CN104484493A - Design method for airship returning back to predetermined fall point recursive orbit - Google Patents

Abstract

The invention provides a design method for an airship returning back to a predetermined fall point recursive orbit. According to the design method for the airship returning back to the predetermined fall point recursive orbit, a sub-satellite point can accurately pass a predetermined fall point by selecting a rail mean anomaly, a rail satisfies recursive characteristics by adjusting the rail semi major axis, a double-layer iteration solution process for two parameters of the rail semi major axis and the rail mean anomaly is established, design parameters which are mutually matched with the rail inclination angle, the rail semi major axis and the rail mean anomaly are obtained, and an airship sub-satellite point track is guaranteed accurately passing through the predetermined fall point at every recursive period.

Description

A kind of airship returns predetermined drop point regression orbit method for designing

Technical field:

The present invention relates to spacecraft orbit design field, be specifically related to a kind of airship and return predetermined drop point regression orbit method for designing.

Background technology

In order to ensure that manned spaceship can provide for spacefarer the chance returning intended landing area in state of landing every day, China's manned astro-engineering manned spaceship Track desigh follows the principle of design of regression orbit always, and first stage of the project carries people to fly, and what adopt with the manned spaceship of the second stage of the project spacecrafts rendezvous is 2 days regression orbits.In three phase spacelabs and space station engineering, manned spaceship orbit height there occurs change with orbit inclination compared with first and second phases of projects.The third stage of the project airship intends employing 3 days regression orbits, is no longer adjusted by the initial phase of Trajectory Maneuver Control to spacelab airship relative to space station.Change within the specific limits in orbit inclination and orbit altitude, under the uncertain condition of track initial phase, the recurrence characteristic of spacecraft orbit and return characteristic and larger change will occur.In order to ensure that the third stage of the project manned spaceship still can return intended landing area, the regression orbit designs in three days based on accurately returning intended landing area need be carried out, for the design of the third stage of the project Manned Spacecraft Return and control enforcement provide foundation.Therefore, it is one of technical essential of spacelab and space station engineering Track desigh that airship returns the design of predetermined drop point regression orbit, rail design method still not relevant at present.

Summary of the invention:

The present invention needs technical solution problem to be to provide a kind of airship to return predetermined drop point regression orbit method for designing.

For solving the problems of the technologies described above, a kind of airship provided by the invention returns predetermined drop point regression orbit method for designing and comprises the steps:

1) preliminary orbit parameter is set, comprises semi-major axis of orbit initial value a ₀, orbital eccentricity initial value e ₀, orbit inclination initial value i ₀, longitude of ascending node initial value D ₀, perigee of orbit argument initial value ω ₀, track Initial mean anomaly M ₀, airship quality and front face area, rail force model, rail force model comprises: earth center gravitation, figure of the earth Gravitational perturbation;

2) Track desigh condition is set, comprises: nominal drop point longitude L ₀, latitude B ₀; Initially return circle q _r; Track recursion period number of days i; Track recursion period number of turns k _i; Drop point longitude convergence threshold ε L; Return circle longitude of ascending node convergence threshold ε λ _n;

3) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

4) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), L (q _r) for initially to return circle q _rsubstar latitude is B ₀longitude; Calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r), λ (q _r) for initially to return circle q _rlongitude of ascending node, λ (q _r+ k _i) for initially to return circle q _r+ k _ilongitude of ascending node;

5) track mean anomaly deviation delta M is calculated according to following formula by returning circle substar difference of longitude Δ L;

$\mathrm{\ΔM}=-\mathrm{\ΔL}\·n/({\mathrm{\ω}}_e-\stackrel{\·}{\mathrm{\Ω}})$

Wherein $\stackrel{\·}{\mathrm{\Ω}}=-1.5J_2\sqrt{\mathrm{\μ}}{R}_e^2\cos i\left[a^{7/2}{(1-e^2)}^2\right]$

for spacecraft orbit plane is at the mean angular velocity of inertial space precession, μ is Gravitational coefficient of the Earth, R _efor terrestrial equator reference radius, a is semi-major axis of orbit, and i is orbit inclination, and e is orbital eccentricity, and n is orbit averaging angular velocity, ω _efor rotational-angular velocity of the earth;

6) track mean anomaly is revised, M=M ₀+ Δ M;

7) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

8) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r);

9) judge whether return circle substar difference of longitude meets Δ L < ε L; If do not meet, then turn back to 5), repeat 5)-9); If meet, then forward 10 to);

10) longitude of ascending node difference Δ λ is enclosed according to following formula by returning _ncalculate semi-major axis of orbit correction amount a;

$\mathrm{\&Delta;a}={\mathrm{\&Delta;\&lambda;}}_n/[C_{\mathrm{Tn}}\&CenterDot;k_i\&CenterDot;({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})]\&CenterDot;\sqrt{\mathrm{\&mu;}/a}/6\mathrm{\&pi;},i=\mathrm{1,2,3}$

Wherein, $\begin{array}{c}{C}_{\mathrm{Tn}}=\{1+\frac{3J_2{R}_e^2}{{8a}^2}[(-12-{22e}^2)+(16+29e^2){\sin }^{2}i+(16-20{\sin }^{2}i)e\cos \mathrm{\&omega;}\\ -(12-15{\sin }^{2}i)e^2\cos 2\mathrm{\&omega;}\left]\right\}\end{array}$

K _ifor the recursion period number of turns, i=1,2,3, k ₁=k; k ₂=2k+1; k ₃=3k+1 and 3k+2, ω _efor rotational-angular velocity of the earth, for spacecraft orbit plane is at the mean angular velocity of inertial space precession, J ₂for terrestrial gravitational perturbation item, ω is perigee of orbit argument;

11) semi-major axis of orbit is revised, a=a ₀+ Δ a;

12) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

13) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r);

14) judge whether return circle substar difference of longitude meets Δ L < ε L and return circle longitude of ascending node difference whether meet Δ λ simultaneously _n< ε λ _n; If do not meet, then turn back to 5), repeat 5)-14); If meet, then forward 15 to);

15) calculate end, be met the designed path parameter track semi-major axis a and the track mean anomaly M that return predetermined drop point and return characteristic, namely meeting the designed path radical returning predetermined drop point and recurrence characteristic is a, e ₀, i ₀, D ₀, ω ₀, M.

The present invention proposes a kind of airship and return predetermined drop point regression orbit method for designing, substar is realized accurately through predetermined drop point by selecting track mean anomaly, by adjustment semi-major axis of orbit, track is met and return characteristic, set up semi-major axis of orbit and the double-deck iterative flow process of track mean anomaly 2 parameters, obtain the design parameter that orbit inclination, semi-major axis of orbit and track mean anomaly are mated mutually, ensure that the every recursion period of airship sub-satellite track is accurately through predetermined drop point.

Accompanying drawing illustrates:

Fig. 1 is the calculation flow chart that airship of the present invention returns the design of predetermined drop point regression orbit.

Fig. 2 is that example 3 days regression orbits initially return the designed path parameter-relation chart that circle is 15 circles.

Fig. 3 is that example 3 days regression orbits initially return the designed path parameter-relation chart that circle is 30 circles.

Fig. 4 is that example 3 days regression orbits initially return the designed path parameter-relation chart that circle is 46 circles.

Fig. 5 is that example 2 days regression orbits initially return the designed path parameter-relation chart that circle is 15 circles.

Fig. 6 is that example 2 days regression orbits initially return the designed path parameter-relation chart that circle is 31 circles.

Embodiment:

A kind of airship returns predetermined drop point regression orbit method for designing, by selecting track mean anomaly to realize substar accurately through predetermined drop point, by adjustment semi-major axis of orbit, track is met and return characteristic, set up semi-major axis of orbit and the double-deck iterative flow process of track mean anomaly 2 parameters, obtain the design parameter that orbit inclination, semi-major axis of orbit and track mean anomaly are mated mutually, ensure that the every recursion period of airship sub-satellite track is accurately through predetermined drop point.

The method comprises the steps:

Step one, set up the algorithm of substar through predetermined drop point

Consider terrestrial gravitational perturbation J ₂the impact of item, spacecraft orbit plane is at the mean angular velocity of inertial space precession for:

$\stackrel{\&CenterDot;}{\mathrm{\&Omega;}}=-1.5J_2\sqrt{\mathrm{\&mu;}}{R}_e^2\cos i\left[a^{7/2}{(1-e^2)}^2\right]---\left(1\right)$

In formula, μ is Gravitational coefficient of the Earth, R _efor terrestrial equator reference radius, a is semi-major axis of orbit, and i is orbit inclination, and e is orbital eccentricity;

Spacecraft sub-satellite track can describe with following equation:

Δλ＝arctan(cos i tan u) (3)

$L={\mathrm{\&lambda;}}_0-({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})t+\mathrm{\&Delta;\&lambda;}---\left(4\right)$

In formula, for geocentric latitude, L is longitude, and u is orbital latitude argument, λ ₀for initial longitude of ascending node, Δ λ is the difference of longitude of orbital latitude argument u at a distance of ascending node, ω _efor rotational-angular velocity of the earth, t is the time of starting at from initial ascending node;

Formula (4) two ends ask longitude L to the difference of time t:

$\mathrm{\&Delta;L}=-({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})\mathrm{\&Delta;t}---\left(5\right)$

The pass of known track mean anomaly M and orbit averaging angular velocity n is:

M＝nt (6)

Formula (6) two ends ask track mean anomaly M to the difference of time t:

ΔM＝n·Δt (7)

Then formula (5) can be rewritten as:

$\mathrm{\&Delta;L}=-({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})\&CenterDot;\mathrm{\&Delta;M}/n---\left(8\right)$

Therefore obtain:

$\mathrm{\&Delta;M}=-\mathrm{\&Delta;L}\&CenterDot;n/({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})---\left(9\right)$

Formula (9) shows, substar difference of longitude Δ L eliminates by adjustment track mean anomaly Δ M;

If track Initial mean anomaly is M ₀, then the track mean anomaly M eliminating substar difference of longitude Δ L is:

M＝M ₀+ΔM (10)

Therefore, by selecting track mean anomaly can realize substar accurately through predetermined drop point; When carrying out sub-satellite track design, it is the substar of benchmark and the difference of longitude of predetermined drop point that Δ L is according to predetermined drop point latitude, by adjustment track mean anomaly Δ M, make Δ L=0, namely obtain the track mean anomaly M of sub-satellite track through predetermined drop point;

Step 2, set up the algorithm of regression orbit

Track often runs the west amount of the moving back λ of a circle longitude of ascending node _nfor:

${\mathrm{\&lambda;}}_n=({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})T_n---\left(11\right)$

In formula, T _nfor terrestrial gravitational perturbation J ₂the node of orbit cycle under item impact;

$\begin{array}{c}{T}_n=T\{1+\frac{3J_2{R}_e^2}{{8a}^2}[(-12-{22e}^2)+(16+29e^2){\sin }^{2}i+(16-20{\sin }^{2}i)e\cos \mathrm{\&omega;}\\ -(12-15{\sin }^{2}i)e^2\cos 2\mathrm{\&omega;}\left]\right\}\end{array}---\left(12\right)$

In formula, T is the orbital period, and ω is perigee of orbit argument;

The pass of orbital period and semi-major axis of orbit is:

$T=2\mathrm{\&pi;}\sqrt{a^3/\mathrm{\&mu;}}---\left(13\right)$

In formula, μ is Gravitational coefficient of the Earth;

Definition:

$\begin{array}{c}{C}_{\mathrm{Tn}}=\{1+\frac{3J_2{R}_e^2}{{8a}^2}[(-12-{22e}^2)+(16+29e^2){\sin }^{2}i+(16-20{\sin }^{2}i)e\cos \mathrm{\&omega;}\\ -(12-15{\sin }^{2}i)e^2\cos 2\mathrm{\&omega;}\left]\right\}\end{array}---\left(14\right)$

Then have:

T _n＝C _Tn·T (15)

Orbital motion after 1 day longitude of ascending node again get back near initial ascending node, the most wide interval of adjacent turn ascending node is the west amount of moving back that track often runs a circle longitude of ascending node;

If k is the integer circle time of sub-satellite track in 1 day, k=int [2 π/λ _n], the condition at 1 day regression orbit longitude of ascending node interval is: k λ _n=2 π, k are the recursion period number of turns of 1 day regression orbit; In like manner, the condition at 2 days regression orbit longitude of ascending node intervals is: (2k+1) λ _n=4 π, 2k+1 are the recursion period number of turns of 2 days regression orbits; The condition at 3 days regression orbit longitude of ascending node intervals is: (3k+1) λ _n=6 π and (3k+2) λ _n=6 π, 3k+1 and 3k+2 are the recursion period number of turns of 3 days regression orbits;

If the recursion period number of turns is k _i, the condition at unified 1 day-3 days regression orbit longitude of ascending node intervals is:

$k_i({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})T_n=2\mathrm{\&pi;i},(i=\mathrm{1,2,3}),k_1=k;k_2=2k+1;k_3=3k+\mathrm{1,3}k+2---\left(16\right)$

Deviation delta T is there is when the node of orbit cycle _ntime, then have:

$k_i({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})(T_n+\mathrm{\&Delta;}{T}_n)=2\mathrm{\&pi;i}+{\mathrm{\&Delta;\&lambda;}}_n,(i=\mathrm{1,2,3})---\left(17\right)$

In formula, Δ λ _nfor the adjacent longitude of ascending node deviation returning circle;

Arrangement formula (17), obtains:

$\mathrm{\&Delta;}{T}_n={\mathrm{\&Delta;\&lambda;}}_n/[k_i\&CenterDot;({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})],(i=\mathrm{1,2,3})---\left(18\right)$

Node of orbit periodic deviation Δ T is asked at formula (15) two ends _ndifference to track cycle T:

ΔT _n＝C _Tn·ΔT (19)

Then have:

$\mathrm{\&Delta;T}={\mathrm{\&Delta;\&lambda;}}_n/[C_{\mathrm{Tn}}\&CenterDot;k_i\&CenterDot;({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})],(i=\mathrm{1,2,3})---\left(20\right)$

Formula (13) two ends ask semi-major axis of orbit a to the difference of track cycle T:

$\mathrm{\&Delta;a}=\sqrt{\mathrm{\&mu;}/a}\&CenterDot;\mathrm{\&Delta;T}/6\mathrm{\&pi;}---\left(21\right)$

Therefore have:

$\mathrm{\&Delta;a}={\mathrm{\&Delta;\&lambda;}}_n/[C_{\mathrm{Tn}}\&CenterDot;k_i\&CenterDot;({\mathrm{\&omega;}}_e-\stackrel{\&CenterDot;}{\mathrm{\&Omega;}})]\&CenterDot;\sqrt{\mathrm{\&mu;}/a}/6\mathrm{\&pi;},(i=\mathrm{1,2,3})---\left(22\right)$

Formula (22) shows, can eliminate the adjacent longitude of ascending node difference Δ λ returning circle by adjustment semi-major axis of orbit Δ a _n;

If semi-major axis of orbit initial value is a ₀, then the adjacent longitude of ascending node difference Δ λ returning circle is eliminated _nsemi-major axis of orbit a be:

a＝a ₀+Δa (23)

When carrying out regression orbit design, Δ λ _nthe longitude of ascending node returning circle for regression orbit is adjacent is poor, by adjustment semi-major axis of orbit Δ a, makes Δ λ _n=0, be namely met the semi-major axis of orbit a of regression orbit characteristic;

Step 3, set up semi-major axis of orbit and the double-deck iterative flow processs of track mean anomaly 2 parameters

Based on step one and step 2, set up the double-deck iterative flow process of semi-major axis of orbit and track mean anomaly 2 parameters, Exact Solution airship meets the orbit parameter returning predetermined drop point and return characteristic, sees Fig. 1.

1) preliminary orbit optimum configurations.Preliminary orbit parameter comprises: semi-major axis of orbit initial value a ₀, orbital eccentricity initial value e ₀, orbit inclination initial value i ₀, longitude of ascending node initial value D ₀, perigee of orbit argument initial value ω ₀, track Initial mean anomaly M ₀, airship quality and front face area, rail force model etc.Rail force model comprises: earth center gravitation, figure of the earth Gravitational perturbation;

2) Track desigh condition is set.Track desigh condition comprises: nominal drop point longitude L ₀, latitude B ₀; Initially return circle q _r; Track recursion period number of days i; Track recursion period number of turns k _i; Drop point longitude convergence threshold ε L; Return circle longitude of ascending node convergence threshold ε λ _n;

3) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

4) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), L (q _r) for initially to return circle q _rsubstar latitude is B ₀longitude; Calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r), λ (q _r) for initially to return circle q _rlongitude of ascending node, λ (q _r+ k _i) for initially to return circle q _r+ k _ilongitude of ascending node;

5) according to formula (9), track mean anomaly correction amount M is calculated by returning circle substar difference of longitude Δ L;

6) track mean anomaly is revised, M=M ₀+ Δ M;

7) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

8) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r);

9) judge whether return circle substar difference of longitude meets Δ L < ε L; If do not meet, then turn back to 5), repeat 5)-9); If meet, then forward 10 to);

10) according to formula (22), by recurrence circle longitude of ascending node difference Δ λ _ncalculate semi-major axis of orbit correction amount a;

11) semi-major axis of orbit is revised, a=a ₀+ Δ a;

12) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

13) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r);

14) judge whether return circle substar difference of longitude meets Δ L < ε L and return circle longitude of ascending node difference whether meet Δ λ simultaneously _n< ε λ _n; If do not meet, then turn back to 5), repeat 5)-14); If meet, then forward 15 to);

15) calculate end, be met the designed path parameter track semi-major axis a and the track mean anomaly M that return predetermined drop point and return characteristic, namely meeting the designed path radical returning predetermined drop point and recurrence characteristic is a, e ₀, i ₀, D ₀, ω ₀, M.

For verifying the validity of the method for the invention, this embodiment gives 2 examples, has carried out the 3 days regression orbit parameter designing and the 2 days regression orbit parameter designing that return predetermined drop point respectively.

Manned spaceship calculating orbital tracking is set as: orbital eccentricity e=0.0005, ascending node of orbit longitude Ω _g=350 °, perigee of orbit argument ω=130 °, orbit inclination is changed to: 42.0 °-43.0 °; Earth aspherical gravitation item 32 × 32 order considered by orbit perturbation model.

The predetermined drop point of manned spaceship is set as: longitude L=110.0 °, geodetic latitude B=42.0 °.

Manned spaceship track sub-satellite track is carried out to the orbit parameter design returned for 3 days and 2 days return through predetermined drop point, solve semi-major axis and the mean anomaly of regression orbit corresponding to different orbit inclination.

(1) 3 day regression orbit parameter designing example

The recursion period of 3 days regression orbits is 46 circles, and the circle that initially returns through drop point is chosen as 15 circles of the 1st day, 30 circles of the 2nd day, 46 circles of the 3rd day.

Table 1, table 2, table 3 are respectively and initially return 3 days regression orbit design results that circle is 15 circles, 30 circles, 46 circles.Orbit inclination i is changed to 43.0 ° from 42.0 °, each orbit inclination corresponding has the design parameter of one group of semi-major axis of orbit and track mean anomaly corresponding with it, H is the orbit altitude that semi-major axis of orbit is corresponding, H=a-6371km, N be design regression orbit return circle longitude of ascending node.

Fig. 2, Fig. 3, Fig. 4 are respectively and initially return 3 days regression orbit design parameter graphs of a relation that circle is 15 circles, 30 circles, 46 circles.Horizontal ordinate is orbit inclination, from 42.0 ° to 43.0 °; Left side ordinate is semi-major axis of orbit, and right side ordinate is track mean anomaly.Each orbit inclination corresponding has the design parameter of one group of semi-major axis of orbit and track mean anomaly corresponding with it.

Table 13 days regression orbits initially return the designed path parameter that circle is 15 circles

i/°	a/km	H/km	M/°	N (15 circle)/°
					42.0	6768.1	397.1	68.3	31.995
42.1	6764.9	393.9	94.5	33.691
					42.2	6761.9	390.9	116.5	35.123
42.3	6760.4	389.4	133.6	36.254
					42.4	6760.3	389.3	148.0	37.205
42.5	6761.0	390.0	160.7	38.051
					42.6	6762.4	391.4	172.6	38.830
42.7	6764.0	393.0	183.1	39.521
					42.8	6765.5	394.5	193.1	40.184
42.9	6767.0	396.0	203.1	40.833
					43.0	6768.3	397.3	212.9	41.468

Table 23 days regression orbits initially return the designed path parameter that circle is 30 circles

i/°	a/km	H/km	M/°	N (30 circle)/°
					42.0	6760.0	389.0	318.2	32.642
42.1	6760.6	389.6	339.0	34.019
					42.2	6762.5	391.5	355.5	35.104
42.3	6764.6	393.6	9.4	36.043
					42.4	6766.7	395.7	22.8	36.909
42.5	6768.2	397.2	35.6	37.736
					42.6	6769.1	398.1	48.2	38.541
42.7	6769.2	398.2	60.3	39.318
					42.8	6768.5	397.5	72.2	40.079
42.9	6767.3	396.2	83.7	40.815
					43.0	6765.7	394.7	94.7	41.530

Table 33 days regression orbits initially return the designed path parameter that circle is 46 circles

i/°	a/km	H/km	M/°	N (46 circle)/°
					42.0	6764.6	393.6	191.7	32.274
42.1	6767.4	396.4	211.6	33.564
					42.2	6768.8	397.8	230.1	34.751
42.3	6768.4	397.4	247.3	35.861
					42.4	6766.9	395.9	263.9	36.917
42.5	6764.7	393.7	278.8	37.888
					42.6	6762.7	391.7	293.4	38.824
42.7	6761.2	390.2	305.6	39.636
					42.8	6760.5	389.5	316.9	40.375
42.9	6760.5	389.5	327.4	41.071
					43.0	6760.9	389.9	337.0	41.707

Within 3 days, regression orbit parameter designing sample result shows:

According to not returning circle on the same day through predetermined drop point, the regression orbit parameter of design is different.Orbit inclination is when 42.0 °-43.0 ° changes, and initially returning circle is 15 circles, and semi-major axis of orbit change is approximately recessed para-curve, and minimum value is 6760.3km, and maximal value is 6768.3km, respective carter height 389.3km to 397.3km, and variation range is about 8km; The change of track mean anomaly is approximately linear increase, from 68.3 ° to 212.9 °, and variation range about 145 °.Initially returning circle is 30 circles, and semi-major axis of orbit change is approximately the para-curve of epirelief, and minimum value is 6760.0km, and maximal value is 6769.2km, respective carter height 389.0km to 398.2km, and variation range is about 9km; The change of track mean anomaly is approximately linear increase, from 318.2 ° to 94.7 °, and variation range about 137 °.Initially returning circle is 46 circles, 2 groups of para-curves recessed after semi-major axis of orbit change is approximately first epirelief, and minimum value is 6760.5km, and maximal value is 6768.8km, respective carter height 389.5km to 397.8km, and variation range is about 8km; The change of track mean anomaly is approximately linear increase, from 191.7 ° to 337.0 °, and variation range about 145 °.

Orbit inclination is when 42.0 °-43.0 ° changes, it is 31.9 °-41.5 ° that 3 days regression orbits 15 enclose the longitude of ascending node scope returned, 30 to enclose the longitude of ascending node scope returned be 32.6 °-41.5 °, and 46 to enclose the longitude of ascending node scope returned be 32.3 °-41.7 °.Within 3 days, regression orbit difference returns the longitude of ascending node scope of circle roughly unanimously, between 31.9 °-41.7 °.

Therefore, return 3 days regression orbits of predetermined drop point, when not returning circle design on the same day according to 1,2,3, semi-major axis of orbit parameter area is basically identical, be about within the scope of 9km at 6760km to 6769km and change, orbit altitude between 389km to 398km, but along with the variation tendency of orbit inclination different.Do not return circle on the same day for 1,2,3,360 ° of approximate dividing equally are 3 intervals by track mean anomaly parameter, and interval border is overlapped.

(2) 2 days regression orbit parameter designing examples

The recursion period of 2 days regression orbits is 31 circles, and the circle that returns through drop point is chosen as 15 circles of the 1st day, 31 circles of the 2nd day.

Table 4, table 5 are respectively and initially return 2 days regression orbit design results that circle is 15 circles, 31 circles.Orbit inclination i is changed to 43.0 ° from 42.0 °, each orbit inclination corresponding has the design parameter of one group of semi-major axis of orbit and track mean anomaly corresponding with it, H is the orbit altitude that semi-major axis of orbit is corresponding, H=a-6371km, N be design regression orbit return circle longitude of ascending node.

Fig. 5, Fig. 6 are respectively and initially return 2 days regression orbit design parameter graphs of a relation that circle is 15 circles, 31 circles.Horizontal ordinate is orbit inclination, from 42.0 ° to 43.0 °; Left side ordinate is semi-major axis of orbit, and right side ordinate is track mean anomaly.Each orbit inclination corresponding has the design parameter of one group of semi-major axis of orbit and track mean anomaly corresponding with it.

Table 42 days regression orbits initially return the designed path parameter that circle is 15 circles

i/°	A/km	H/km	M/°	N(Q15)/°
					42.0	6715.4	344.4	18.1	32.195
42.1	6717.9	346.9	38.3	33.482
					42.2	6718.6	347.6	57.5	34.697
42.3	6717.5	346.5	75.7	35.855
					42.4	6715.3	344.3	92.5	36.925
42.5	6712.9	341.9	107.8	37.919
					42.6	6711.2	340.2	121.5	38.809
42.7	6710.3	339.3	133.6	39.605
					42.8	6710.0	339.0	144.7	40.336
42.9	6710.5	339.5	154.9	41.001
					43.0	6711.4	340.4	164.7	41.642

Table 52 days regression orbits initially return the designed path parameter that circle is 31 circles

i/°	A/km	H/km	M/°	N(Q31)/°
					42.0	6715.4	344.4	198.2	32.182
42.1	6717.9	346.9	218.7	33.499
					42.2	6718.6	347.6	238.0	34.725
42.3	6717.4	346.4	256.1	35.885
					42.4	6715.3	344.3	272.7	36.947
42.5	6713.0	342	288.0	37.933

42.6	6711.2	340.2	301.5	38.810
					42.7	6710.2	339.2	313.6	39.600
42.8	6710.0	339.0	325.0	40.341
					42.9	6710.4	339.4	335.1	41.005
43.0	6711.3	340.3	344.7	41.639

Within 2 days, regression orbit parameter designing sample result shows:

Orbit inclination is when 42.0 °-43.0 ° changes, initially returning circle is 15 circles and 31 circles, semi-major axis of orbit Changing Pattern is basically identical, 2 groups of para-curves recessed after semi-major axis of orbit change is approximately first epirelief, minimum value is 6710.0km, maximal value is 6718.6km, respective carter height 339.0km to 347.6km, and variation range is about 9km; Initially returning circle is 15 circles and 31 circles, and the change of track mean anomaly is approximately linear increase.15 circle for initially to return circle, track mean anomaly from 18.1 ° to 164.7 °, scope about 147 °; 31 circle for initially to return circle, track mean anomaly from 198.2 ° to 344.7 °, scope about 147 °.2 groups of track mean anomaly intervals do not have covering 360 °, have the vacancy of 2 sections about 33 °.

Orbit inclination is when 42.0 °-43.0 ° changes, and 2 days regression orbits 15 circle returns that to enclose the longitude of ascending node scope returned with 31 basically identical, between 32.2 °-41.6 °.

Therefore, return 2 days regression orbits of predetermined drop point, when not returning circle design on the same day according to 1,2, semi-major axis of orbit parameter area is basically identical, be about within the scope of 9km at 6710km to 6719km and change, orbit altitude between 340km to 348km, and along with the variation tendency of orbit inclination identical.Do not return circle on the same day for 1,2,360 ° of approximate dividing equally are 2 intervals by track mean anomaly parameter, but interval border has 2 sections of vacancies.

The parameter designing sample result of 3 days regression orbits and 2 days regression orbits shows, what the present invention proposed returns predetermined drop point regression orbit method for designing, realize sub-satellite track by selecting track mean anomaly accurately to realize track return characteristic through predetermined drop point, adjustment semi-major axis of orbit, devise the regression orbit that orbit inclination, semi-major axis of orbit and track mean anomaly are mated mutually, ensure that the every recursion period of airship sub-satellite track is accurately through predetermined drop point.

According to not returning on the same day, 3 days regression orbits exist and within 1 day, return, within 2 days, return the 3 groups of regression orbits returned with 3 days, and within 2 days, regression orbit exists the 2 groups of regression orbits returning for 1 day and returned with 2 days.

The regression orbit parameter do not returned on the same day is different, but for an orbit inclination, semi-major axis of orbit and track mean anomaly are unique match.For orbit inclination 42.0 °-43.0 °, the orbit altitude of 3 days regression orbits is between 389km to 398km; Do not return circle on the same day for 1,2,3, track mean anomaly scope is slightly larger than 120 °.The orbit altitude of 2 days regression orbits is between 330km to 348km; Do not return circle on the same day for 1,2, track mean anomaly scope is slightly less than 180 °.

The parameter designing case verification of 3 days regression orbits and 2 days regression orbits airship returns predetermined drop point regression orbit method for designing, has good engineer applied and is worth.

Above-described specific descriptions, have been described in detail object of the present invention, technical scheme and beneficial effect, and institute it should be understood that and the foregoing is only instantiation of the present invention, the protection domain be not intended to limit the present invention.

Claims (1)

1. airship returns a predetermined drop point regression orbit method for designing, it is characterized in that comprising the steps:

1) preliminary orbit parameter is set, comprises semi-major axis of orbit initial value a ₀, orbital eccentricity initial value e ₀, orbit inclination initial value i ₀, longitude of ascending node initial value D ₀, perigee of orbit argument initial value ω ₀, track Initial mean anomaly M ₀, airship quality and front face area, rail force model, rail force model comprises: earth center gravitation, figure of the earth Gravitational perturbation;

2) Track desigh condition is set, comprises: nominal drop point longitude L ₀, latitude B ₀; Initially return circle q _r; Track recursion period number of days i; Track recursion period number of turns k _i; Drop point longitude convergence threshold ε L; Return circle longitude of ascending node convergence threshold ε λ _n;

3) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

4) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), L (q _r) for initially to return circle q _rsubstar latitude is B ₀longitude; Calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r), λ (q _r) for initially to return circle q _rlongitude of ascending node, λ (q _r+ k _i) for initially to return circle q _r+ k _ilongitude of ascending node;

5) track mean anomaly deviation delta M is calculated according to following formula by returning circle substar difference of longitude Δ L;

$\mathrm{\&Delta;M}=-\mathrm{\&Delta;L}\&CenterDot;n/({\mathrm{\&omega;}}_e-\stackrel{.}{\mathrm{\&Omega;}})$

Wherein $\stackrel{.}{\mathrm{\&Omega;}}=-1.5J_2\sqrt{\mathrm{\&mu;}}{R}_e^2\cos i/\left[a^{7/2}{(1-e^2)}^2\right]$

for spacecraft orbit plane is at the mean angular velocity of inertial space precession, μ is Gravitational coefficient of the Earth, R _efor terrestrial equator reference radius, a is semi-major axis of orbit, and i is orbit inclination, and e is orbital eccentricity, and n is orbit averaging angular velocity, ω _efor rotational-angular velocity of the earth;

6) track mean anomaly is revised, M=M ₀+ Δ M;

7) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

8) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r);

9) judge whether return circle substar difference of longitude meets Δ L < ε L; If do not meet, then turn back to 5), repeat 5)-9); If meet, then forward 10 to);

10) longitude of ascending node difference Δ λ is enclosed according to following formula by returning _ncalculate semi-major axis of orbit correction amount a;

$\mathrm{\&Delta;a}=\mathrm{\&Delta;}{\mathrm{\&lambda;}}_n/[C_{\mathrm{Tn}}\&CenterDot;k_i\&CenterDot;({\mathrm{\&omega;}}_e-\stackrel{.}{\mathrm{\&Omega;}})]\&CenterDot;\sqrt{\mathrm{\&mu;}/a}/6\mathrm{\&pi;},i=\mathrm{1,2,3}$

Wherein, $\begin{array}{c}{C}_{\mathrm{Tn}}=\{1+\frac{3J_2{R}_e^2}{8a^2}[(-12-22e^2)+(16+29e^2){\sin }^{2}i+(16-20{\sin }^{2}i)e\cos \mathrm{\&omega;}\\ -(-12-15{\sin }^{2}i)e^2\cos 2\mathrm{\&omega;}\left]\right\}\end{array}$

K _ifor the recursion period number of turns, i=1,2,3, k ₁=k; k ₂=2k+1; k ₃=3k+1 and 3k+2, ω _efor rotational-angular velocity of the earth, for spacecraft orbit plane is at the mean angular velocity of inertial space precession, J ₂for terrestrial gravitational perturbation item, ω is perigee of orbit argument;

11) semi-major axis of orbit is revised, a=a ₀+ Δ a;

12) numerical integration calculates each circle latitude is B ₀substar longitude L, calculate each circle longitude of ascending node λ _n;

13) calculating returns circle substar difference of longitude Δ L=L ₀-L (q _r), calculate and return circle longitude of ascending node difference Δ λ _n=λ (q _r+ k _i)-λ (q _r);

14) judge whether return circle substar difference of longitude meets Δ L < ε L and return circle longitude of ascending node difference whether meet Δ λ simultaneously _n< ε λ _n; If do not meet, then turn back to 5), repeat 5)-14); If meet, then forward 15 to);

15) calculate end, be met the designed path parameter track semi-major axis a and the track mean anomaly M that return predetermined drop point and return characteristic, namely meeting the designed path radical returning predetermined drop point and recurrence characteristic is a, e ₀, i ₀, D ₀, ω ₀, M.