CN110736469A - Asteroid detection accurate orbit transfer method based on sun-ground rotation coordinate system - Google Patents

Asteroid detection accurate orbit transfer method based on sun-ground rotation coordinate system Download PDF

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CN110736469A
CN110736469A CN201911074223.1A CN201911074223A CN110736469A CN 110736469 A CN110736469 A CN 110736469A CN 201911074223 A CN201911074223 A CN 201911074223A CN 110736469 A CN110736469 A CN 110736469A
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乔栋
李翔宇
黄江川
贾飞达
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Beijing University of Technology
Beijing Institute of Technology BIT
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/24—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 specially adapted for cosmonautical navigation
    • G—PHYSICS
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    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/02—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by astronomical means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation

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Abstract

The invention discloses a method for accurate orbit transfer of asteroid exploration based on a sun-ground rotating coordinate system, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: searching for an optimal interstellar transfer opportunity by using the contour map; establishing a day-ground rotating coordinate system, and converting the optimal transfer opportunity into the rotating coordinate system; based on an elliptic restrictive trisomy kinetic equation, considering the constraint of the starting height of the earth, and correcting the orbit in a rotation system by a second-order differential correction algorithm; and the orbit transfer from the earth to the target asteroid can be realized with high precision and high efficiency by the detector. According to the invention, the earth escape orbit and the solar-centric transfer orbit are considered at the same time, and the splicing of the conical orbits is not needed, so that the precision of orbit design can be improved.

Description

Asteroid detection accurate orbit transfer method based on sun-ground rotation coordinate system
Technical Field
The invention relates to asteroid detection orbit transfer methods under a sun-ground rotating coordinate system, in particular to a high-precision asteroid detection transfer method suitable for considering real ephemeris, and belongs to the technical field of aerospace.
Background
The asteroid is called as the activating stone of the solar system, the research on the asteroid is helpful for people to know the key information of the formation and evolution of the solar system and the origin of life, meanwhile, the observation shows that the asteroid has rich resources, and the development of asteroid detection is helpful for future resource development and utilization, so that asteroid detection is the hot topic in the field of deep space detection.
The asteroid transfer orbit design for detecting the asteroid is a precondition for developing the asteroid detection task, and the total speed increment of the detection task is determined, so that the fuel consumption and the system scale of the detector are determined. The traditional asteroid exploration orbit design firstly carries out transmitter opportunity search based on a two-body model, then completes the design of an earth escape orbit by a conical curve splicing principle, and completes the orbit splicing. The calculation process is cumbersome.
The developed method for designing the minor planet transfer orbit in the prior art [1] (see Hulkower N D, Lau CO, Bender D F. optimal two-impulse transfer for representing the inter-planet-target design. journal of guide, Control, and Dynamics 1984; 7(4):458-461.) gives a method for searching the detection opportunity of the minor planet by using a contour map, which can obtain the optimal two-impulse transfer orbit and the transmission opportunity is independent of time, but does not consider the orbit of the earth emission section.
In the prior art [2] (see: Wang Y., Qiao D., Cui P.. Design of Optimal Impulse transfers from the Sun-Earth library Point to the autonomous [ J ]. Advance in space research.2015., 56(1):176-186) a track Design method for small celestial body detection by using a three-system invariant manifold is proposed, but the method is only suitable for a detector starting from a balance Point track and is not suitable for a detection track Design starting from the Earth.
Disclosure of Invention
The invention discloses an asteroid detection accurate orbit transfer method based on a sun-ground rotating coordinate system, which aims to solve the technical problem of providing high-precision asteroid orbit transfer methods for designing an earth escape section and a sun-center transfer section , and has the advantages of high precision, high efficiency and good convergence.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for accurate orbit transfer of asteroid exploration based on a sun-ground rotating coordinate system, which searches for an optimal interstellar transfer opportunity by utilizing a contour map. And establishing a day-ground rotating coordinate system, and converting the optimal transfer opportunity into the rotating coordinate system. Based on an elliptic restrictive trisomy kinetic equation, the orbit is corrected under a rotation system through a second-order differential correction algorithm by considering the constraint of the departure height of the earth. And the orbit transfer from the earth to the target asteroid can be realized with high precision and high efficiency by the detector. The invention simultaneously considers the earth escape orbit and the solar-centric transfer orbit without splicing the conical orbits. Meanwhile, the influence of the gravity of the earth is always considered in the transfer process, so that the precision of the track design can be improved.
The invention discloses a method for accurate orbit transfer of asteroid detection based on a sun-ground rotating coordinate system, which comprises the following steps:
and , determining the optimal interplanetary transfer opportunity under the two-body model by utilizing the transmission opportunity search according to the selected detection target.
Determining a target according to the detection task, giving a search interval of emission time and transfer time, and transmitting time T to any party sAnd a transfer time TfDetermining the earth position speed r at the departure time according to the ephemerisE(Ts),vE(Ts) And the minor planet position r at the moment of arrivala(Ts+Tf),va(Ts+Tf). And solving the Lambert problem to obtain the velocity increment delta v required by the transfer. Traversing the transmitting time and the transferring time, namely obtaining a contour map of the transmitting opportunity and obtaining the optimal transferring speed incrementChance of (1), denoted as Ts *,Tf *And determining a centroid segment transfer orbit gamma.
Step two: and establishing a daily and terrestrial rotation coordinate system and an elliptic constraint trisomy kinetic equation.
And selecting a sun-ground connecting line as an x axis, using the centroid of a sun-ground system as an origin to establish a rotating coordinate system, wherein a z axis is the angular velocity direction of the earth, and a right-hand coordinate system is formed by the y axis, the x axis and the z axis. Due to the eccentricity of the earth relative to the orbital motion of the sun, an elliptical restrictive three-body dynamic model is established to describe the motion of the detector under a solar-earth rotating coordinate system, and the motion of the detector is described as formula (1):
Figure BDA0002261876330000021
wherein μ ═ m2/(m1+m2) Denotes the mass coefficient of the system, m1Is the solar mass, m2Is the earth mass. Angular velocity ω and angular acceleration of coordinate system rotation from two body motionsRespectively as follows:
Figure BDA0002261876330000024
wherein a and E represent the semi-major axis and eccentricity of the earth's orbit, respectively, E is the angle of approach point, and G is the gravitational constant.
Selecting the semimajor axis of the earth as unit length AU and the reciprocal of the revolution average angular velocity of the earth as unit time TU, then
Figure BDA0002261876330000025
normalized distances from the motion detector to the sun and earth, respectively, where R represents the solar-to-ground distance normalized to , and R is 1-e, also related to the off-point anglecos(E)。
Step three: and converting the position speed state of the sun core segment transfer track into a rotating coordinate system.
Dividing the orbit gamma of the sunset transfer segment into a plurality of segments, and recording the position speed of an end point as ri(Ts+ti),vi(Ts+ti) ( i 1, 2.., n) for a time Ts+tiAnd obtaining the position and speed r of the earth at the corresponding moment according to the ephemerisE(Ts+ti),vE(Ts+ti) So as to determine the instantaneous coordinate axis orientation of the earth rotation system, obtain a transformation matrix P for transforming the inertial system into the rotation system, and record the position and speed of the earth under the rotation system as RE,VEThe position of the detector in the rotation system relative to the earth is Res＝P(ri-rE(Ts+ti))/AU。
Relative to the earth at a velocity of
Figure BDA0002261876330000031
The position speed of the detector under the solar-terrestrial rotation system is Ri＝Res+RE,Vi＝Ves+VE。
Because the size and the mass of the minor planet are small, the position of the detector reaching the minor planet is superposed with the position of the minor planet, so that the state of the detector and the minor planet in the rotating system at the intersection moment is obtained, and the state is used as an initial value to carry out orbit design in the rotating system.
And step four, giving the initial orbit height of the earth, and correcting the transfer orbit under the solar-terrestrial rotation system by adopting a second-order differential correction algorithm to realize the integration design of the earth escape orbit and the solar-centric transfer orbit under the rotation system.
series R obtained by step threei,ViAnd (3) performing reverse integration according to equation (1) for an initial value, and performing reverse design of the transfer orbit from the earth to the asteroid. Due to the influence of ephemeris and gravity, the orbit searched by the transmitter is discontinuous under a rotation system, and position and speed continuity needs to be obtained through second-order differential correctionWhile the orbit needs to meet the initial orbit height from the earth.
The method for realizing the splicing of the two sections of tracks based on the second-order differential correction method comprises the following steps that th section of tracks are from o to p, and p is from p to f, wherein p is the connection point of the two sections, and the initial state of 3 target end points is
Figure BDA0002261876330000034
And
Figure BDA0002261876330000036
corresponding to time to，tpAnd tf. To be provided with
Figure BDA0002261876330000037
Track recursion is carried out by taking points as initial values and the elapsed time tp-toReaching point p. By varying the speed of o-point Vox,Voy,Voz]So that the position of the point p coincides with the position of the point p. The controlled variable is
Figure BDA0002261876330000038
Speed change of point [ delta V ]ox,δVoy,δVoz]TThe integration time is fixed, and the corresponding p point position changes [ delta R [ ]px,δRpy,δRpz]TComprises the following steps:
Figure BDA0002261876330000032
and (4) repeating iteration according to the formula (4) until the position error of the point p and the point p is within an allowable range, and performing position correction on the lower tracks according to the method for splicing the two tracks until all the tracks are continuous.
For the initial state of earth departure, additional terminal constraints need to be considered:
Figure BDA0002261876330000033
wherein R isHIs the radius of the earth, Res,VesFor the position and speed of the detector at the time of earth departure
Figure BDA0002261876330000041
Wherein δ H | | | Res||-RH-200，δQ＝Res·Ves
Wherein
Figure BDA0002261876330000043
Figure BDA0002261876330000044
After th-order differential correction, the locus is continuous in position, but has abrupt changes of speed at the p point, the speed is corrected by the second-order differential correction, and the orbit state transition matrix from the o point to the p point is recorded as follows:
Figure BDA0002261876330000046
then it is corresponding to
Figure BDA0002261876330000047
Wherein:
where-represents the result corresponding to p points from o point integration, and + represents the result corresponding to p points from f point integration. By solving equation (7), a differential correction change amount can be obtained in which the speed of the connecting point is continuous.
For n tracks, there are n +1 connection points
Figure BDA0002261876330000052
The corresponding differential correction relation can be obtained:
δΔV＝MδR (8)
wherein: delta V ═ delta V1… δΔVn-1]T，δR＝[R0t0… Rntn]T
After the velocity correction is completed, since the position of the target point is also changed, the position correction is also performed, and the iteration is repeated until the position error and the velocity error are within the allowable range, the orbit with continuous positions and velocities is obtained, and the orbit meeting the earth departure constraint, namely the design of the earth escape orbit and the solar-centered transfer orbit under the rotation system is realized.
Step five: the transfer orbit obtained under the rotating system is converted into the inertial system to obtain an accurate transfer orbit, and according to the obtained transfer orbit, the detector can realize the orbit transfer from the earth to the target small planet with high precision and high efficiency.
The position and the speed of the transfer orbit obtained in the rotation system are recorded as R and V, and the conversion matrix from the rotation system to the inertia system is obtained as N-P according to the ephemerisTThe position and velocity under the centroid inertia system are:
Figure BDA0002261876330000054
the orbit is an accurate earth-asteroid transfer orbit under the geocentric inertial system, the orbit transfer is carried out according to the obtained earth-asteroid transfer orbit, and the detector can realize the orbit transfer from the earth to a target asteroid with high accuracy and high efficiency.
Has the advantages that:
1. the invention discloses a method for accurate orbital transfer of asteroid detection based on a sun-earth rotation coordinate system, which considers the perturbation influence of the earth gravity on an orbit in the process of orbit design and can improve the orbital transfer accuracy.
2. The asteroid detection accurate orbit transfer method based on the sun-ground rotating coordinate system disclosed by the invention designs the earth starting section orbit and the sun-center transfer section orbit without splicing conical curves, and has the advantages of high precision and high efficiency.
3. The invention discloses a planetoid detection accurate orbit transfer method based on a sun-ground rotating coordinate system, which adopts second-order differential correction to correct the orbit and has good convergence.
Drawings
FIG. 1 is a schematic flow chart of a precise orbital transfer method for asteroid exploration based on a sun-earth rotation coordinate system.
Figure 2 line contour plot of the transmit opportunity for the small planet 2016HO3 in the present example.
FIG. 3 is a schematic diagram of a restricted three-body model rotational coordinate system.
Fig. 4 asteroid 2016HO3 day of rotation is a lower segment transfer orbit in the present example.
Fig. 5 shows that the minor planet 2016HO3 optimally transfers its orbit under the inertial system.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference is made to the following description taken in conjunction with the accompanying drawings and examples.
Example 1:
as shown in fig. 1, taking a detected target asteroid 2016HO3 as an example, the asteroid detection precise orbit transfer method based on the sun-ground rotating coordinate system disclosed in this embodiment includes the following specific implementation steps:
and , determining the optimal interplanetary transfer opportunity under the two-body model by utilizing the transmission opportunity search according to the selected detection target.
Determining a detection target according to the detection task, giving a search interval with the emission time of 2024-2025 and the transfer time of less than 400 days, and emitting time T to any party sAnd a transfer time TfDetermining the earth position speed r at the departure time according to the ephemerisE(Ts),vE(Ts) And the position r of the small celestial body at the time of arrivala(Ts+Tf),va(Ts+Tf). And solving the Lambert problem to obtain the velocity increment delta v required by the transfer. The emission opportunity search graph obtained by traversing the emission time and the transfer time is shown in fig. 2, and the opportunity of the optimal arrival speed increment is obtained from the graph, namely the departure time 2024, 5, 8 and 296 days. The required arrival speed increment is 1.40 km/s. Determining the centroid transition trajectory is shown in fig. 2.
Step two: and establishing a daily and terrestrial rotation coordinate system and an elliptic constraint trisomy kinetic equation.
A sun-ground connecting line is selected as an x axis, a centroid of a sun-ground system is selected as an origin to establish a rotating coordinate system, a z axis is the angular velocity direction of the earth, a right-hand coordinate system is formed by the y axis, the x axis and the z axis, and a schematic diagram of the coordinate system is shown in FIG. 3. Due to the eccentricity of the earth relative to the orbital motion of the sun, an elliptical restrictive three-body dynamic model is established to describe the motion of the detector under a solar-earth rotating coordinate system, and the motion of the detector is described as formula (1):
wherein μ ═ m2/(m1+m2) Denotes the mass coefficient of the system, m1Is the solar mass, m2Is the earth mass. Angular velocity ω and angular acceleration of coordinate system rotation from two body motions
Figure BDA0002261876330000072
Respectively as follows:
Figure BDA0002261876330000073
Figure BDA0002261876330000074
wherein a and E represent the semi-major axis and eccentricity of the earth's orbit, respectively, E is the angle of approach point, and G is the gravitational constant.
Selecting the semimajor axis of the earth as unit length AU and the reciprocal of the revolution average angular velocity of the earth as unit time TU, then
Figure BDA0002261876330000075
The normalized distances from the motion detector to the sun and earth, respectively, where R denotes the normalized distance in time of day and earth, again with respect to the off-point angle R1-eco (e).
Step three: and converting the position speed state of the sun core segment transfer track into a rotating coordinate system.
Dividing the track of the sunset transfer section into 4 sections, and recording the position and the speed of an end point as ri(Ts+ti),vi(Ts+ti) (i-1, 2,3,4) corresponding to a time Ts+tiAnd obtaining the position and speed r of the earth at the corresponding moment according to the ephemerisE(Ts+ti),vE(Ts+ti) So as to determine the instantaneous coordinate axis orientation of the earth rotation system, obtain a transformation matrix P for transforming the inertial system into the rotation system, and record the position and speed of the earth under the rotation system as RE,VEThe position of the detector in the rotation system relative to the earth is Res＝P(ri-rE(Ts+ti))/AU。
Relative to the earth at a velocity of
Figure BDA0002261876330000076
The position speed of the detector under the solar-terrestrial rotation system is Ri＝Res+RE,Vi＝Ves+VE。
The transfer track obtained in step two is switched to the rotating system, and the end points of each segment are shown in FIG. 4.
And step four, giving the initial orbit height of the earth starting to be 200km, and correcting the transfer orbit under the solar-terrestrial rotation system by adopting a second-order differential correction algorithm so as to realize integration design of the earth escape orbit and the solar-centric transfer orbit under the rotation system.
series R obtained by step threei,ViAnd (3) performing reverse integration according to equation (1) for an initial value, and performing reverse design of the transfer orbit from the earth to the asteroid. Due to the influence of ephemeris and gravity of the earth, the orbit obtained by searching of a transmitter is discontinuous under a rotating system, a transfer orbit with continuous position and speed is obtained through second-order differential correction, and the position vector of an initial state relative to the earth under a rotating coordinate system is
R＝[0.000043037794819-0.0000020280073270.000008780836522]T，
Velocity vector of
V＝[0.079169330447528-0.025642181017723-0.393957446314097]T。
The transfer orbit under the rotating train is shown in fig. 4.
Step five: and converting the transfer orbit obtained under the rotating system into the inertial system to obtain an accurate transfer orbit, and according to the obtained transfer orbit, the detector realizes the orbit transfer from the earth to the target small planet with high precision and high efficiency.
The position and the speed of the transfer orbit obtained in the rotation system are recorded as R and V, and the conversion matrix from the rotation system to the inertia system is obtained as N-P according to the ephemerisTThe position and velocity under the centroid inertia system are:
Figure BDA0002261876330000081
the orbit obtained in the step four is transformed into the corresponding earth emission initial state rs＝[-1465.12,-6276.71,-1313.95]Tkm，vs＝[-1.177,-2.182,-11.734]km/s. The transfer orbit under the inertial system is integrated as shown in fig. 5.
The above detailed description, while indicating the objects, aspects and advantages of the present invention, is given by way of illustration , it is understood that the above description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. An accurate orbit transfer method for asteroid detection based on a sun-ground rotating coordinate system is characterized in that: comprises the following steps of (a) carrying out,
step , according to the selected detection target, utilizing the transmission opportunity search to determine the optimal interplanetary transfer opportunity under the two-body model;
step two: establishing a daily and terrestrial rotation coordinate system and an elliptic restrictive three-body kinetic equation;
step three: converting the position speed state of the sun core section transfer track into a rotating coordinate system;
giving the initial orbit height of the earth, correcting the transfer orbit under the sun-earth rotation system by adopting a second-order differential correction algorithm, and realizing body design of the earth escape orbit and the sun-center transfer orbit under the rotation system;
step five: the transfer orbit obtained under the rotating system is converted into the inertial system to obtain an accurate transfer orbit, and according to the obtained transfer orbit, the detector can realize the orbit transfer from the earth to the target small planet with high precision and high efficiency.
2. The method of claim 1, wherein step is performed by,
determining a target according to the detection task, giving a search interval of emission time and transfer time, and transmitting time T to any party sAnd a transfer time TfDetermining the earth position speed r at the departure time according to the ephemerisE(Ts),vE(Ts) And the minor planet position r at the moment of arrivala(Ts+Tf),va(Ts+Tf) (ii) a By passingSolving the Lambert problem to obtain the velocity increment delta v required by the transfer; traversing the transmitting time and the transferring time, namely obtaining a transmitting opportunity contour map, obtaining the opportunity of the optimal transferring speed increment, and recording as Ts *,
Figure FDA0002261876320000011
Determining the centrosegment transfer orbit gamma.
3. The asteroid detection precise orbital transfer method based on the solar-terrestrial rotating coordinate system according to claim 2, characterized in that: the second step is realized by the method that,
selecting a sun-ground connecting line as an x axis, using a centroid of a sun-ground system as an origin to establish a rotating coordinate system, wherein a z axis is the angular velocity direction of the earth, and a right-hand coordinate system is formed by a y axis, the x axis and the z axis; due to the eccentricity of the earth relative to the orbital motion of the sun, an elliptical restrictive three-body dynamic model is established to describe the motion of the detector under a solar-earth rotating coordinate system, and the motion of the detector is described as formula (1):
Figure FDA0002261876320000012
wherein μ ═ m2/(m1+m2) Denotes the mass coefficient of the system, m1Is the solar mass, m2Is the earth mass; angular velocity ω and angular acceleration of coordinate system rotation from two body motions
Figure FDA0002261876320000013
Respectively as follows:
Figure FDA0002261876320000021
wherein a and E respectively represent the orbit semi-major axis and eccentricity of the earth, E is an angle of approach point, and G is a gravitational constant;
selecting the semimajor axis of the earth as unit length AU and the reciprocal of the revolution average angular velocity of the earth as unit time TU, then
Figure FDA0002261876320000023
normalized distances from the motion detector to the sun and earth, respectively, where R represents the solar-to-ground distance normalized to , also related to the off-point angle R1-eco (E).
4. The asteroid detection precise orbital transfer method based on the solar-terrestrial rotating coordinate system according to claim 1 or 2, characterized in that: the third step is to realize the method as follows,
dividing the orbit gamma of the sunset transfer segment into a plurality of segments, and recording the position speed of an end point as ri(Ts+ti),vi(Ts+ti) (i 1, 2.., n) for a time Ts+tiAnd obtaining the position and speed r of the earth at the corresponding moment according to the ephemerisE(Ts+ti),vE(Ts+ti) So as to determine the instantaneous coordinate axis orientation of the earth rotation system, obtain a transformation matrix P for transforming the inertial system into the rotation system, and record the position and speed of the earth under the rotation system as RE,VEThe position of the detector in the rotation system relative to the earth is Res＝P(ri-rE(Ts+ti))/AU；
Relative to the earth at a velocity of
Figure FDA0002261876320000024
The position speed of the detector under the solar-terrestrial rotation system is Ri＝Res+RE,Vi＝Ves+VE；
Because the size and the mass of the minor planet are small, the position of the detector reaching the minor planet is superposed with the position of the minor planet, so that the state of the detector and the minor planet in the rotating system at the intersection moment is obtained, and the state is used as an initial value to carry out orbit design in the rotating system.
5. The method of claim 4 for accurate orbital transfer of asteroid probe based on a day-to-earth rotating coordinate system, characterized in that: the implementation method of the fourth step is that,
series R obtained by step threei,ViPerforming reverse integration according to equation (1) for an initial value, and performing reverse design of the transfer orbit from the earth to the asteroid; due to the influence of ephemeris and gravity of the earth, the orbit obtained by searching of a transmitter is discontinuous under a rotation system, a transfer orbit with continuous position and speed is obtained through second-order differential correction, and meanwhile, the orbit needs to meet the initial orbit height from the earth;
the method for realizing the splicing of the two sections of tracks based on the second-order differential correction method comprises the following steps that the th section of track is from o to p, the second section of track is from p to f, wherein p is the connection point of the two sections, and the initial state of 3 target end points is
Figure FDA0002261876320000025
And
Figure FDA0002261876320000026
corresponding to time to，tpAnd tf(ii) a To be provided with
Figure FDA0002261876320000027
Track recursion is carried out by taking points as initial values and the elapsed time tp-toReach point p; by varying the speed of o-point Vox,Voy,Voz]So that the position of the point p and the position of the point p coincide; the controlled variable is
Figure FDA0002261876320000028
Speed change of point [ delta V ]ox,δVoy,δVoz]TThe integration time is fixed, and the corresponding p point position changes [ delta R [ ]px,δRpy,δRpz]TComprises the following steps:
Figure FDA0002261876320000031
repeating iteration according to the formula (4) until the position error of the point p and the point p is in an allowable range, and performing position correction on the lower sections of tracks according to the method for splicing the two sections of tracks in the same way until all the tracks are continuous;
for the initial state of earth departure, additional terminal constraints need to be considered:
Figure FDA0002261876320000032
wherein R isHIs the radius of the earth, Res,VesFor the position and speed of the detector at the time of earth departure
Figure FDA0002261876320000033
Wherein δ H | | | Res||-RH-200，δQ＝Res·Ves
Figure FDA0002261876320000034
Wherein
Figure FDA0002261876320000035
S2＝[0 0 0]，
Figure FDA0002261876320000036
Figure FDA0002261876320000037
After -stage differential correction, the locus is continuous in position but has sudden changes of speed at the p point, the speed is corrected by the second-stage differential correction, and the orbit state transition matrix from the o point to the p point is recorded as follows:
then it is corresponding to
Figure FDA0002261876320000042
Wherein:
wherein-represents the result corresponding to p point from o point integration, and + represents the result corresponding to p point from f point integration; solving the equation (7) to obtain a differential correction change quantity which enables the speed of the connecting point to be continuous;
for n tracks, there are n +1 connection pointsThe corresponding differential correction relation can be obtained:
δΔV＝MδR (8)
wherein: delta V ═ delta V1…δΔVn-1]T，δR＝[R0t0…Rntn]T
Figure FDA0002261876320000045
After the velocity correction is completed, since the position of the target point is also changed, the position correction is also performed, and the iteration is repeated until the position error and the velocity error are within the allowable range, the orbit with continuous positions and velocities is obtained, and the orbit meeting the earth departure constraint, namely the design of the earth escape orbit and the solar-centered transfer orbit under the rotation system is realized.
6. The method for planetoid exploration precision orbital transfer based on a day-to-earth rotating coordinate system according to claim 5, characterized in that: the fifth step is to realize that the method is that,
the position and the speed of the transfer orbit obtained in the rotation system are recorded as R and V, and the conversion matrix from the rotation system to the inertia system is obtained as N-P according to the ephemerisTThe position and velocity under the centroid inertia system are:
rs＝N(R-RE)×AU,
Figure FDA0002261876320000051
the orbit is an accurate earth-asteroid transfer orbit under the geocentric inertial system, the orbit transfer is carried out according to the obtained earth-asteroid transfer orbit, and the detector can realize the orbit transfer from the earth to a target asteroid with high accuracy and high efficiency.
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