Method for calculating evolution of geosynchronous orbit debris inclination vector

Abstract

The geosynchronous orbit debris inclination vector evolution calculation method disclosed by the application comprises the following steps: firstly, calculating the influence of the J2 term of the earth's non-spherical perturbation on the change rate of the inclination debris, calculating the angular frequency of the geosynchronous orbit debris inclination vector, the period of the precession and the angular rate of the precession under the influence of the J2 term; then, calculating the frequency of the geosynchronous orbit debris inclination vector precession, the period of the precession and the angular rate of the precession caused by the sun's gravity and the moon's gravity respectively; finally, synthesizing and calculating the different angular frequencies, the periods of the inverse precession and the angular rates of the precession. The geosynchronous orbit debris inclination vector evolution calculation method disclosed by the application separately calculates the effects of the J2 term of the earth and the sun and the moon, and compared with the traditional geosynchronous orbit debris inclination vector evolution calculation method which adopts complete numerical calculation, the method has the advantages of fast calculation speed and can be used for the analysis and calculation of the long-term evolution of the geosynchronous orbit debris orbit.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of space debris evolution analysis method, and particularly relates to a geosynchronous orbit debris inclination vector evolution calculation method. BACKGROUND

[0002] Although the geosynchronous orbit debris accounts for a small proportion in space debris, the collision risk and threat of the geosynchronous orbit debris are relatively large due to a large number of spacecrafts in orbit on the geosynchronous orbit. The traditional geosynchronous orbit debris inclination vector evolution calculation method focuses on the influence of the earth J2 term, and adopts integral prediction of the inclination vector evolution, which leads to the integral error becoming larger and larger with the prolongation of time, and the calculation is time-consuming, which is not conducive to long-term prediction of the geosynchronous orbit debris inclination vector evolution. SUMMARY

[0003] The purpose of the present application is to provide a geosynchronous orbit debris inclination vector evolution calculation method, which solves the problem of slow speed of the existing geosynchronous orbit debris inclination vector evolution calculation method.

[0004] The technical scheme adopted by the present application is: a geosynchronous orbit debris inclination vector evolution calculation method, which comprises the following steps: firstly, calculating the influence of the earth non-spherical perturbation main term J2 term on the inclination debris change rate, calculating the angular frequency, the period of precession and the angular rate of precession of the geosynchronous orbit debris inclination vector under the influence of the J2 term; then, calculating the frequency, the period of precession and the angular rate of precession of the geosynchronous orbit debris inclination vector precession caused by the sun gravity and the moon gravity respectively; finally, synthesizing and calculating the different angular frequency, the period of retrograde precession and the angular rate of precession.

[0005] The present application is characterized in that,

[0006] Specifically, the following steps are included:

[0007] Step 1, calculating the change rate of the debris inclination vector under the action of the earth non-spherical perturbation main term J2 term;

[0008] Step 2, calculating the angular frequency, the period and the angular rate of the debris inclination vector under the action of the earth non-spherical perturbation main term J2 term;

[0009] Step 3, calculating the change rate of the debris inclination vector under the action of the sun gravity;

[0010] Step 4, calculating the angular frequency, the period and the angular rate of the debris inclination vector under the action of the sun gravity;

[0011] Step 5, calculating the change rate of the debris inclination vector under the action of the moon gravity;

[0012] Step 6, calculating the angular frequency, the period and the angular rate of the debris inclination vector under the action of the moon gravity;

[0013] Step 7, calculate the rate of change of the inclination vector of the debris under the action of the Earth's non-spherical perturbation main term J2, the sun's gravity and the moon's gravity;

[0014] Step 8: calculate the angular frequency, period and angular rate of the inclination vector of the debris under the action of the Earth's non-spherical perturbation main term J2, the sun's gravity and the moon's gravity.

[0015] The rate of change of the inclination vector of the debris under the action of the Earth's non-spherical perturbation main term J2 is calculated in step 1 by formula (1):

[0016]

[0017] In formula (1), i is the orbital inclination, μ is the Earth's gravity constant, ω e is the spin angular rate of the Earth, R e is the Earth's equatorial radius, i x = sin i cos Ω is the x component of the inclination vector, i y = sin i cos Ω is the y component of the inclination vector, Ω is the ascending node right ascension, J2 is the numerical value of the Earth's non-spherical perturbation main term J2, and r is the geocentric distance of the debris.

[0018] The angular frequency, period and angular rate of the inclination vector of the debris under the action of the Earth's non-spherical perturbation main term J2 are calculated in step 2 by formulas (2), (3) and (4) in turn:

[0019]

[0020]

[0021]

[0022] In formula (2), K J2 is the angular frequency of the inclination vector of the debris under the action of the J2 term; in formula (3), T J2 is the period of the inclination vector of the debris under the action of the J2 term; and in formula (4), γ J2 is the angular rate of the inclination vector of the debris under the action of the J2 term.

[0023] The rate of change of the inclination vector of the debris under the action of the sun's gravity is calculated in step 3 by formula (5):

[0024]

[0025] In formula (5), n is the orbital angular rate of the debris, n s is the angular rate of the sun's apparent motion, and i s is the ecliptic-oblique angle.

[0026] In step 4, the angular frequency, period and angular velocity of the debris inclination vector under the action of the sun's gravity are calculated in turn by formula (6), (7), (8):

[0027]

[0028]

[0029]

[0030] In formula (6), K s is the angular frequency of the debris inclination vector under the action of the sun's gravity; in formula (7), T s is the period of the debris inclination vector under the action of the sun's gravity; in formula (8), γ s is the angular velocity of the debris inclination vector under the action of the sun's gravity.

[0031] In step 5, the rate of change of the debris inclination vector under the action of the moon's gravity is calculated by formula (9):

[0032]

[0033] In formula (9), n m is the angular velocity of the moon's orbital motion, i m is the angle between the ecliptic and the equator, Ω m is the ecliptic longitude of the ascending node,

[0034] In step 6, the angular frequency, period and angular velocity of the debris inclination vector under the action of the moon's gravity are calculated in turn by formula (10), (11), (12):

[0035]

[0036]

[0037]

[0038] In formula (10), K L is the angular frequency of the debris inclination vector under the action of the moon's gravity; in formula (11), T L is the period of the debris inclination vector under the action of the moon's gravity; in formula (12), γ L is the angular velocity of the debris inclination vector under the action of the moon's gravity.

[0039] In step 7, the rate of change of the debris inclination vector under the action of the earth's non-spherical perturbation main term J2, the sun's gravity and the moon's gravity is calculated by formula (13):

[0040]

[0041] in:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] In step 8, the angular frequency, period, and angular rate of the Earth's non-spherical perturbation principal term J2, and the debris tilt vector under the influence of solar and lunar gravity are calculated sequentially using formulas (20), (21), and (22):

[0049]

[0050]

[0051]

[0052] The beneficial effects of this invention are: the method for calculating the inclination vector evolution of geosynchronous orbit debris in this invention addresses the complex perturbation forces affecting the orbital inclination of geosynchronous orbit debris by calculating the effects of the Earth's J2 term and the gravitational forces of the Sun and Moon separately. Compared with traditional methods for calculating the inclination vector evolution of geosynchronous orbit debris using fully numerical calculations, this method has a faster calculation speed and can be used for the analysis and calculation of the long-term orbital evolution of geosynchronous orbit debris. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the method for calculating the inclination vector evolution of geosynchronous orbit debris according to the present invention. Detailed Implementation

[0054] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0055] This invention provides a method for calculating the inclination vector evolution of geosynchronous orbit debris. The method includes first calculating the influence of the Earth's non-spherical perturbation principal term J2 on the rate of change of the inclination vector of the geosynchronous orbit debris, and then calculating the angular frequency, precession period, and precession angular rate of the geosynchronous orbit debris inclination vector under the influence of the J2 term. Next, the frequency, period, and angular rate of the precession of the geosynchronous orbit debris inclination vector caused by solar and lunar gravity are calculated separately. Finally, the different angular frequencies, inverse precession periods, and precession angular rates are synthesized for calculation. Specifically, the method includes the following steps:

[0056] Step 1: Calculate the rate of change of the debris tilt vector under the action of the principal term J2 of the Earth's non-spherical perturbation:

[0057]

[0058] Where i is the orbital inclination, Ω is the right ascension of the ascending node, μ is the Earth's gravitational constant, and ω e R is the Earth's spin angular rate. e i is the radius of the Earth's equator. x =sinisinΩ is the x-component of the tilt vector, i y =sinicosΩ is the y-component of the tilt vector, J2 is the value of the principal term J2 of the Earth's non-spherical perturbation, and r is the geocentric distance of the debris.

[0059] Step 2: Calculate the angular frequency, period, and angular rate of the debris tilt vector under the action of the principal term J2 of the Earth's non-spherical perturbation:

[0060]

[0061]

[0062]

[0063] Where K J2 T is the angular frequency of the fragment tilt vector under the action of the J2 term. J2 γ is the period of the fragment tilt vector under the action of the J2 term. J2 Let J2 be the angular velocity of the fragment tilt vector under the action of the J2 term.

[0064] Step 3: Calculate the rate of change of the debris tilt vector under the influence of solar gravity:

[0065]

[0066] Where n is the orbital angular velocity of the debris, n s Let i be the angular velocity of the apparent motion of the sun. s It is the angle between the yellow and red ecliptic.

[0067] Step 4: Calculate the angular frequency, period, and angular rate of the debris tilt vector under the influence of solar gravity:

[0068]

[0069]

[0070]

[0071] Where K sT is the angular frequency of the debris tilt vector under the influence of solar gravity. s γ is the period of the debris tilt vector under the influence of solar gravity. s Let be the angular velocity of the debris tilt vector under the influence of solar gravity.

[0072] Step 5: Calculate the rate of change of the debris tilt vector under the influence of lunar gravity:

[0073]

[0074] Where n m Let i be the angular velocity of the lunar orbital motion. m It is the angle between the ecliptic and the equator, Ω. m It is the right ascension of the ascending intersection of the lunar orbit.

[0075] Step 6: Calculate the angular frequency, period, and angular rate of the debris tilt vector under the influence of lunar gravity:

[0076]

[0077]

[0078]

[0079] Where K L T is the angular frequency of the debris tilt vector under the influence of lunar gravity. L γ is the period of the debris tilt vector under the influence of lunar gravity. L Let be the angular velocity of the debris tilt vector under the influence of lunar gravity.

[0080] Step 7: Synthesize and calculate the main term J2 of the Earth's non-spherical perturbation, and the rate of change of the debris tilt vector under the influence of solar and lunar gravity:

[0081]

[0082] in

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Step 8: Synthesize and calculate the angular frequency, period, and angular rate of the debris tilt vector under the influence of the Earth's non-spherical perturbation principal term J2 and the gravitational forces of the Sun and Moon:

[0090]

[0091]

[0092]

[0093] Example

[0094] In calculating the rate of change of the debris tilt vector under the influence of the principal term J2 of the Earth's non-spherical perturbation, the unit of the tilt vector is radians, and the unit of the Earth's equatorial radius is meters. The change in the debris tilt vector under the influence of J2 can be obtained by summing the numerical values ​​of the rate of change over time. In calculating the rate of change of the debris tilt vector under the influence of solar and lunar gravity, the unit of the orbital angular rate is radians per second.

[0095] calculate

[0096]

[0097] Then for any possible V(i) x (t0),i y (t0)), V(i) x (t),i y (t))=V(i x (t0),i y (t0) is the invariant manifold of the tilt vector motion of geosynchronous orbit debris under the combined effects of perturbation. The linear system of tilt vector motion under the combined effects of perturbation is a gradient-conjugate system. The ascending intersection of the ecliptic longitude Ω... ms Changes cause the angle of intersection i m Right ascension Ω, the ascending intersection with the white orbit m The change of V, therefore any given V m (i x (t0),i y (t0)), each Ω ms Corresponding to an invariant manifold, thus any given V m (i x (t0),i y For each (t0), there exists a family of invariant manifolds. The trajectory of the tilt vector under the combined action of perturbation is a submanifold of this family of invariant manifolds.

Claims

1. A method for calculating the inclination vector evolution of geosynchronous orbit debris, characterized in that, Includes the following steps: Step 1: Calculate the rate of change of the fragment tilt vector under the action of the principal term J2 of the Earth's non-spherical perturbation using formula (1): （1） In equation (1), For the track inclination angle, The gravitational constant of Earth, This represents the Earth's spin angular rate. The radius of the Earth's equator. For the tilt angle vector x Quantity, For the tilt angle vector y Quantity, Right ascension of the ascending node, Let J2 be the value of the principal term J2 of the Earth's non-spherical perturbation. The distance from the Earth's center to the fragment; Step 2: Calculate the angular frequency, period, and angular rate of the debris tilt vector under the action of the principal term J2 of the Earth's non-spherical perturbation using formulas (2), (3), and (4) in sequence: （2） （3） （4） In equation (2), Let J be the angular frequency of the fragment tilt vector under the action of the J2 term; in equation (3), Let J2 be the period of the fragment tilt vector under the action of the J2 term; in equation (4), The angular velocity of the fragment tilt vector under the action of term J2; Step 3: Calculate the rate of change of the debris tilt vector under the influence of solar gravity using formula (5): （5） In equation (5), The orbital angular velocity of the debris. Let be the angular velocity of the apparent motion of the sun. i s It is the angle between the yellow and red ecliptic; Step 4: Calculate the angular frequency, period, and angular rate of the debris tilt vector under solar gravitational influence using formulas (6), (7), and (8) in sequence: （6） （7） （8） In equation (6), Let be the angular frequency of the debris tilt vector under the influence of solar gravity; in equation (7), Let be the period of the debris tilt vector under the influence of solar gravity; in equation (8), The angular velocity of the debris tilt vector under the influence of solar gravity; Step 5: Calculate the rate of change of the debris tilt vector under the influence of lunar gravity using formula (9): （9） In equation (9), Let be the angular velocity of the moon's orbital motion. It is the angle between the lunar orbit and the equator. It is the right ascension of the ascending intersection of the lunar orbit. ; Step 6: Calculate the angular frequency, period, and angular rate of the debris tilt vector under lunar gravity using formulas (10), (11), and (12) in sequence: （10） （11） （12） In equation (10), Let be the angular frequency of the debris tilt vector under the influence of lunar gravity; in equation (11), Let be the period of the debris tilt vector under the influence of lunar gravity; in equation (12), This is the angular velocity of the debris tilt vector under the influence of lunar gravity; Step 7: Calculate the rate of change of the debris tilt vector under the influence of the Earth's non-spherical perturbation principal term J2 and the gravitational forces of the Sun and Moon using formula (13): （13） in: （14） （15） （16） （17） （18） （19）； Step 8: Calculate the angular frequency, period, and angular rate of the Earth's non-spherical perturbation principal term J2, and the debris tilt vector under the influence of solar and lunar gravity, sequentially using formulas (20), (21), and (22): （20） （21） （22）。

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