CN1843851A - Detector emission method employing force-borrow mechanism to select space detection target - Google Patents

Abstract

The invention relates to a method for emitting detector which can select the detected target via swing-by mechanism, belonging to the technique of deep space detecting rail transfer. It can solve the problems of approachability evaluation of detected target with long semi long axis or large eccentric rate. The inventive method comprises: calculating optimized dual impulse transfer track; selecting swing-by track type; and assembling the swing-by tracks. First calculating the optimized dual impulse transfer track from the target star to emitting star; using the emitting star as swing-by star; using the parameter of dual impulse transfer at the emitting star as the match parameter in swing-by flying; using the heliocentric large-ellipse orbit whose period is several times of the revolution period of emitting star and the deep space device at aphelion, to search for the emitting parameter of said match condition. The invention guides in the swing-by mechanism to realize the expansion of former dual impulse transfer, to improve the approachability of the target with long semi long axis or large eccentric rate.

Description

The detector emission method of employing force-borrow mechanism to select space detection target

Technical field

The invention belongs to survey of deep space transfer orbit technical field, relate to a kind of detector emission method of employing force-borrow mechanism to select space detection target.

Background technology

Earlier 1990s, the space research unit of the U.S., European Space Agency and Japan and other countries and mechanism, started once more and be intended to deepen the deep space secret is further explored in solar understanding, thus the climax of the survey of deep space activity of the development law in announcement universe.At this moment, the emphasis of the detection of a target begins to turn to numerous minor planet and comet in the solar system, be that those volumes are less, lighter weight, out-of-shape, revolving property is fixing, gravitational field is more weak and the little celestial body target of non-cooperation type pockety, and the eight major planets of the solar system and satellite thereof.

For interstellar probe mission, the selection of scientific exploration target is undoubtedly the first step of task design and planning, also is an important step.When selecting the detection of a target, at first to consider its accessibility.The accessibility Study on Evaluation of therefore carrying out the interspace detection of a target is very important and necessary.The quality of target accessibility is normally estimated by the realization and the size of total velocity increment of the intersection required by task of target star.

In existing interspace detection of a target accessibility evaluation method, formerly method [1] (referring to Hulkower, N.D., Lau, C.O., and Bender, D.F., Optimum Two-Impulse Transfer for PreliminaryInterplanetary Trajectory Design, Journal of Guidance, Control and Dynamic, 1984,7:458-461; Helin, E.F., Hulkower, N.D., Bender, D.F., The Discovery of 1982 DB, the Most Accessible Asteroid Known, Icarus, 1984,57:42-47; C.O.Lau, N.D.Hulkower, " Accessibility of Near-Earth Asteroids ", Journal of Guidance, Control andDynamic, May-June 1987,10 (3): 225-232) based on the optimum two pulse methods of calculating of antarafacial non co axial elliptical orbit, optimum total velocity increment contour map and the conic section splicing method by drawing given true anomaly of having provided combines to determine the method for target accessibility.This method not only can estimate from the earth and directly be transferred to the velocity increment that two pulses of the required minimum of little celestial body are shifted, and this method be " a time freedom " in the hope of the separating of two pulse transfer orbits of global optimum.This method is the classical way that carries out target selection and accessibility analysis.

Formerly method [2] is (referring to Ettore Perozzi, Alessandro Rossi, Giovanni B.Valsecchi, Basic targeting strategies for rendezvous and flyby missions to the near-Earth asteroids, Planetary and Space Science, 2001,49:3-22; Apostolos A.Christou, The statistics offlight opportunities to accessible near-Earth asteroids, Planetary and Space Science, 2003,51:221-231; Richard P.Binzel, Ettore Perozzi, Andrew S.Rivkin, AlessandroRossi, Alan W.harris, Schelte J.Bus, Giovanni B.Valsecchi, Stephen M.Slivan, Dynamical and compositional assessment of near-Earth object mission targets, Meteoritics ﹠amp; Planetary Science 39, No.3,351-366,2004) estimate the accessibility of the detection of a target by the total velocity increment that adopts classical Huo Man transfer method to calculate the intersection required by task.This method is calculated easy, is suitable for large-scale calculating and search.

Along with further carrying out of development of technology and survey of deep space task, trend towards requiring the detection of a target to have both scientific value and technology realizability gradually to the selection of the detection of a target.With regard to technical realizability, mainly consider its accessibility.The method formerly of estimating detection of a target accessibility mainly contains two kinds: a kind of is the total velocity increment that calculates the intersection required by task by employing global optimum two pulse branch modes, and another kind is by adopting classical Huo Man transition strategy to calculate total velocity increment of intersection required by task.Adopt two pulse transition strategies of these classics, the result who estimates is the accessibility of those tracks little celestial body close with the earth fine (total velocity increment of realizing the intersection required by task is less), and those have than big science and are worth, but semi-major axis of orbit accessibility big or the little celestial body that eccentricity is bigger very poor (total velocity increment and the emitted energy of realizing the intersection required by task are all very big, have exceeded the degree that present human technology can realize).This just makes the designer of task probably scientists be thought that the target eliminating that has scientific value is outside the optional detection of a target.

Summary of the invention

The technical problem to be solved in the present invention is to overcome above-mentioned existing methods technical difficulty, provide a kind of design simple, the detector emission method of technical feasible employing force-borrow mechanism to select space detection target is estimated this difficult problem thereby can solve semi-major axis of orbit the accessibility big or detection of a target that eccentricity is bigger.

The detector emission method of employing force-borrow mechanism to select space detection target of the present invention comprises: optimum two pulse transfer orbits are asked for, three parts of swing-by trajectory type selecting and swing-by trajectory splicing.Ask for optimum two pulse transfer orbits earlier from the target star to the emission celestial body, launching celestial body as borrowing the power celestial body, matching parameter when parameter at emission celestial body place is shifted in two pulses as swing-by flight, to be about the deep space at place, day heart highly elliptic orbit and aphelion of emission celestial body period of revolution integral multiple motor-driven the employing cycle then, the emission parameter of search Satisfying Matching Conditions, i.e. reverse recursion layout strategy.Concrete technical method is:

1, the detector emission method of employing force-borrow mechanism to select space detection target is characterized in that described method is:

One, adopts the optimum two pulse methods of calculating of antarafacial non co axial elliptical orbit, draw optimum total velocity increment contour map of given true anomaly by formula (1)～(4) and Newton iteration method, determine the zone that globally optimal solution two pulses transfer may occur, adopt the SQP method to obtain two pulse transfer orbits of global optimum from the target celestial body to the emission celestial body;

$\frac{\∂{\stackrel{\→}{I}}_1}{\∂p_t}=\±\left(\frac{1}{2}{p}_t\right)(v-z{\stackrel{\→}{U}}_1)---\left(1\right)$

$v=\frac{\sqrt{{\mathrm{\μp}}_t}({\stackrel{\→}{r}}_2-{\stackrel{\→}{r}}_1)}{|{\stackrel{\→}{r}}_1\×{\stackrel{\→}{r}}_2|}---\left(3\right)$

$z=\sqrt{\frac{\mathrm{\μ}}{p_t}}\mathrm{tg}\left(\frac{\mathrm{\θ}}{2}\right)---\left(4\right)$

In the formula:

With

The unit direction vector of celestial body and target celestial body position is launched in expression respectively, and μ is a gravity constant, p ₁For transfer orbit partly hand over string, With

Be respectively initial and terminal position vector, θ is an angle change amount;

Two, the power celestial body is borrowed in the emission celestial body conduct of selecting two pulses to shift, it is bigger slightly than emission celestial body period of revolution integral multiple that detector enters airborne period from the emission of emission celestial body, the perihelion radius is on average the revolve round the sun day heart highly elliptic orbit of radius of emission celestial body, according to the parameter of target celestial body, determine day cycle P of the big elliptical transfer orbit of the heart by formula (5)～(7) ₁, the aphelion speed v _a, the aphelion radius r _a:

$r_a=\frac{r_p^2{v}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">p</figure-callout>}}^2}{2{\mathrm{\&mu;}}_{\mathrm{zun}}-r_p{v}_p^2}---\left(5\right)$

$v_a=\frac{v_p{r}_p}{\mathrm{ra}}---\left(6\right)$

$P_l=\mathrm{\&pi;}\sqrt{\frac{{(r_a+r_p)}^2}{2{\mathrm{\&mu;}}_{s\mathrm{un}}}}---\left(7\right)$

In the formula: μ _ZunBe the gravity constant of the sun, r _pBe the perihelion radius;

Matching parameter when three, shifting parameter at emission celestial body place as swing-by flight with two pulses, the employing cycle is about day heart highly elliptic orbit of emission celestial body period of revolution integral multiple and adjusts the deep space of locating the aphelion motor-driven, and the place applies a motor-driven Δ v of deep space in the aphelion _m, make the perihelion radius less than the orbit radius of launching celestial body, the track of the track of detector and emission celestial body is tangent, by adopting C ₃Be hyperbola hypervelocity square method different orbital segments is stitched together, utilize formula (8)～(12) to determine the major semiaxis a of the motor-driven back of detector deep space track _r, orbit period P _r, eccentric ratio e _r, the detector Returning ball the aphelion speed v _a, the flight time t when being transmitted into and launch the celestial body intersection _a:

v _ar＝v _a-Δv _m (8)

$a_r=\frac{1}{\frac{2}{r_a}-\left(\frac{v_{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}{{\mathrm{\&mu;}}_{\mathrm{sun}}}\right)}---\left(9\right)$

$P_r=2\mathrm{\&pi;}\sqrt{\frac{a_r^3}{{\mathrm{\&mu;}}_{\mathrm{zun}}}}---\left(10\right)$

$e_r=\left(\frac{r_a}{a_r}\right)-1---\left(11\right)$

$T_c=\left(\frac{P_1}{2}\right)+\left(\frac{P_r}{2}\right)+t_{\mathrm{ep}}---\left(12\right)$

In the formula: t _EpTime for detector from crossplot point to the preliminary orbit perihelion.

Groundwork of the present invention: the velocity increment that adopts two classical pulse transfer methods to calculate the intersection required by task comprises two parts: the velocity increment when velocity increment during emission and intersection.The big or bigger target of eccentricity for semi-major axis, the relative velocity increment is less in the time of can intersection occurring usually, and required velocity increment is very big during emission, thus cause total velocity increment and emitted energy all very big.Just be based on this point, we consider swing-by flight mechanism is incorporated in the accessibility evaluation method of the interspace detection of a target.Swing-by flight can effectively reduce the required emitted energy of interstellar probe mission, and then reduces total velocity increment.Simultaneously,, adopt the emission celestial body to borrow power and the motor-driven strategy design transfer orbit that combines of deep space here, replace two pulse transfer methods in order to reduce dynamic (dynamical) requirement and to avoid dependence to the time.

The present invention is relevant with the survey of deep space transfer orbit, the selection of particularly survey of deep space target and accessibility evaluation analysis.This method will be used in aspects such as the target selection, accessibility assessment of survey of deep space (particularly little celestial body survey), and the design that also can be the survey of deep space task provides a kind of with planning and estimates and the new way of analyzing.

The present invention is with method [1] formerly, formerly the difference of method [2] is, the present invention realizes expansion that original two pulses are shifted by introducing the power mechanism of borrowing, and improves the accessibility of the big or eccentricity of semi-major axis than general objective.Its advantage is:

1) reduces velocity increment and the emitted energy that semi-major axis target celestial body big or that eccentricity is bigger is realized the intersection required by task,, provide important reference for having both choosing of the scientific value and the technology realizability detection of a target;

2) the power celestial body is borrowed in the emission celestial body conduct of selecting two pulses to shift, has reduced the complexity of method of designing, has also avoided time-constrain is introduced evaluation method simultaneously;

3) layout strategy of reverse recursion has been preserved the data message of original optimum two pulse transfer orbits effectively, has avoided unnecessary double counting;

4) the interspace detection of a target accessibility evaluation method of this gravitation mechanism also is " a time freedom ", can be used for the prediction of intersection chance.

Description of drawings

Fig. 1 is the scheme drawing that two pulses are shifted, and Fig. 2 is the total velocity increment contour map of optimum two pulses of intersection 4015 minor planet intersections, and Fig. 3 is emission celestial body swing-by flight scheme drawing, the property relationship figure that Fig. 4 shifts for emission celestial body swing-by flight, and Fig. 5 is the M of conjecture _L0And the graph of a relation between the matching error δ C, Fig. 6 borrows the flight path figure of power transfer scheme and 4015 minor planet intersections for the employing earth 2 annual period.

The specific embodiment

The specific embodiment one: present embodiment describes in detail in conjunction with Fig. 1～6 couple the present invention:

1) the emission celestial body is to the scheme drawing of optimum two this section of pulse transfer orbit tracks of target celestial body, as shown in Figure 1.

Here definition: ${\stackrel{\&RightArrow;}{I}}_1={\stackrel{\&RightArrow;}{V}}_{x1}$ (the hyperbola hypervelocity during emission), ${\stackrel{\&RightArrow;}{I}}_2={\stackrel{\&RightArrow;}{V}}_{x2}$ (the hyperbola hypervelocity during intersection).Suppose that detector with the speed that the emission celestial body separates is

, the speed when the intersection of target celestial body is , then be:

${\stackrel{\&RightArrow;}{V}}_{\mathrm{tl}}=\&PlusMinus;(\stackrel{\&RightArrow;}{v}+z{\stackrel{\&RightArrow;}{U}}_1)={\stackrel{\&RightArrow;}{I}}_1+{\stackrel{\&RightArrow;}{V}}_I---\left(1\right)$

${\stackrel{\&RightArrow;}{V}}_{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">t</figure-callout>}2}=\&PlusMinus;(\stackrel{\&RightArrow;}{v}-z{\stackrel{\&RightArrow;}{U}}_2)={\stackrel{\&RightArrow;}{V}}_A-{\stackrel{\&RightArrow;}{I}}_2---\left(2\right)$

Here

With It is respectively the velocity vector that emission celestial body and target celestial body revolve around the sun, more than in two formulas+number be meant " short distance " (promptly the track of realizing by the angle change amount θ less than the π radian shifts) ,-number be meant " long-range " (promptly shifting) by the track of realizing less than the change amount of 2 π radians greater than the π radian.

With The unit direction vector of expression emission celestial body and target celestial body position respectively, v and z can be by following equation (3) and (4) gained:

$v=\frac{\sqrt{{\mathrm{\&mu;p}}_t}({\stackrel{\&RightArrow;}{r}}_2-{\stackrel{\&RightArrow;}{r}}_1)}{|{\stackrel{\&RightArrow;}{r}}_1\&times;{\stackrel{\&RightArrow;}{r}}_2|}---\left(3\right)$

$z=\sqrt{\frac{\mathrm{\&mu;}}{p_t}}\mathrm{tg}\left(\frac{\mathrm{\&theta;}}{2}\right)---\left(4\right)$

Here, μ is a gravity constant, p _tFor transfer orbit partly hand over string,

With

Be respectively initial and terminal position vector.

To p _tPartial derivative can get:

$\frac{\&PartialD;{\stackrel{\&RightArrow;}{I}}_1}{\&PartialD;p_t}=\&PlusMinus;\left(\frac{1}{2}{p}_t\right)(v-z{\stackrel{\&RightArrow;}{U}}_1)---\left(5\right)$

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

$p_{\min }=\frac{r_1{r}_2-{\stackrel{\&RightArrow;}{r}}_1\&CenterDot;{\stackrel{\&RightArrow;}{r}}_2}{r_1+r_2-\sqrt{2(r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+{\stackrel{\&RightArrow;}{r}}_1\&CenterDot;{\stackrel{\&RightArrow;}{r}}_2)}}---\left(7\right)$

$p_{\max }=\frac{r_1{r}_2-{\stackrel{\&RightArrow;}{r}}_1\&CenterDot;{\stackrel{\&RightArrow;}{r}}_2}{r_1+r_2-\sqrt{2(r_1{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">r</figure-callout>}}_2+{\stackrel{\&RightArrow;}{r}}_1\&CenterDot;{\stackrel{\&RightArrow;}{r}}_2)}}---\left(8\right)$

Here adopt the method for Newton iteration can be in the hope of satisfying the p of optimal solution _tTo the position, can try to achieve the p that satisfies optimal solution for each of the revolution orbit at emission celestial body and its place of target celestial body _t, and a p _tCan calculate two J (detector is at the required total velocity increment of day heart transfer orbit) i.e. J under " long-range " situation _LongJ under " short distance " situation _Short, only keep wherein less one here.The mean anomaly of given different emission celestial bodies and the mean anomaly of intersection celestial body just can obtain optimum two pulses by (5)～(8) formula and Newton iteration method and shift contour map.Here be the target celestial body with 4015 minor planets, the earth is the emission celestial body, provides the contour map of its optimum two pulse transfer orbits, as shown in Figure 2.

Can obtain the zone that required total velocity increment minimum is shifted in two pulses by Fig. 2, thereby guess and better initial, solve accurate optimum two pulse transfer orbits by adopting SQP (SQP) method, concrete parameter is as shown in table 1.The mean anomaly of the earth when the power of borrowing during the mean anomaly of the earth that global optimum's two pulse transfer methods find the solution out when emission can be used as by means of the power scheme.

2) swing-by trajectory type selecting

Swing-by flight can effectively reduce the required emitted energy of interstellar probe mission and total velocity increment, adopts the swing-by flight technology to remove to expand two classical pulse transition strategies here.In order to reduce dynamic (dynamical) requirement and to avoid the dependence of time, adopt the emission celestial body to borrow the strategy of power.This swing-by flight strategy can be described as: it is bigger slightly than emission celestial body period of revolution integral multiple that detector enters airborne period from the emission of emission celestial body, and the perihelion radius is on average the revolve round the sun day heart highly elliptic orbit of radius of emission celestial body.The place applies a velocity pulse in the aphelion, make the perihelion radius less than the orbit radius of launching celestial body, the track of the track of detector and emission celestial body is tangent, so just can utilize the pendulum effect of getting rid of of emission celestial body, reduces the emitted energy of detector and total velocity increment.This swing-by flight strategy as shown in Figure 3.

Suppose that emission celestial body revolution orbit is a circular orbit, from the detector speed V of emission celestial body emission _∞Bigger slightly than nominal orbital velocity, direction is parallel to the speed V that launches celestial body _E, in this case, aircraft is at the perihelion setting in motion of heliocentric orbit, then the speed V of perihelion _pFor:

v _p＝V _E+V _∞ (9)

Detector from emission celestial body when emission with respect to day the heart the position be r _p, the heliocentric place that then has the detector heliocentric place to equal to launch celestial body, that is:

r _p＝r _l (10)

Known r _pAnd v _p, promptly can determine detector aphelion radius r _a, speed v _aWith detector preliminary orbit cycle P _lFor:

$r_a=\frac{r_p^2{\mathrm{<figure-callout\; id="2"\; label="v\; p"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">v</figure-callout>}}_p^{}}{2{\mathrm{\&mu;}}_{\mathrm{sun}}-r_p{v}_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">p</figure-callout>}}^2},v_a=\frac{v_p{r}_p}{r_a},P_l=\mathrm{\&pi;}\sqrt{\frac{{(r_a+r_p)}^2}{2{\mathrm{\&mu;}}_{\mathrm{sun}}}}---\left(11\right)$

Here μ _SunIt is the gravity constant of the sun.The orbit period of detector preliminary orbit period ratio nominal is long slightly, if this track recursion is arrived perihelion, the emission celestial body must be in original position.If hypothesis adds a motor-driven Δ v of deep space at the place, aphelion _m, adding the power operated purpose of deep space is the speed v of revising the place, aphelion _a, make its can with earth intersection, so aphelion speed v of Returning ball _ArFor:

v _ar＝v _a-Δv _m (12)

Detector is constant at the radius at place, aphelion, but reduces at the radius at perihelion place, so just can intersect with emission celestial body revolution orbit, realizes swing-by flight.The aphelion speed v _ArWith the aphelion radius r _aKnown, as just can to determine to return and launch celestial body intersection section track some other character from the aphelion.The major semiaxis a of the motor-driven back of detector deep space track _r, orbit period P _r, eccentric ratio e _rBe:

$a_r=\frac{1}{\frac{2}{r_a}-\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="v\; ar"\; filenames="A20061001000800153.png"\; state="\{\{state\}\}">v</figure-callout>}}_{\mathrm{ar}}^{}}{{\mathrm{\&mu;}}_{\mathrm{sun}}}\right)},P_r=2\mathrm{\&pi;}\sqrt{\frac{a_r^3}{{\mathrm{\&mu;}}_{\mathrm{sun}}}},e_r=\left(\frac{r_a}{a_r}\right)-1---\left(13\right)$

Surveying the flight time of row device when being transmitted into and launch the celestial body intersection is:

$T_e=\left(\frac{P_l}{2}\right)+\left(\frac{P_r}{2}\right)+t_{\mathrm{ep}}---\left(14\right)$

Here t _EpTime for detector from crossplot point to the preliminary orbit perihelion, this time can find the solution by Kepler's equations.In order to select to borrow the type of power track, here with the earth as the emission celestial body, provide the performance of this transfer orbit.Aphelion behind the swing-by flight half through with the relation of total velocity increment as shown in Figure 4.

As seen from Figure 4, for aphelion behind the swing-by flight half through in 1.6 to 5.5AU (1AU=1.4959787 * 10 ⁸Borrowing in the power type km), it is minimum that the 2 circannian earth (emission celestial body) are borrowed the required total velocity increment of power.This is an important properties, because minor planet and comet majority are all in this distance range.Therefore, select the 2 circannian earth to borrow power transfer orbit, this transfer scheme to comprise that the motor-driven and earth of deep space borrows power, be approximately 2 years by means of flight time of force detector from earth transmission with to the earth.

3) swing-by trajectory splicing

It is the cycle with emission celestial body period of revolution integral multiple that detector enters one from the emission of emission celestial body, and the perihelion radius is the day heart highly elliptic orbit of the average revolution orbit radius of emission celestial body.At the place, aphelion, apply a velocity pulse, make detector track and emission sphere intersect.If the mean anomaly of detector corresponding emission celestial body when emission is M _L0, emission celestial body cooresponding mean anomaly when swing-by flight is M _S, flight time t then from the deep space maneuver point to swing-by flight point _eFor:

$t_e=\left\{\begin{array}{cc}\left[\frac{(M_S-M_{L0})\mathrm{\&pi;}}{180}\right](T/2\mathrm{\&pi;})& \mathrm{\&pi;}<M_S-{\mathrm{<figure-callout\; id="0"\; label="M\; L"\; filenames="A20061001000800152.png"\; state="\{\{state\}\}">M</figure-callout>}}_L<2\mathrm{\&pi;}\\ [\frac{(M_S-M_{L0})\mathrm{\&pi;}}{180}+2\mathrm{\&pi;}](T/2\mathrm{\&pi;})& 0<M_S-{\mathrm{<figure-callout\; id="0"\; label="M\; L"\; filenames="A20061001000800152.png"\; state="\{\{state\}\}">M</figure-callout>}}_L<\mathrm{\&pi;}\end{array}\right.---\left(15\right)$

Here T is the orbit period of emission celestial body revolution.By finding the solution Lambert problem from the deep space maneuver point to swing-by flight point, the hyperbola hypervelocity v in the time of can obtaining flying into by means of the power celestial body _∞-Hyperbola hypervelocity v when flying out by means of the power celestial body _∞+Can from the parameter of two pulse transfer orbits, obtain.By adopting C ₃Coupling (C ₃Be hyperbola hypervelocity square) method is stitched together different orbital segments.C ₃Coupling, promptly detector flies into by means of the hyperbola of power celestial body hypervelocity and flies out by means of the equal and opposite in direction of the hyperbola hypervelocity of power celestial body.Suppose matching error δ C ₃For:

δC ₃＝|‖v _∞+‖-‖v _∞-‖| (16)

If the hypothesis earth is the emission celestial body, 4015 minor planets are the target celestial body, adopt the 2 circannian earth to borrow power, then the mean anomaly M of the earth when emission _L0With matching error δ C ₃Relation as shown in Figure 5.

As shown in Figure 5, there be twice by means of power, because curve of error is through twice zero point.Near zero point, get initial value, adopt Newton method etc. can try to achieve the parameter of coupling accurately then.The 2 circannian earth borrow total velocity increment of power transfer scheme to comprise: the velocity increment Δ V during emission _l, aphelion place the motor-driven Δ V of deep space _mVelocity pulse Δ V during with intersection _aBorrow the parameter of power transfer scheme as shown in table 1 with the optimum two pulses transfer and the 2 circannian earth of 4015 minor planet intersections.The flight path that the 2 circannian earth are borrowed power (2) flight scheme as shown in Figure 6.

Table 1 is the comparison of method and the inventive method formerly

	The mean anomaly M of earth during emission l(degree)	Minor planet mean anomaly M during intersection a(degree)	Total velocity increment Δ V (km/s)	Energy C during emission 3(km 2/s 2)	Flight time T f(my god)
						Optimum two pulses (method formerly), the 2 circannian earth borrow power (1) (the inventive method) the 2 circannian earth to borrow power (2) (the inventive method)	257.175 210.871 301.289	311.274 311.274 311.274	6.799 6.409 5.632	67.119 26.497 25.630	1328.9 2106.4 2014.7

As can be seen from Table 1, compare, adopt that the inventive method is minimum can to make total velocity increment Δ V and emitted energy C with method formerly ₃Reduce 1.168km/s and 41.489km respectively ²/ s ²

From the design process of borrowing the power transfer orbit as can be seen: the mean anomaly M the when flight path of detector can be by emission _l, the mean anomaly M during swing-by flight _s, the mean anomaly M during intersection _aDescribe, and this transfer scheme is freely or to ephemeris to be freely to the time.This method relatively is fit to estimate the accessibility of interspace target celestial body.Total velocity increment of the inventive method is by the velocity increment in when emission, and the velocity increment during the motor-driven and intersection of the deep space at place, aphelion is formed.It is cost to increase motor-driven and flight time of deep space that this method can reduce emitted energy and total velocity increment.This method is suitable for the big or bigger little celestial body of eccentricity of semi-major axis.The evaluation result of the inventive method compares with the result of formerly method [1] and method [2] evaluation formerly, and is as shown in table 2.

Table 2 the inventive method and method formerly are for the comparison of estimating big semi-major axis or WITH HIGH-ECCENTRIC target minor planet accessibility

Minor planet	Aphelion Q (AU)	Eccentric ratio e	This task				Method [2] formerly	Method [1] formerly
									The inventive method		Method formerly
			ΔV total (km/s)	C 3 (km 2/s 2)	ΔV total (km/s)	C 3 (km 2/s 2)							ΔV total (km/s)	ΔV total (km/s)
							(7341)1991VK (4179)Toutatis (3288)Seleucus (3908)Nyx (8034)1992LR	2.776 4.122 2.962 2.812 2.579	0.506 0.635 0.457 0.459 0.409	4.968 5.092 5.180 5.193 5.339	25.34 25.15 26.48 25.41 26.49	5.776 6.159 5.887 5.595 5.578			56.80 63.45 51.24 38.62 34.73	7.6 8.3 8.0 6.9 6.6	-- -- 5.912 -- --

(1627)lvar (3551)Verenia (6489)Golevka (433)Eros (3352)McAuliffe (4015) WilsonHarrington (887)Alinda (13651)1997BR (31345)1998PG (3102)Krok (1685)Toro (1620)Geographos (2100)Ra-Shalom (6178)1986DA (2063)Bacchus (7753)1988XB (B3671)Dionysus (35396)1997XF11 (8201)1994AH2 (2201)Oljato

2.603 3.113 4.009 1.783 2.572 4.285 3.885 1.744 2.805 3.116 1.963 1.663 1.195 4.457 1.455 2.174 3.389 2.141 4.330 3.721

0.397 0.488 0.605 0.223 0.369 0.623 0.563 0.306 0.392 0.449 0.436 0.335 0.437 0.587 0.349 0.482 0.542 0.484 0.709 0.713

5.389 5.398 5.446 5.547 5.552 5.632 5.635 5.668 5.948 6.039 6.051 6.148 6.353 6.355 6.386 6.421 6.631 6.701 6.899 6.911

26.36 25.65 26.48 25.40 25.26 25.63 25.38 26.20 25.37 26.02 25.47 25.67 25.62 26.42 25.30 25.65 26.48 26.05 26.31 26.40

6.108 6.476 6.499 5.935 5.891 6.799 6.812 8.155 6.437 6.845 7.675 8.795 7.939 7.622 7.094 6.750 7.795 7.174 8.111 8.040

50.59 63.92 63.94 38.38 36.48 67.12 69.24 128.7 42.75 53.54 71.52 88.50 85.52 74.16 49.36 36.61 68.75 41.07 67.69 68.34

8.2 8.9 8.3 7.6 7.4 8.6 9.4 9.5 8.2 8.8 7.6 8.2 9.7 9.1 6.8 6.8 9.8 7.0 9.9 9.4

6.117 6.483 -- 5.947 5.900 -- 6.852 -- -- 6.855 7.675 8.537 7.949 -- 7.105 -- -- -- -- 8.037

In table 2, Q and e represent asteroidal aphelion distance and eccentricity respectively.The minor planet that is listed in the table 2 all has very high scientific value.As shown in table 2, by adopting the inventive method, the total velocity increment Δ V and the emitted energy C of minor planet intersection required by task ₃All have obviously less.4015 minor planets (e=0.623, the result is as shown in table 1) that for example may originate from comet; According to radar observation, the minor planet 4179 (e=0.635) of special spin states is arranged, compare with method formerly, adopt the inventive method to make total velocity increment and emitted energy reduce 17.32% and 60.36% respectively; May originate from 6489 minor planets (e=0.605) of No. 4 huge minor planet Vesta surface relics, adopt the inventive method, make total velocity increment and emitted energy reduce 1.0530km/s and 37.46km respectively ²/ s ²Or the like.From table 2, it can also be seen that some targets (for example 4179,1627,3551,6489,4015,887,13651 etc.) have all shown good accessibility.

Claims (1)

1, the detector emission method of employing force-borrow mechanism to select space detection target is characterized in that described method is:

One, adopts the optimum two pulse methods of calculating of antarafacial non co axial elliptical orbit, draw optimum total velocity increment contour map of given true anomaly by formula (1)～(4) and Newton iteration method, determine the zone that globally optimal solution two pulses transfer may occur, adopt the SQP method to obtain two pulse transfer orbits of global optimum from the target celestial body to the emission celestial body;

$\frac{\&PartialD;{\stackrel{\&RightArrow;}{I}}_1}{\&PartialD;p_t}=\&PlusMinus;\left(\frac{1}{2}{p}_t\right)(v-z{\stackrel{\&RightArrow;}{U}}_1)---\left(1\right)$

$v=\frac{\sqrt{\mathrm{\&mu;}{p}_t}({\stackrel{\&RightArrow;}{r}}_2-{\stackrel{\&RightArrow;}{r}}_1)}{|{\stackrel{\&RightArrow;}{r}}_1\&times;{\stackrel{\&RightArrow;}{r}}_2|}---\left(3\right)$

$z=\sqrt{\frac{\mathrm{\&mu;}}{p_t}}\mathrm{tg}\left(\frac{\mathrm{\&theta;}}{2}\right)---\left(4\right)$

In the formula:

With

The unit direction vector of celestial body and target celestial body position is launched in expression respectively, and μ is a gravity constant, p _tFor transfer orbit partly hand over string,

With Be respectively initial and terminal position vector, θ is an angle change amount;

Two, the power celestial body is borrowed in the emission celestial body conduct of selecting two pulses to shift, it is bigger slightly than emission celestial body period of revolution integral multiple that detector enters airborne period from the emission of emission celestial body, the perihelion radius is on average the revolve round the sun day heart highly elliptic orbit of radius of emission celestial body, according to the parameter of target celestial body, determine day cycle P of the big elliptical transfer orbit of the heart by formula (5)～(7) _l, the aphelion speed v _a, the aphelion radius r _a:

$r_a=\frac{r_p^2{v}_p^2}{2{\mathrm{\&mu;}}_{\mathrm{sun}}-r_p{v}_p^2}---\left(5\right)$

$v_a=\frac{v_p{r}_p}{r_a}---\left(6\right)$

$P_l=\mathrm{\&pi;}\sqrt{\frac{{(r_a+r_p)}^2}{2{\mathrm{\&mu;}}_{\mathrm{sun}}}}---\left(7\right)$

In the formula: μ _ZunBe the gravity constant of the sun, r _pBe the perihelion radius;

Matching parameter when three, shifting parameter at emission celestial body place as swing-by flight with two pulses, the employing cycle is about day heart highly elliptic orbit of emission celestial body period of revolution integral multiple and adjusts the deep space of locating the aphelion motor-driven, and the place applies a motor-driven Δ v of deep space in the aphelion _m, make the perihelion radius less than the orbit radius of launching celestial body, the track of the track of detector and emission celestial body is tangent, by adopting C ₃Be hyperbola hypervelocity square method different orbital segments is stitched together, utilize formula (8)～(12) to determine the major semiaxis a of the motor-driven back of detector deep space track _r, orbit period P _r, eccentric ratio e _r, the detector Returning ball the aphelion speed v _a, the flight time t when being transmitted into and launch the celestial body intersection _c:

v _ar＝v _a-Δv _m (8)

$a_r=\frac{1}{\frac{2}{r_a}-\left(\frac{v_{\mathrm{ar}}^2}{{\mathrm{\&mu;}}_{\mathrm{sun}}}\right)}---\left(9\right)$

$P_r=2\mathrm{\&pi;}\sqrt{\frac{a_r^3}{{\mathrm{\&mu;}}_{\mathrm{sun}}}}---\left(10\right)$

$e_r=\left(\frac{r_a}{a_r}\right)-1---\left(11\right)$

$T_e=\left(\frac{P_l}{2}\right)+\left(\frac{P_r}{2}\right)+t_{\mathrm{ep}}---\left(12\right)$

In the formula: t _EpTime for detector from crossplot point to the preliminary orbit perihelion.

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