、r pn A small function of Δ is much smaller than T n For the second term f2, the optimal parameter t p It has a quadratic function relationship with t0, so we have

[0098]

[0099] a3=f3(i n ,r pn ) (10)

[0100] In the above formula, the constant term a3 contains f3(i n ,r pn ) function value, compared with the f2 function value, a3 is larger, indicating that the influence of f3 is greater than that of f2. The third term f3 represents the perigee inclination i n and perigee height r pn There is a coupling relationship between the two factors, as shown in the following formula:

[0101]

[0102] The transfer time of the nominal orbit is T n , perigee inclination i n , perigee height r pn And the termination point termination time t0. The design parameters corresponding to the optimal lunar termination orbit are recorded as The final optimal perigee transfer time is obtained by normalizing formula (8)-formula (11) and using a large amount of simulation data. for:

[0103]

[0104] In the above formula, t0 / T n ∈(0,1), the normalized r′ pn∈(0.03,1),i′ n ∈(0.05,1), the extreme values ​​on both sides cannot be obtained. Combining the coefficients a and d, it can be seen intuitively that The most influential factor is the nominal orbit transfer time T n , followed by the termination time t0, and the smallest impact is the perigee height r of the nominal orbit pn and the perigee inclination i n The above direct formula for parameter estimation is obtained after analyzing, extracting and fitting the characteristics of a large number of optimization simulation results after calculating the optimization model after the two-stage conversion in step three.

[0105] The simulation shows that the near-month transfer time t of each feasible variable p The corresponding perigee height r in the feasible region F′ p is a range. You can search through simulation The corresponding r p The lower bound of the range r pmin , according to the fixed perigee transfer time t p The velocity increment Δv and the perigee height r p It is a positive monotonic relationship. At this point, we can get the two design parameters of the optimal lunar abort orbit

[0106] (2) Searching for the optimal perigee transfer time The lower bound r of the perigee height of the corresponding feasible region F′ pmin , denoted as the perigee height of the optimal lunar termination orbit

[0107] The optimal perigee transfer time The corresponding feasible domain F′ has {r p ,t p}Satisfy the preset constraints; r p is the perigee height of the lunar termination orbit, t p is the perigee transfer time;

[0108] The present invention adopts the binary search method to search for the optimal perigee transfer time The lower bound r of the perigee height of the corresponding feasible region F′ pmin , the specific steps are:

[0109] Find the parameters that make the termination trajectory converge and the parameters that terminate the orbit convergence is the optimal perigee transfer time, r p1 is the height of the perigee of the convergent orbit around the moon, r p2It is recorded as the perigee height of the non-convergent orbit around the moon;

[0110] In r p1 and r p2 Use the binary search method to obtain a certain convergence accuracy | r p1 -r p2 |<εSearch parameters The boundary between the convergence and non-convergence of the termination orbit is the lower bound r of the perigee height of the termination orbit around the moon in the feasible domain F′. pmin , ε is the accuracy requirement of the perigee height value.

[0111] The accuracy requirement of the perigee height value is not more than 1m.

[0112] Parameter {r p ,t p The method for determining whether the aborted orbit converges or not can refer to the Two-Parameter Design of Lunar Emergency Return Orbit.

[0113] (3) According to the optimal perigee transfer time and the perigee height of the optimal lunar abort orbit Solve the initial velocity solution of the lunar abort orbit under the lunar abort orbit optimization model, and then obtain the optimal lunar abort orbit.

[0114] The method for solving the initial velocity solution of the lunar abort orbit under the lunar abort orbit optimization model is:

[0115] Firstly, the pseudo-state two-body splicing method is used to obtain a rough value of the initial velocity solution of the lunar abort orbit, and then the differential correction method is used to obtain the initial velocity solution of the lunar abort orbit.

[0116] Example:

[0117] This section uses the simulation case of the real nominal orbit of Apollo 13 as a demonstration of the method. The nominal orbit of Apollo 13 Earth-Moon transfer is a hybrid orbit. The actual short-term continuous maneuver in the middle is simplified to a pulse maneuver and the separation of the Saturn V engine and the attitude adjustment of the command module and service module during the Earth-Moon transfer are ignored. Its orbital parameters and normalized values ​​are shown in Table 1. According to this method, the optimal lunar abort orbit is solved, and the optimal lunar abort orbit design parameters are used. The results are shown in Table 2. From the results in Table 2, it can be seen that, compared with the solution obtained by the direct estimation method of the optimal lunar abort orbit and the theoretical optimal solution, the optimal solution obtained by the direct estimation method has a smaller error, which is within the acceptable range of the project. The result obtained by the method of the present invention can be used as the initial estimate of the high-precision solution of the optimal fuel lunar abort orbit, and can also be used as a design result directly for the emergency return top-level mission design.

[0118] Table 1 Apollo 13 nominal orbit related parameters

[0119]

[0120] Table 2 Comparison of Apollo 13 optimal abort orbit calculations

[0121]

[0122]

[0123] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for directly estimating the optimal lunar abort orbit, characterized in that The steps include: Transfer time T according to the nominal orbit n 、Perimenal inclination i n 、perilun point height r pn And the termination time t0, solve the optimal perigee transfer time Searching for the best perigee transfer time The lower bound r of the perigee height of the corresponding feasible region F is pmin , denoted as the perigee height of the optimal lunar termination orbit Establish the constraints of the lunar abort orbit and solve the optimal perigee transfer time and the perigee height of the optimal lunar abort orbit The corresponding lunar abort orbit is injected into the velocity solution to obtain the optimal lunar abort orbit.

2. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that The nominal orbit refers to the Earth-Moon transfer orbit.

3. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that The stop time t0 refers to the transfer time from the perigee end on the nominal orbit to the stop point, wherein the stop point is the position point on the nominal orbit for the stop return, and the stop time t0 is used to characterize the position of the stop point on the nominal orbit.

4. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that: The optimal perigee transfer time for:

5. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that: The feasible domain F is defined as: F={{r p ,t p }V=H(r p ,t p ,G)} The function H is obtained by taking the feasible parameters {r p ,t p } and the reentry constraint G determine the function of the initial velocity of the abort orbit around the moon. The feasible domain is the feasible parameters {r p ,t p }, r p is the perigee height of the lunar termination orbit, t p This is the time for the perigee transfer.

6. The method for directly estimating the optimal lunar abort orbit according to claim 4, characterized in that: The reentry constraint G is: in, h E is the reentry point altitude; is the constraint target value of the reentry point height; γ E is the flight path angle of the spacecraft at the reentry point; is the constraint target value of the flight path angle of the spacecraft at the re-entry point.

7. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that: Using the binary method to search for the optimal perigee transfer time The lower bound r of the perigee height of the corresponding feasible region F is pmin , that is, the perigee height of the optimal lunar abort orbit The specific steps are: Find the parameters that make the termination trajectory converge and the parameter that stops the trajectory from converging is the optimal perigee transfer time, r p1 is the height of the perigee of the convergent orbit around the moon, r p2 It is recorded as the perigee height of the non-convergent orbit around the moon; In r p1 and r p2 Use the binary search method to obtain a certain convergence accuracy | r p1 -r p2 |<εSearch parameters The boundary between the convergence and non-convergence of the termination orbit is the lower bound r of the perigee height of the termination orbit around the moon in the feasible domain F. pmin , ε is the accuracy requirement of the perigee height value.

8. The method for directly estimating the optimal lunar abort orbit according to claim 7, characterized in that: The accuracy requirement ε of the perigee height value is not more than 1 m.

9. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that: By the parameter perigee height and perigee time The constraints for determining an abort orbit around the moon are: in: r p is the lunar center position vector of the perigee of the lunar termination orbit; v p is the lunar center velocity vector at the perigee of the lunar termination orbit; r p is the perigee height of the termination orbit around the moon; R Lunar is the radius of the moon; R E ,V E are the position and velocity vector of the reentry point relative to the center of the earth respectively; γ E is the flight path angle at the reentry point; R earth is the radius of the Earth; h E is the reentry point altitude.

10. The method for directly estimating the optimal lunar abort orbit according to claim 1, characterized in that: Solving the parameter perigee height and perigee time The corresponding solution for the injection velocity of the lunar abort orbit is: First, the pseudo-state two-body splicing method is used to obtain the estimated value of the injection velocity solution of the lunar abort orbit. Then, the differential correction method is used under a high-precision dynamic model to obtain the exact solution of the injection velocity of the lunar abort orbit.

Images