CN102999616A - Orbital element based interstellar flight launch opportunity searching method - Google Patents

Abstract

The invention relates to an orbital element based interstellar flight launch opportunity searching method, in particular relates to an interstellar flight detector launch opportunity searching and selecting method, and belongs to the field of aerospace technology. The method comprises the following steps of: firstly determining an optimal dual-impulse rendezvous opportunity of a target celestial body and a launch celestial body; establishing the corresponding relationship between ephemeris of the launch celestial body and the mean anomaly in launch; calculating the rendezvous time of the launch celestial body and the target celestial body by the ephemeris of the launch celestial body; acquiring the state of the target celestial body in rendezvous through the ephemeris of the target celestial body, and converting the state into the orbital element, so as to obtain the mean anomaly of the target celestial body corresponding to the preset rendezvous time; and if the mean anomaly is matched with the optimal mean anomaly, judging that the launch opportunity is the optimal launch opportunity of the area, otherwise, readjusting the date corresponding to the optimal launch mean anomaly. The orbital element based interstellar flight launch opportunity searching method provided by the invention has the advantages and effects that the interstellar flight optimal launch opportunity can be searched rapidly with less calculation quantity and high efficiency, meanwhile, the cycle property of the launch opportunity can be accurately recognized and the like.

Description

A kind of space flight launching opportunity searching method based on orbital tracking

Technical field

The present invention relates to a kind of space flight launching opportunity searching method based on orbital tracking, the method that relates in particular to a kind of space flight detector launching opportunity search and select belongs to field of aerospace technology.

Background technology

The search of launching opportunity is the key link in interstellar probe mission design and the planning.In the method for the space flight detector launching opportunity search that has developed, formerly technology [1] is (referring to Sergeyensky A.B., Yin N.H.Interplanetary Mission Design Handbook, Vol.1, Part 1:Earth to Venus Ballistic Mission Opportunities 1991-2005.Jet Propulsion Laboratory, Pasadena, CA, Nov 1983, JPL D:82-43) Pork-chop figure method is proposed, namely by given expection launch time section and time of arrival section, find the solution corresponding Lambert problem, draw out pork-chop figure, then guess according to pork-chop figure preferably initial value, adopt optimized algorithm, search out optimum launching opportunity.The shortcoming of the method is that calculated amount is large, and counting yield is low, because the party's nature of law is a kind of exhaust algorithm.

Formerly technology [2] is (referring to Vasile M., Ceriotti M.Radice G.Global Trajectory Optimization:Can we Prune the solution Space when considering deep space manoeuveres.ESA Report, Ariadna ID 06/4101, Con.Num.20273/06/NL/HE) the launching opportunity search problem that is about to interspace detection is described as take the function of speed increment as the search target, adopts the intelligent optimization algorithm of the search of overall importance such as genetic algorithm to obtain optimum launching opportunity.Although the search efficiency of the method increases than pork-chop figure method, only can search at every turn and obtain institute to the unique result in interval, and can't distinguish periodicity, this is so that relatively large deviation may occur when the larger launching opportunity of span search time.

Efficiently, the launching opportunity searching method is problem demanding prompt solution in interstellar probe mission design and the planning fast.Though adopt Pork-chop figure method can obtain comparatively intuitively the variation tendency of launching opportunity in section preset time, essence belongs to exhaustive method, calculated amount is large, and counting yield is low.Though the intelligent optimization algorithm of employing genetic algorithm etc. can improve search efficiency, because the optimizing algorithm periodicity that can't distinguish launching opportunity of limitting itself, and relatively large deviation may appear.

Summary of the invention

The objective of the invention is to take into account in order to overcome existing searching method the defective of counting yield and precision, propose a kind of space flight launching opportunity searching method based on orbital tracking, can realize efficient, fast search launching opportunity.

A kind of space flight launching opportunity searching method based on orbital tracking is achieved through the following technical solutions: at first obtained by the Optimum two-impulse transfer method between any two non-coplanar non co axial elliptical orbits and target celestial body between the contour map of global optimum's two pulse intersections; Mean anomaly and the corresponding flight time of target celestial body when the mean anomaly of the earth, intersection when obtaining global optimum two pulses and shift emission by contour map.Obtain the x time corresponding to mean anomaly of the earth by the ephemeris of the earth, extrapolate time with the target celestial body intersection by the flight time.The state of target celestial body when obtaining intersection by the ephemeris of target celestial body, convert it into orbital tracking, thereby obtain the mean anomaly of predetermined corresponding target celestial body of intersection time, if this mean anomaly is complementary with the mean anomaly of optimum, then this launching opportunity is the launching opportunity of this zone optimum, otherwise readjusts optimum date corresponding to earth transmission mean anomaly.

Concrete steps are:

Step 1, determine target celestial body with the emission celestial body optimum two pulse intersection chances

Optimum two-impulse transfer method by between any two non-coplanar non co axial elliptical orbits obtains launching the contour map of global optimum's two pulse intersections between celestial body and the target celestial body; Found the minimum point span of the required speed increment of optimum two pulse intersections by the contour map correspondence, in this scope, choose arbitrarily a value, launch the initial value of celestial body and target celestial body mean anomaly during as emission and intersection, the Optimal Rendezvous mean anomaly of target celestial body reached by launching the detector flight time of celestial body to target celestial body when the optimum of emission celestial body was launched mean anomaly, intersection when obtaining global optimum's two pulses transfer emission by Newton iteration method.

The corresponding relation of mean anomaly when the celestial body ephemeris is launched in step 2, foundation with emission

Time interval according to the given launching opportunity of task, obtain launching celestial body at position and the speed state of this time interval by the planet ephemeris, and convert it into the form of orbital tracking, find the corresponding relation of emission celestial body launch time and mean anomaly, find further that the step 1 gained is optimum to be launched all launch times corresponding to mean anomaly.

Step 3, the corresponding relation of mean anomaly when setting up target celestial body ephemeris and intersection

Launch time and the flight time of the emission celestial body that is obtained by step 2, obtain all predetermined intersection times (launch time+flight time) of detector and target celestial body, ephemeris by target celestial body obtains corresponding target celestial body position and speed state of each predetermined intersection time, convert it into the form of orbital tracking, thereby obtain predetermined intersection mean anomaly corresponding to each predetermined intersection time of target celestial body.

Whether step 4, differentiation emission celestial body and target celestial body satisfy the geometric relationship of Optimal Rendezvous

The Optimal Rendezvous mean anomaly that the predetermined intersection mean anomaly that obtains according to step 3 and step 1 are tried to achieve, consistent or difference is less than the ε principle of (ε is according to determining task time and accuracy requirement) according to the two, and intersection time corresponding to launch time corresponding to this predetermined intersection mean anomaly and Optimal Rendezvous mean anomaly of choosing is as the optimum transmit chance in the given launching opportunity time interval.

Beneficial effect

The inventive method is described the geometric relationship that the celestial body launching opportunity changes by orbital tracking, the contrast prior art, can realize that fast search, calculated amount that the space flight optimum transmitter is understood are little, efficient is high, can accurately distinguish advantage and the effects such as periodicity of launching opportunity simultaneously.

Description of drawings

Fig. 1 is the space flight launching opportunity searching method process flow diagram based on orbital tracking of the present invention;

Fig. 2 is the contour map of the total speed increment of Optimum two-impulse transfer track in the embodiment.

Embodiment

The below to be surveying 6489 Golevka asteroids as example from earth transmission, and by reference to the accompanying drawings the embodiment of the inventive method elaborated.

A kind of space flight launching opportunity searching method based on orbital tracking, its basic procedure as shown in Figure 1, the concrete steps of present embodiment comprise:

Step 1, determine the optimum two pulse intersection chances of target celestial body and the earth

Adopt Optimum two-impulse transfer method between any two non-coplanar non co axial elliptical orbits to obtain and target celestial body between the contour map of global optimum's two pulse intersections.

Optimum two-impulse transfer method between any two non-coplanar non co axial elliptical orbits is described as: ignore the required time of earth parking orbit of leaving, the perigee of earth parking orbit is r _P1With the apogee be r _A1, then sentence escape hyperbolic curve hypervelocity V at the perigee _{∞ 1}The gravitational field of the earth of escaping out enters the increment Delta V of the required speed of the solar system ₁For:

$\mathrm{\Δ}{V}_1=\sqrt{V_{\∞1}^2+2{\mathrm{\μ}}_1/r_{p1}}-\sqrt{{2\mathrm{\μ}}_1{r}_{a1}/\left[r_{p1}(r_{a1}+r_{p1})\right]}---\left(1\right)$

μ wherein ₁Be Gravitational coefficient of the Earth.

Detector applies a pulse at the asteroidal object height of distance place and makes it to form surround orbit, and applying pulse point is pericenter, then required speed increment Δ V ₂For:

$\mathrm{\Δ}{V}_2=\sqrt{V_{\∞2}^2+(2{\mathrm{\μ}}_2/r_{p2})}-\sqrt{{2\mathrm{\μ}}_2{r}_{a2}/\left[r_{p2}(r_{a2}+r_{p2})\right]}---\left(2\right)$

μ wherein ₂Be asteroidal gravitational constant, r _P2And r _A2Be respectively pericenter and the apocenter of asteroid target flying around orbit.

Definition I ₁=V _{∞ 1}, I ₂=V _{∞ 2}, then detector at the required total speed increment of day heart transfer orbit is:

$J=\mathrm{\Δ}{V}_1+\mathrm{\Δ}{V}_2=\sqrt{I_1\·I_1+\left(\frac{{2\mathrm{\μ}}_1}{r_{p1}}\right)}-\sqrt{\frac{{2\mathrm{\μ}}_1{r}_{a1}}{r_{p1}(r_{a1}+r_{p1})}}+\sqrt{I_2\·I_2+\left(\frac{{2\mathrm{\μ}}_2}{r_{p2}}\right)}-\sqrt{\frac{{2\mathrm{\μ}}_2{r}_{a2}}{r_{p2}(r_{a2}+r_{p2})}}---\left(3\right)$

If detector during from earth transmission the mean anomaly of the earth be M ₁, asteroidal mean anomaly was M when detector arrived the target asteroid ₂, then try to achieve by the earth and asteroidal other orbital elements and set out and position vector when arriving, if time and the direction of motion of detector for known flight just can further be tried to achieve the escape hyperbolic curve V that exceeds the speed limit _{∞ 1}And V _{∞ 2}

The mean anomaly M of the earth during for fixed transmission ₁Asteroidal mean anomaly M during with arrival target asteroid ₂Two pulse optimization problems of transfer orbit, if selected direction of motion only has the required total speed increment of flight time t and transfer orbit relevant so.The classical way of finding the solution Lambert problem that is provided by Gauss as can be known, the latus rectum p of transfer orbit _tWith the flight time direct relation is arranged.Then the required total speed increment J of heart transfer orbit on the same day has hour:

$\frac{\∂J}{{\∂p}_t}=\frac{\∂\mathrm{\Δ}{V}_1}{\∂p_t}+\frac{\∂\mathrm{\Δ}{V}_2}{{\∂p}_t}=0---\left(4\right)$

To can get behind (3) formula substitution (4) formula abbreviation:

$\frac{I_1\·(\∂I_1/\∂p_t)}{\mathrm{\Δ}{V}_1+\sqrt{\frac{{2\mathrm{\μ}}_1{r}_{a1}}{r_{p1}(r_{a1}+r_{p1})}}}+\frac{I_2\·(\∂I_2/\∂p_t)}{\mathrm{\Δ}{V}_2+\sqrt{\frac{{2\mathrm{\μ}}_2{r}_{a2}}{r_{p2}(r_{a2}+r_{p2})}}}=0---\left(5\right)$

Can get the speed V that detector separates with the earth after finding the solution _F1Speed V with the target asteroid rendezvous time _T2Be respectively:

V _t1=±(v+zU ₁)=I ₁+V _E （6）

V _t2=±(v-zU ₂)=V _A-I ₂ （7）

V wherein _EAnd V _AIt is respectively the velocity that the earth and target asteroid revolve around the sun, more than in two formulas+number refer to " short distance " (track of namely realizing by the Angulation changes amount θ less than the π radian shifts) ,-number refer to " long-range " (namely shifting by the track of realizing less than the change amount of 2 π radians greater than the π radian).U ₁And U ₂The unit direction vector that represents respectively the earth and target asteroid position, v and z can be tried to achieve by following equation (8):

$v=\sqrt{{\mathrm{\μp}}_t}(r_2-r_1)/|r_1\×r_2|,$ $z=\sqrt{\mathrm{\μ}/p_t}\mathrm{tg}(\mathrm{\θ}/2)---\left(8\right)$

Here, r ₁And r ₂Be respectively the initial and terminal position vector of detector, θ is r ₁And r ₂The angle of vector.I ₁, I ₂To p _tPartial derivative can get:

$\∂I_1/\∂p_t=\±(p_t/2)(v-{\mathrm{zU}}_1),$ $\∂I_2/\∂p_t=\stackrel{\‾}{+}(p_t/2)(v+{\mathrm{zU}}_2)---\left(9\right)$

p _tIn solution procedure, satisfy certain boundary condition, its maximal value p _MaxWith minimum value p _MinBe respectively:

$p_{\min }=\frac{r_1{r}_2-r_1\·r_2}{r_1+r_2+\sqrt{2(r_1{r}_2+r_1\·r_2)}},$ $p_{\max }=\frac{r_1{r}_2-r_1\·r_2}{r_1+r_2-\sqrt{2(r_1{r}_2+r_1\·r_2)}}---\left(10\right)$

Adopt the method for Newton iteration to try to achieve the p that satisfies optimum solution _tTo the position, can try to achieve the p that satisfies optimum solution for each of the revolution orbit at the earth and its place of asteroid _t, and a p _tCan calculate the i.e. J in " long-range " situation of two J _lJ in " short distance " situation _s, present embodiment only keeps wherein less one.

Suppose that earth parking orbit is highly to be the circular orbit of 200km, arrive that detector forms the circular parking orbit that height is 10km behind the 6489 Golevka asteroids, the contour map of the speed increment that the Optimum two-impulse transfer track is total, as shown in Figure 2.

Adopt as seen from Figure 2 two pulses to shift the required minimum total speed increment of detection 6489 Golevka asteroids and be about 7.0km/s, corresponding better intersection chance has twice: 1) mean anomaly is about 180 degree when launching, and the mean anomaly during intersection is about 50 degree; Mean anomaly is about 170 degree when 2) launching, and the mean anomaly during intersection is about 300 degree.The employing Newton iterative is found the solution, and the result is as shown in table 1

Table 1 is surveyed optimum two pulses of 6489 Golevka

Δ V wherein _TotalBe total speed increment,

Mean anomaly during for emission,

Mean anomaly during for intersection, T _fBe the flight time.

Step 2, set up the corresponding relation of earth ephemeris and when emission mean anomaly

Suppose to choose from the time period of the earth and be [2010,2015], then can be respectively in this time interval two suboptimums emission time corresponding to mean anomaly by planet ephemeris DE405:

Chance for the first time: from launch time and the mean anomaly of the earth

1. 0 o'clock on the 02nd July in 2010 (M _LBe 175.76 degree)

2. 12 o'clock on the 01st July in 2011 (M _LBe 175.85 degree)

3. 0 o'clock on the 29th June in 2012 (M _LBe 175.70 degree)

4. 0 o'clock on the 02nd July in 2013 (M _LBe 175.76 degree)

5. 12 o'clock on the 30th June in 2014 (M _LBe 175.84 degree)

6. 14 o'clock on the 30th June in 2015 (M _LBe 175.72 degree)

Chance for the second time: from launch time and the mean anomaly of the earth

1. 0 o'clock on the 26th June in 2010 (M _LBe 171.48 degree)

2. 0 o'clock on the 28th June in 2011 (M _LBe 171.37 degree)

3. 0 o'clock on the 25th June in 2012 (M _LBe 171.43 degree)

4. 0 o'clock on the 27th June in 2013 (M _LBe 171.44 degree)

5. 0 o'clock on the 27th June in 2014 (M _LBe 171.28 degree)

6. 12 o'clock on the 25th June in 2015 (M _LBe 171.44 degree)

Step 3, the corresponding relation of mean anomaly when setting up target celestial body ephemeris and intersection

By optimum launch time with the flight time can be calculated and the schedule time of target celestial body intersection, the flight time of chance is 216.37 days for the first time, and then predetermined intersection time and the corresponding mean anomaly of its correspondence are:

1. 09 o'clock on the 03rd February in 2011 (M _RBe 328.55 degree)

2. 21 o'clock on the 02nd February in 2012 (M _RBe 58.63 degree)

3. 09 o'clock on the 11st January in 2013 (M _RBe 143.52 degree)

4. 09 o'clock on the 03rd February in 2014 (M _RBe 239.41 degree)

5. 21 o'clock on the 01st February in 2015 (M _RBe 329.24 degree)

6. 23 o'clock on the 01st February in 2016 (M _RBe 59.46 degree)

The flight time of chance is 1247.76 days for the second time, and then predetermined intersection time and the corresponding mean anomaly of its correspondence are:

1. 18 o'clock on the 24th November in 2013 (M _RBe 221.95 degree)

2. 18 o'clock on the 26th November in 2014 (M _RBe 312.65 degree)

3. 18 o'clock on the 24th November in 2015 (M _RBe 42.36 degree)

4. 18 o'clock on the 25th November in 2016 (M _RBe 133.06 degree)

5. 18 o'clock on the 25th November in 2017 (M _RBe 223.26 degree)

6. 06 o'clock on the 24th November in 2018 (M _RBe 313.09 degree)

Whether step 4, the differentiation earth and target celestial body satisfy the geometric relationship of Optimal Rendezvous

If predetermined intersection mean anomaly is consistent with the Optimal Rendezvous mean anomaly or approach, then should launch time and the intersection time be better launching opportunity, otherwise launch time corresponding to mean anomaly need readjust earth optimum and launch the time.Can find out preferably that by above analytic process launching opportunity is (ε in the present embodiment=3 °):

For the chance first time (flight time is 216.37 days)

2. 12 o'clock on the 01st July in 2011 (M _LBe 175.85 degree)

21 o'clock on the 02nd February in 2012 (M _RBe 58.63 degree)

Do not satisfy optimum launching condition

6. 14 o'clock on the 30th June in 2015 (M _LBe 175.72 degree)

23 o'clock on the 01st February in 2016 (M _RBe 59.46 degree)

Do not satisfy optimum launching condition

For the chance second time (flight time is 1247.76 days)

2. 0 o'clock on the 28th June in 2011 (M _LBe 171.37 degree)

18 o'clock on the 26th November in 2014 (M _RBe 312.65 degree)

Satisfy optimum launching condition

Speed increment 6.548km/s

6. 12 o'clock on the 25th June in 2015 (M _LBe 171.44 degree)

06 o'clock on the 24th November in 2018 (M _RBe 313.09 degree)

Satisfy optimum launching condition

Speed increment 6.552km/s

So far, finished based on the search of the space flight launching opportunity of orbital tracking.Can find out that from the speed increment that Search Results obtains the speed increment of twice chance is extremely near twice Δ V corresponding to chance in the table 1 _TotalValue proves that thus the inventive method has advantage and the effects such as periodicity of accurately distinguishing launching opportunity.

Claims (4)

1. space flight launching opportunity searching method based on orbital tracking is characterized in that: may further comprise the steps:

Step 1, employing contour map are determined target celestial body and the optimum two pulse intersection chances of launching celestial body, comprise that the Optimal Rendezvous mean anomaly of target celestial body when the optimum of launching celestial body when shifting emission is launched mean anomaly, intersection reached by the detector flight time of emission celestial body to target celestial body;

Step 2, according to the time interval of the given launching opportunity of task, obtain launching celestial body at position and the speed state of this time interval by the planet ephemeris, change into the orbital tracking form, find the corresponding relation of emission celestial body launch time and mean anomaly, find according to corresponding relation that the step 1 gained is optimum to be launched all launch times corresponding to mean anomaly;

Launch time and the flight time of step 3, the emission celestial body that obtained by step 2, obtain all predetermined intersection times of detector and target celestial body, ephemeris by target celestial body obtains corresponding target celestial body position and speed state of each predetermined intersection time, change into the orbital tracking form, obtain predetermined intersection mean anomaly corresponding to each predetermined intersection time of target celestial body;

Whether step 4, differentiation emission celestial body and target celestial body satisfy the geometric relationship of Optimal Rendezvous

The Optimal Rendezvous mean anomaly that the predetermined intersection mean anomaly that obtains according to step 3 and step 1 are tried to achieve, consistent or difference is less than the principle of ε according to the two, and intersection time corresponding to launch time corresponding to predetermined intersection mean anomaly and Optimal Rendezvous mean anomaly of choosing is as the optimum transmit chance in the given launching opportunity time interval.

2. a kind of space flight launching opportunity searching method based on orbital tracking according to claim 1, it is characterized in that: the concrete methods of realizing of the optimum two pulse intersection chances between any two non-coplanar non co axial elliptical orbits is: by the contour map of global optimum's two pulse intersections between emission celestial body and the target celestial body, correspondence finds the minimum point span of the required speed increment of optimum two pulse intersections; In span, choose arbitrarily a value, as emission and the initial value of intersection time emission celestial body with the target celestial body mean anomaly, the Optimal Rendezvous mean anomaly of target celestial body and by launching the detector flight time of celestial body to target celestial body when the optimum emission mean anomaly of emission celestial body, intersection when adopting Newton iteration method to obtain global optimum's two pulses to shift emission.

3. a kind of space flight launching opportunity searching method based on orbital tracking according to claim 1 is characterized in that: the predetermined intersection time is launch time and flight time sum.

4. a kind of space flight launching opportunity searching method based on orbital tracking according to claim 1 is characterized in that: ε is according to determining task time and accuracy requirement.

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