Fast spinning weak gravitation target safe landing area assessment method

Abstract

The invention discloses a method for evaluating a safe landing area of a fast-spinning weak-gravity target, and belongs to the field of aerospace. The implementation method comprises the following steps: acquiring basic parameters of the small celestial body, wherein the basic parameters comprise a three-dimensional shape model, density, rotation axis direction, rotation angular velocity and friction angle; establishing a global coordinate system by taking the geometric center of the small celestial body model as an original point, and establishing a local coordinate system on the surface of the global coordinate system; according to the three-dimensional shape model and the density, the gravitational potential around the small celestial body is calculated, and the gravitational acceleration borne by the spacecraft at the landing point is calculated in combination with the position vector of the landing point; based on the rotation angular velocity of the small celestial body, the centrifugal force acceleration borne by the spacecraft at the landing point is calculated. And the resultant acceleration of the spacecraft in the normal direction is obtained by combining the propelling force acceleration of the spacecraft, and the friction force is calculated according to the friction angle. And calculating to obtain the dynamic characteristics of the spacecraft in different areas so as to judge whether the spacecraft can stably land or not, thereby realizing the identification of the safe landing area on the surface of the small celestial body.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for identifying a safe landing area of a fast-spinning weak-gravity target surface, especially for a weak-gravity celestial body with a small mass and a large spin speed, and belongs to the technical field of aerospace. BACKGROUND

[0002] In the current field of space exploration, the detection of small celestial bodies has gradually become a research hotspot. Small celestial bodies, such as asteroids, attract the attention of many research teams due to their unique physical properties and potential scientific research value and resource development prospects. The main goal of asteroid exploration at the present stage is to achieve soft landing and sampling return of small celestial bodies. However, the landing task on the surface of a small celestial body faces many challenges, one of which is the accurate identification of a safe landing area.

[0003] Currently, the existing small celestial body landing area evaluation methods have significant limitations. Traditional optical image analysis relies on visual judgment of the topography of the surface of a small celestial body and can only obtain two-dimensional visual information, which cannot reveal the surface dynamics characteristics and cannot meet the landing evaluation requirements in complex dynamic environments such as fast-spinning small celestial bodies. The analysis method based on limited field detection data is not universal and accurate due to the large differences in the characteristics of small celestial bodies, high cost and long period of field detection, and the difficulty in comprehensive coverage of data. The existing dynamic modeling methods are mainly for large mass celestial bodies and cannot effectively simulate the real dynamic environment of the surface of a small celestial body with small mass, weak gravity, and complex rotation, making it difficult to accurately predict the dynamic response of a spacecraft landing and judge the safety of a landing area. In summary, the existing methods are seriously lacking in comprehensiveness, accuracy, and universality, and there is an urgent need for a new method to accurately identify a safe landing area of a small celestial body to ensure the smooth progress of the exploration mission. SUMMARY

[0004] The existing small celestial body landing area evaluation methods have the technical problem of lacking comprehensiveness, accuracy, and universality. Specifically, traditional optical image analysis cannot deeply understand the dynamic characteristics of the surface of a small celestial body; analysis based on limited field detection data lacks universality and accuracy; and existing dynamic modeling cannot effectively simulate the special surface dynamic environment of a small celestial body, resulting in the inability to accurately identify a safe landing area and affecting the smooth development of a small celestial body exploration mission. The purpose of the present application is to provide a method for evaluating a safe landing area of a fast-spinning weak-gravity target, which can better adapt to various small celestial bodies and significantly improve the universality and accuracy of the evaluation; can accurately simulate the special surface dynamic environment of a small celestial body with small mass, weak gravity, and large centrifugal force due to rotation, thereby more accurately identifying a safe landing area on the surface of a small celestial body. The present application divides the surface of an asteroid into regions that meet different stability conditions to identify a safe landing area on the surface of a small celestial body.

[0005] The purpose of the present application is achieved by the following technical solutions:

[0006] The application discloses a fast-spinning weak-gravity target safe landing area evaluation method, basic parameters of a small celestial body are acquired, including a three-dimensional shape model, density, a rotation axis direction, a rotation angular velocity and a friction angle. A global coordinate system is established with the geometric center of the small celestial body model as an origin, and a local coordinate system is established on the surface of the small celestial body. According to the three-dimensional shape model and the density of the small celestial body, the gravity potential around the small celestial body is calculated, and the gravitational acceleration suffered by a spacecraft at a landing point is calculated in combination with a position vector of the landing point; based on the rotation angular velocity of the small celestial body, the centrifugal force acceleration suffered by the spacecraft at the landing point is calculated. In combination with the propulsion force acceleration of the spacecraft itself, the resultant acceleration of the spacecraft in the normal direction is obtained, and the friction force is calculated according to the friction angle. The dynamic characteristics suffered by the spacecraft in different areas are calculated to determine whether the spacecraft can land stably. The application completes the identification of the safe landing area on the surface of the small celestial body by dividing the surface of the asteroid into areas meeting different stable conditions.

[0007] The application discloses a fast-spinning weak-gravity target safe landing area evaluation method, including the following steps:

[0008] Step one: acquiring basic parameters of a small celestial body; the basic parameters include a three-dimensional shape model, density, a rotation axis direction, a rotation angular velocity and a friction angle of the small celestial body;

[0009] Step two: according to the basic parameters acquired in step one, a global coordinate system with the geometric center as an origin and a local coordinate system on the surface are established, and z-direction unit vectors y-direction unit vectors x-direction unit vectors The conversion relationship of the vector suffered by the spacecraft between the global coordinate system and the local coordinate system is obtained;

[0010] Step three: according to the three-dimensional shape model, the density, the rotation axis direction and the rotation angular velocity of the small celestial body, the gravitational acceleration and the centrifugal force acceleration suffered by the spacecraft at different positions on the surface of the small celestial body are calculated;

[0011] Step four: in combination with the propulsion force acceleration of the spacecraft itself and the friction angle, the friction force between the spacecraft and the surface of the small celestial body is obtained;

[0012] Step five: based on the gravitational acceleration, the centrifugal force acceleration, the propulsion force acceleration and the friction force calculated in steps three and four, a detailed classification of the dynamic characteristics suffered by the spacecraft on the surface of the small celestial body is given, and specific landing unstable situations corresponding to each classification are determined;

[0013] Step 6: Based on step 5, calculate the dynamic characteristics of the spacecraft in different areas on the surface of the small celestial body and complete the division of the safe landing area, that is, realize the safe landing area assessment of the fast-spin weak gravity target.

[0014] Furthermore, the implementation method of step 2 is:

[0015] The geometric center of the small celestial body is the coordinate origin, the rotation axis direction is the Z axis direction, the long axis direction of the ellipsoid is the X axis direction, and the Y axis direction is determined according to the right-hand rule to establish the O-XYZ coordinate system, which is called the global coordinate system. The position vector of the landing point is R = [x, y, z] T , defined by the following parametric equation (1):

[0016]

[0017] Among them, θ∈[-π / 2,π / 2] is the latitude of the small body model, is the model's longitude. a, b, and c represent the three perpendicular semi-axes of the ellipsoid. A local coordinate system o-xyz is established on the surface of the asteroid, where the origin is the spacecraft landing point on the asteroid's surface, and the xy plane is the tangent plane to the asteroid's surface at that origin. The z axis is parallel to the normal vector to the tangent plane.

[0018] The normal vector U is expressed as

[0019]

[0020] Unit normal vector It is expressed as follows.

[0021]

[0022] The y-axis points to the rotation axis of the small celestial body in the northern hemisphere and points in the opposite direction of the rotation axis in the southern hemisphere. The y-axis vector N is as follows

[0023]

[0024] After unitization, it is expressed as

[0025]

[0026] Performing a cross product operation on U and N yields the vector E in the x direction, which indicates the east direction.

[0027]

[0028] Calculated Finally, the acceleration vector received by the spacecraft on the surface of the small celestial body is transformed into the local coordinate system for analysis, and the conversion relationship between the vector received by the spacecraft in the global coordinate system and the local coordinate system is obtained.

[0029] Furthermore, the method for determining the acceleration of gravity in step 3 is as follows:

[0030] For the non-spherical small celestial body model, the gravitational potential Φ around the small celestial body is obtained based on the three-dimensional shape model and density calculation in step 1 g The gravitational acceleration is calculated through the gravitational potential, and the expression is The acceleration due to gravity is expressed in the local coordinate system as in, is the acceleration due to gravity a g The transformation matrix from the global coordinate system to the local coordinate system. The gravitational acceleration is then decomposed along the local coordinate system into the normal component perpendicular to the tangent plane. and the tangential component in the tangent plane

[0031] Furthermore, the method for determining the centrifugal acceleration in step 3 is:

[0032] In the global coordinate system, the centrifugal acceleration is obtained by formula (7):

[0033]

[0034] Where ω0 is the rotational angular velocity of the small celestial body based on step 1. In the local coordinate system, the centrifugal acceleration is expressed as Will Decomposed into normal components perpendicular to the tangent plane and the tangential component parallel to the surface

[0035]

[0036] Furthermore, the method for determining the propulsion acceleration in step 3 is:

[0037] For fast-spinning small celestial bodies, the spacecraft can achieve landing on its surface by actively applying propulsion to improve the landing stability. Propulsion acceleration in the local coordinate system Decomposed into normal components perpendicular to the tangent plane and the tangential component parallel to the surface

[0038] Furthermore, the method for determining the friction force in step 4 is:

[0039] For a spacecraft on the surface of a small celestial body, the friction acceleration is determined by the total acceleration of the spacecraft in the normal direction and the friction angle based on step 1. The normal total acceleration includes the acceleration of gravity, centrifugal force, and propulsion force. The expression of friction acceleration is:

[0040]

[0041] γ is the friction angle. Friction exists only when the normal resultant of the spacecraft is negative.

[0042] Further, step five is implemented by,

[0043] F is the thrust force acting on the spacecraft. p The ratio between the thrust force and the gravity acting on the spacecraft.

[0044]

[0045] Where m is the mass of the spacecraft.

[0046] C t C represents the ratio between the tangential thrust force and the gravity. n C represents the ratio between the normal thrust force and the gravity. The normal acceleration component of the thrust force The tangential acceleration component of the thrust force There are two unstable cases for the spacecraft landing on the surface of the small celestial body,

[0047] Case one, the spacecraft has an effective weight along the normal direction downward, when the combined acceleration of the tangential gravity acceleration and the tangential centrifugal acceleration acting on the spacecraft exceeds the combined acceleration of the friction force acceleration and the tangential thrust force acceleration of the spacecraft, the spacecraft will move along the tangential direction, which is represented as:

[0048]

[0049] Case two, if the combined acceleration of the gravity acceleration and the thrust force acceleration along the normal direction is less than the centrifugal force acceleration along the normal direction, or the normal combined acceleration is positive, the landing instability behavior of the spacecraft will be represented as the spacecraft being thrown along the direction perpendicular to the surface of the small celestial body:

[0050]

[0051] Further, step six is implemented by,

[0052] Based on step five, the region meeting formula (12) is called the tangential unstable region, the region meeting formula (13) is called the normal unstable region, and the remaining region is the tangential stable region. Based on the above definitions of the three regions, the dynamics characteristics of each region on the surface of the small celestial body model are calculated, and the identification of the safe landing region on the surface of the small celestial body is completed.

[0053] Advantages:

[0054] 1. The fast-spinning weak-gravity target safe landing area evaluation method disclosed in the application breaks through the limitation of optical image analysis that can only obtain two-dimensional visual information, provides a more accurate evaluation method for comprehensively understanding the landing environment of small celestial bodies based on the three-dimensional shape model of small celestial bodies.

[0055] 2. The fast-spining weak-gravity target safe landing area evaluation method disclosed in the application comprehensively considers the three-dimensional shape model, density, rotation axis direction and other basic parameters of small celestial bodies, effectively overcomes the method limitations caused by large differences in small celestial body characteristics, and makes the method better adapt to various small celestial bodies and have good universality.

[0056] 3. The fast-spining weak-gravity target safe landing area evaluation method disclosed in the application can accurately simulate the special surface dynamic environment with large centrifugal force by calculating the influence of the rotation of small celestial bodies on the dynamic characteristics of the spacecraft, and improves the reliability of safe landing area identification. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 The fast-spining weak-gravity target safe landing area evaluation method disclosed in the application is a flow chart.

[0058] Figure 2 The local coordinate system in the example of the application is shown in the figure.

[0059] Figure 3 The small celestial body surface gravity acceleration size distribution in the example of the application is shown in the figure.

[0060] Figure 4 The small celestial body surface centrifugal force acceleration size distribution in the example of the application is shown in the figure.

[0061] Figure 5 The landing area distribution diagram when the spacecraft propulsion force acceleration is 0 m / s in the example of the application is shown in the figure. 2

[0062] Figure 6 The landing area distribution diagram when the spacecraft propulsion force acceleration is 0.00005 m / s in the example of the application is shown in the figure. 2

[0063] Figure 7 The landing area distribution diagram when the spacecraft propulsion force acceleration is 0.00015 m / s in the example of the application is shown in the figure. 2 DETAILED DESCRIPTION

[0064] In order to better illustrate the purpose and advantages of the application, the content of the application will be further described below in combination with the drawings and examples.

[0065] Example 1: ​​​

[0066] The embodiment discloses

[0067] The method for identifying the safe landing area on the surface of a small celestial body with an ellipsoidal shape is taken as an example, and Figure 1 The embodiment discloses a method for evaluating the safe landing area of a fast-spinning weak-gravity target, and the implementation steps are as follows:

[0068] Step 1: Obtain the basic parameters of the small celestial body; the basic parameters include the three-dimensional shape model, the density, the direction of the rotation axis, the rotation angular velocity and the friction angle of the small celestial body.

[0069] In order to construct an accurate dynamic model, a large amount of basic data about the target fast-rotating small celestial body needs to be collected first. This includes the three-dimensional shape model, the density ρ, the direction of the rotation axis, the rotation angular velocity ω0 and the friction angle γ of the small celestial body. The three-dimensional shape model of the small celestial body can be obtained by using astronomical observation equipment such as a radio telescope and an optical telescope to obtain the contour image of the small celestial body, and then using image processing and analysis techniques to accurately map the shape. The density of the small celestial body can be obtained by using spectral analysis and other means to understand the material properties of the small celestial body, thereby obtaining the density information and the friction angle data. The direction of the rotation axis and the rotation angular velocity of the small celestial body can be obtained through long-term observation records.

[0070] In the embodiment, the x-axis half-length of the ellipsoidal small celestial body is a = 29.4 m, the y-axis half-length and the z-axis half-length are equal, b = c = 14.1 m. The density of the small celestial body is ρ = 2.7 × 10 3 kg / m 3 , and the rotation angular velocity is 0.00373732 rad / s.

[0071] Step 2: According to the basic parameters obtained in step 1, establish a global coordinate system with the geometric center as the origin and a local coordinate system on the surface, and obtain the z-direction unit vector y-direction unit vector x-direction unit vector Get the conversion relationship between the vector received by the spacecraft in the global coordinate system and the local coordinate system.

[0072] Taking the geometric center of the small celestial body as the coordinate origin and the direction of the rotation axis as the Z-axis direction, the long-axis direction of the ellipsoidal body is the X-axis direction, and the Y-axis direction is determined according to the right-hand rule. A O-XYZ coordinate system is established, which is called a global coordinate system. The position vector of the landing point is R = [x, y, z] T , which can be defined by the following parameter equation (1):

[0073]

[0074] where θ ∈ [-π / 2, π / 2] is the latitude of the small celestial body model, is the longitude of the model; a, b, c represent the three perpendicular semi-axes of the ellipsoid respectively. A local coordinate system o-xyz is established on the surface of the small celestial body, where the coordinate origin is the landing point of the spacecraft on the surface of the small celestial body, the xy plane is the tangent plane of the surface of the small celestial body at the origin, the z axis is parallel to the normal vector of the tangent plane, and the normal vector U is expressed as

[0075]

[0076] The unit vector is expressed in the following form:

[0077]

[0078] The y-axis points to the rotation axis of the small celestial body in the northern hemisphere and points to the opposite direction of the rotation axis in the southern hemisphere; the vector N in the y direction is expressed in the following form

[0079]

[0080] After unitization, the vector in the y direction is expressed as

[0081]

[0082] Then, the cross product operation is performed on U and N to obtain the vector E in the x direction, which represents the east direction;

[0083]

[0084] The calculation result is After that, the conversion relationship between the vector received by the spacecraft and the global coordinate system and the local coordinate system is obtained, and the acceleration vector received by the spacecraft on the surface of the small celestial body can be converted to the local coordinate system for analysis. Figure 2 FIG. 1 is a schematic diagram of the local coordinate system.

[0085] Step three: the gravitational acceleration and the centrifugal force acceleration received by the spacecraft at different positions on the surface of the small celestial body are calculated according to the shape model, density, rotation axis direction and rotation angular velocity of the small celestial body.

[0086] Gravity is a key factor affecting the safe landing of a spacecraft. For a non-spherical small celestial body model, the gravitational potential Φ around the small celestial body is calculated based on the three-dimensional shape model and the density p in step one g ; the gravitational acceleration is calculated through the gravitational potential, and the expression is The gravitational acceleration in the local coordinate system is expressed as wherein is the gravitational acceleration a gThe transformation matrix from the global coordinate system to the local coordinate system. Then the gravity acceleration is decomposed along the local coordinate system into a normal component perpendicular to the tangent plane and a tangential component in the tangent plane

[0087] The gravity acceleration distribution of the ellipsoidal small body surface in this embodiment is shown in Figure 3 The gravity acceleration at the ends of the long axis is the minimum gravity acceleration region on the entire surface, with a minimum value of 1.0219 x 10 -5 m / s 2 ; the gravity acceleration at the north and south poles is the maximum gravity acceleration region on the entire surface, with a maximum value of 1.2322 x 10 -5 m / s 2 .

[0088] In the global coordinate system, the centrifugal acceleration is obtained by formula (7)

[0089]

[0090] where ω0 is the rotation angular velocity of the small body based on step one; in the local coordinate system, the centrifugal acceleration is expressed as In order to better analyze the influence of the centrifugal acceleration on the motion state of the probe on the small body surface, the centrifugal acceleration is decomposed into a normal component perpendicular to the tangent plane and a tangential component parallel to the surface

[0091]

[0092]

[0093] The centrifugal acceleration distribution of the ellipsoidal small body surface in this embodiment is shown in Figure 4 The centrifugal acceleration at the ends of the long axis is the maximum centrifugal acceleration region on the entire small body surface, with a maximum value of 4.1065 x 10 -4 m / s 2 ; the centrifugal acceleration at the north and south poles is the minimum centrifugal acceleration region on the entire small body surface, with a minimum value of 1.1891 x 10 - 5 m / s 2 .

[0094] In-depth research on the dynamics of the small body surface and simulation of the spacecraft landing process, the spacecraft can use its own thrust device to assist in achieving stable landing and adhesion. For fast-spinning small bodies, the spacecraft can achieve landing on its surface by actively applying propulsion force to improve the stability of landing. The propulsion acceleration in the local coordinate system decomposition into a normal component perpendicular to the tangent plane and a tangential component parallel to the surface

[0095] In this example, three cases are calculated, namely no propulsion force, propulsion force F p = 0.001 N and propulsion force F p = 0.003 N, and the direction of the propulsion force is assumed to be perpendicular to the tangent plane.

[0096] The normal acceleration component perpendicular to the tangent plane affects the interaction between the probe and the surface of the small body in the normal direction and the motion state of the probe. For example, it determines whether the probe can stably contact the surface of the small body. In addition, the normal acceleration component also affects the size of the friction between the small body and the spacecraft. The tangential acceleration component parallel to the tangent plane mainly affects the motion of the probe on the surface of the small body in the tangential direction, including the sliding, rolling and other motion trends on the surface.

[0097] Step four: combine the propulsion force acceleration and the friction angle applied by the spacecraft itself to obtain the friction force between the spacecraft and the surface of the small body.

[0098] After the spacecraft contacts the surface of the small body, the acceleration generated by the friction force should also be discussed. For the spacecraft on the surface of the small body, the friction force acceleration is determined by the normal combined acceleration of the spacecraft and the friction angle based on step one. The normal combined acceleration includes the gravitational acceleration, the centrifugal force acceleration and the propulsion force acceleration; the expression of the friction force acceleration is:

[0099]

[0100] where γ is the friction angle, is the normal component of the gravitational acceleration, is the normal component of the centrifugal force acceleration, is the normal component of the propulsion force acceleration; the friction force exists only when the normal force of the spacecraft is negative. In this example, based on step one, the value of the friction angle is γ = 35°.

[0101] Step five: based on the gravitational acceleration, centrifugal force acceleration, propulsion force acceleration and friction force calculated in steps three and four, give a detailed classification of the dynamic characteristics of the spacecraft on the surface of the small body, and clearly define the specific landing instability situation corresponding to each classification.

[0102] The parameter C represents the ratio between the propulsion force F p acting on the spacecraft and the gravitational force of the spacecraft on the surface of the small body;

[0103]

[0104] where m is the mass of the spacecraft, in this embodiment, the mass of the spacecraft is 20 kg; C t represents the ratio of the tangential propulsion force to the gravity; C n represents the ratio of the normal propulsion force to the gravity; the normal acceleration component of the propulsion force the tangential acceleration component of the propulsion force For the spacecraft landing on the surface of a small celestial body, there are two unstable situations,

[0105] Situation one, the spacecraft has an effective weight along the normal direction downward, when the tangential gravity acceleration acting on the spacecraft and the tangential centrifugal acceleration The combined acceleration is greater than the friction force acceleration a f and the combined acceleration of the tangential propulsion force acceleration of the spacecraft , the spacecraft will move along the tangential direction, which is represented as:

[0106]

[0107] Situation two, if the gravity acceleration along the normal direction and the combined acceleration of the propulsion force acceleration is less than the centrifugal force acceleration along the normal direction or the normal combined acceleration is positive, then the landing instability behavior of the spacecraft will be manifested as the spacecraft being thrown along the direction perpendicular to the surface of the small celestial body:

[0108]

[0109] Step six: based on step five, calculate the dynamic characteristics of the spacecraft in different regions on the surface of the small celestial body, complete the division of the safe landing region, that is, realize the safe landing region evaluation of the fast-spinning weak-gravity target.

[0110] Based on step five, the region meeting formula (12) is called the tangential unstable region, the region meeting formula (13) is called the normal unstable region, and the remaining region is the tangential stable region. The dynamic characteristics of the spacecraft in different regions on the surface of the small celestial body model are calculated. When the spacecraft does not apply propulsion force, there are only normal unstable regions and tangential unstable regions on the surface of the ellipsoidal small celestial body. As shown in Figure 5 , the normal unstable region occupies most of the area of the small celestial body, and the tangential unstable region is mainly concentrated in the regions where the centrifugal acceleration of the small celestial body north and south poles is relatively small.

[0111] When the spacecraft applies a propulsion force F p= 0.001 N, the distribution of the three regions is shown in Fig. 4. In this case, the polar regions satisfy the tangential stability condition, which makes the polar regions the safest landing regions. Compared with the case without the propulsion force, the latitude of the normal instability region is reduced, and the area of the normal instability region is reduced; the area of the tangential instability region is enlarged. This shows that the application of the propulsion force changes the distribution of the three types of landing regions on the surface of the small celestial body. Figure 6

[0112] When the spacecraft applies a propulsion force F p = 0.003 N, the distribution of the three regions is shown in Fig. 4. In this case, the polar regions satisfy the tangential stability condition, which makes the polar regions the safest landing regions. Compared with the case without the propulsion force, the latitude of the normal instability region is reduced, and the area of the normal instability region is reduced; the area of the tangential instability region is enlarged. This shows that the application of the propulsion force changes the distribution of the three types of landing regions on the surface of the small celestial body. Figure 7

[0113] The above detailed description further describes the purpose, technical solutions and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the application should be included in the protection scope of the application.​​

Claims

1. A method for assessing the safe landing area of ​​a fast-spinning, weak-gravity target, characterized by: The steps include: Step 1: Obtain basic parameters of the small celestial body; the basic parameters include the small celestial body's three-dimensional shape model, density, rotation axis direction, rotation angular velocity, and friction angle; Step 2: Based on the basic parameters obtained in step 1, establish a global coordinate system with the geometric center as the origin and a local coordinate system of the surface, and obtain the unit vector in the z direction , y-direction unit vector x-direction unit vector Obtain the transformation relationship between the global coordinate system and the local coordinate system of the vector acting on the spacecraft; Step 3: Calculate the gravitational acceleration and centrifugal acceleration experienced by the spacecraft at different locations on the surface of the asteroid based on the asteroid's three-dimensional shape model, density, rotation axis direction, and rotation angular velocity. Step 4: Combine the propulsion acceleration and friction angle exerted by the spacecraft itself to obtain the friction between the spacecraft and the surface of the small celestial body; Step 5: Based on the gravitational acceleration, centrifugal acceleration, propulsive acceleration, and friction calculated in Steps 3 and 4, provide a detailed classification of the dynamic characteristics of the spacecraft on the surface of the small celestial body, and identify the specific landing instability scenarios corresponding to each classification. Step 6: Based on step 5, calculate the dynamic characteristics of the spacecraft in different areas on the surface of the small celestial body and complete the division of the safe landing area, that is, realize the safe landing area assessment of the fast-spin weak gravity target.

2. The method according to claim 1, wherein: The implementation method of step 2 is: The geometric center of the small celestial body is taken as the coordinate origin, the rotation axis direction is the Z axis direction, the long axis direction of the ellipsoid is the X axis direction, and the Y axis direction is determined according to the right-hand rule to establish the O-XYZ coordinate system, which is called the global coordinate system; the position vector of the landing point is R = [x, y, z] T , defined by the following parametric equation (1): Among them, θ∈[-π / 2,π / 2] is the latitude of the small body model, is the longitude of the model; a, b, and c represent the three perpendicular semi-axes of the ellipsoid respectively; a local coordinate system o-xyz is established on the surface of the small celestial body, where the coordinate origin is the landing point of the spacecraft on the surface of the small celestial body, and the xy plane is the tangent plane of the small celestial body surface at the origin; the z axis is parallel to the normal vector of the tangent plane; the normal vector U is expressed as Its unit vector It is expressed as follows; The y-axis points to the rotation axis of the small celestial body in the northern hemisphere and points in the opposite direction of the rotation axis in the southern hemisphere; the vector N in the y direction is as follows After unitization, it is expressed as Perform a cross product operation on U and N to obtain the vector E in the x direction, indicating the east direction; Calculated After that, the conversion relationship between the global coordinate system and the local coordinate system of the vector acting on the spacecraft is obtained, and the acceleration vector received by the spacecraft on the surface of the small celestial body can be converted into the local coordinate system for analysis.

3. The method according to claim 2, wherein: The method for determining the acceleration of gravity in step 3 is as follows: For the non-spherical small celestial body model, the gravitational potential Φ around the small celestial body is obtained based on the three-dimensional shape model and density calculation in step 1 g ; The gravitational acceleration is calculated through the gravitational potential, and the expression is The acceleration due to gravity is expressed in the local coordinate system as in, is the acceleration due to gravity a g The transformation matrix from the global coordinate system to the local coordinate system; then the gravitational acceleration is decomposed along the local coordinate system and subdivided into the normal component perpendicular to the tangent plane and the tangential component in the tangent plane 4. The method according to claim 3, wherein: The method for determining the centrifugal acceleration in step 3 is: In the global coordinate system, the centrifugal acceleration is obtained by formula (7): Where ω0 is the rotational angular velocity of the small celestial body based on step 1; in the local coordinate system, the centrifugal acceleration is expressed as Will Decomposed into normal components perpendicular to the tangent plane and the tangential component parallel to the surface 5. The method according to claim 4, wherein: The method for determining the propulsion acceleration in step 3 is: For fast-spinning small celestial bodies, the spacecraft can achieve landing on its surface by actively applying propulsion to improve the landing stability; the propulsion acceleration in the local coordinate system Decomposed into normal components perpendicular to the tangent plane and the tangential component parallel to the surface 6. The method according to claim 5, wherein: The method for determining friction in step 4 is: For a spacecraft on the surface of a small celestial body, the friction acceleration is determined by the total acceleration of the spacecraft in the normal direction and the friction angle based on step 1. The normal total acceleration includes the normal component of the gravitational acceleration, the normal component of the centrifugal acceleration, and the normal component of the propulsion acceleration. The expression of the friction acceleration is: γ is the friction angle; friction only exists when the resultant force in the normal direction of the spacecraft is negative.

7. The method according to claim 6, wherein: The implementation method of step five is: The parameter C represents the thrust F acting on the spacecraft. p The ratio between the gravitational force on the surface of the small celestial body and the gravitational force on the spacecraft; Where m is the mass of the spacecraft; C t Indicates the ratio of tangential propulsion force to gravity; C n Indicates the ratio of the normal propulsion force to gravity; the normal acceleration component of the propulsion force Tangential acceleration component of the propulsive force There are two unstable situations when a spacecraft lands on the surface of a small celestial body. Case 1: The spacecraft has an effective weight in the normal direction downward. When the combined acceleration of the tangential gravitational acceleration and the tangential centrifugal acceleration acting on the spacecraft exceeds the combined acceleration of the friction acceleration and the tangential propulsion acceleration of the spacecraft, the spacecraft will move in the tangential direction, which can be expressed as: Case 2: If the combined acceleration of gravity and propulsion along the normal direction is less than the centrifugal acceleration along the normal direction, or the normal combined acceleration is positive, the landing instability of the spacecraft will manifest as the spacecraft being thrown in a direction perpendicular to the surface of the small celestial body:

8. The method according to claim 7, wherein: The implementation method of step six is: Based on step five, the area that meets formula (12) is called the tangentially unstable area, the area that meets formula (13) is called the normally unstable area, and the remaining areas are tangentially stable areas. Based on the above definitions of the three areas, the dynamic characteristics of each area on the surface of the small celestial body model are calculated to complete the identification of the safe landing area on the surface of the small celestial body.

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