RU2531433C1 - Method to determine parameters of space object orbit - Google Patents

Abstract

FIELD: measurement equipment.

SUBSTANCE: invention relates to the methods of detection of orbits of space objects (SO), for instance, space rubbish, on-board facilities of a spacecraft (SC). The method consists in calculation of a focal parameter, true anomaly, eccentricity and inclination of the orbit of the SO of interest by analytical formulas based on laws of Keller motion. Calculations are carried out without use of iteration procedures, on the basis of detection of distances between SO and SC and certain angles in serial moments of time. This source data is produced by processing of SO images on board of a SC, produced with the help of a binocular system of optical sensors and CCD matrices.

EFFECT: increased efficiency of detection of SO orbits on board of a SC and thus safety of SC flights.

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Description

 The invention relates to the field of astronautics, namely to determining the parameters of the orbit of a space object (KO), for example, space debris, by the onboard means of the spacecraft (KA).

The invention can be used to ensure the safety of spacecraft flights by detecting and accurately determining the motion parameters of potentially dangerous spacecraft by the on-board complex, assessing the dynamics of the spacecraft and spacecraft approaching and determining the need to generate an impulse for the corrective maneuver of spacecraft evasion from spacecraft.

The well-known "Method for determining the parameters of the orbit of a spacecraft" patent RU No. 2150414, published 06/10/2000 - (D1), which consists in measuring the trajectory parameters, transferring to the control complex the totality of the measured values of the trajectory parameters with their subsequent accumulation and processing using the least squares method. Moreover, after the end of the iterative process, separate anomalous values are excluded, the accuracy of the measurements of the processed path parameters is corrected, and then the processing is cyclically repeated until it is completed and the optimal estimation of the orbital parameters of the spacecraft motion in the measurement zone of the performed communication session is obtained. The main disadvantage of this method is the low efficiency of trajectory measurements of the parameters of a space object and, therefore, the calculation of orbital data due to the limitation of the radio visibility zones of the object by ground means and the cyclic repetition of processing calculations.

The well-known "Parallactic method for determining the coordinates of an object" patent RU No. 2027144, published 01/20/1995 - (D2), based on the use of a binocular system of optical sensors spaced at a basic distance relative to each other and having parallel optical axes. The technical means that implement this method are described in the information sources: “Recognition in auto-control systems” / Shibanov GP, M .: Mechanical Engineering, 1973, p.176-188 - (D3); “Holographic pattern identification” / G. Vasilenko, M.: Soviet Radio, 1977, fig. 4.21, p. 282-283 - (D4). This method allows on the basis of the measured parallactic displacement of the tracks of the passage of space objects recorded in CCDs (CCDs with charge coupling) to determine the distances - Δr (Fig. 1) between the spacecraft and the space object and the angle - β (Fig. 2 3) between the plane of motion of the spacecraft and the direction from the spacecraft to the space object. The main disadvantage of this method is the relatively low speed when determining orbital parameters in connection with the use of computational algorithms associated with the need for iterative calculations when solving boundary value problems.

The closest set of essential features to the invention is the method described in the scientific journal "American Institute of Aeronautics and Astronautics" (US) in the publication Mark Psiaki "Autonomous orbit determination for two spacecraft from relative position measurements)) under the number AIAA-98-4560, published on 08/10/1998 - (D5), its Internet address is http://arc.aiaa.org/doi/abs/10.2514/6.1998-4560. This method uses measurements of the distance and lateral displacement of the spacecraft relative to the second spacecraft, the determination of the distances between which is carried out using laser rangefinders. In the aggregate of essential features, this method is selected as a prototype of the invention. The main disadvantage limiting the application of this method is the obligatory availability of laser location means on both space objects.

In the invention, this problem is solved by using a binocular system of optical sensors located on board the spacecraft.

The essence of the invention is to calculate the parameters of the orbit of a space object: the focal parameter - P (t _i ), the true anomaly - ϑ (t _i ), the eccentricity - e (t _i ) and the inclination of the orbit - i _{to the} space object at time t _i in accordance with mathematical dependencies obtained by the analytical method. Moreover, the calculations are carried out according to the obtained analytical formulas without using iterative computing processes. The initial information is the determination of the absolute value and orientation of the vector connecting the center of mass of the controlled spacecraft and the position of the spacecraft.

Also, the essence of the claimed method for determining the parameters of the orbit of a space object is to determine on board the spacecraft at time t _i , where i = 1, 2, 3, ..., the values of the radius vector connecting the center of the Earth with the location of the spacecraft - r _ka (t _i ), the values of the latitude of the satellite sub-satellite points - φ _ka (t _i ), the distance between the spacecraft and the space object - Δr (t _i ), the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the cosmos nical object β (t _i), wherein the further determined at points in time t _i-board optical sensors the angle between the direction from the spacecraft to the space object and the local horizon lying in the plane formed by the provisions of a spacecraft, a space object and the center of the Earth - θ ( t _i), calculating a value of the radius vector - r _to (t _i) space object connecting center of the Earth to space position of the object at time t _i and the angular distance between the current position of the spacecraft and braid nical object at time t _i - δr (t _i) in accordance with the mathematical relations:

, $$r_{\mathrm{to}\mathrm{about}}{}_{(t_i)}=\sqrt{r_{\mathrm{to}\mathrm{but}(t_i)}^2+\Delta r{(t_i)}^2-2r_{\mathrm{to}\mathrm{but}}(t_i)\Delta r(t_i)\cos [\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="00000015.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+\theta (t_i)]}$$

,

, $$\delta r(t_i)=\arcsin \left\{\frac{\Delta r(t_i)}{r_{\mathrm{to}\mathrm{about}}(t_i)}\sin [\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="00000015.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+\theta (t_i)]\right\}$$

,

Where:

r _кa (t _i ) is the radius vector of the spacecraft connecting the center of the Earth with the position of the spacecraft at time t _i ;

Δr (t _i ) is the distance between the centers of mass of the spacecraft and the space object at time t _i ;

θ (t _i ) is the angle between the direction from the spacecraft to the space object and the local horizon lying in the plane formed by the positions of the spacecraft, space object and the center of the Earth at time t _i ;

δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ,

calculate the angular distance between the positions of the space object - Δν (t _i , t _{i + 1} ) for two successive measurement times t _i and t _{i + 1} according to the formula:

Δν (t _i , t _{i + 1} ) = arccos [cosσ (t _i ) cosδr (t _{i + 1} ) -sinσ (t _i ) sinδr (t _{i + 1} ) cosα (t _i )],

Where:

σ (t _i ) = arccos [cosδr (t _i ) cosδr _ka (t _i ) -sinδr (t _i ) sinδr _ka (t _i ) cosβ (t _i )];

α (t _i ) = π-β (t _{i + 1} ) -δ (t _i );

; $$\delta (t_i)=\arcsin \left[\sin \delta (t_i)r(t_i)\frac{\sin \beta (t_i)}{\sin \sigma (t_i)}\right]$$

;

σ (t _i ) is the angular distance between the position of the spacecraft at time t _{i + 1} and the space object at time t _i ;

δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ;

δr _кa (t _i ) is the angular distance between the positions of the spacecraft at time t _i and t _{i + 1} ;

β (t _i ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _i ;

α (t _i ) is the angle between the plane formed by the positions of the spacecraft and the space object at time t _{i + 1,} and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i ;

β (r _{i + 1} ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _{i + 1} ;

δ (t _i ) is the angle between the plane of motion of the spacecraft and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i ,

calculating orbital space object: focal parameter - P (t _i), the true anomaly - θ (t _i), the eccentricity - e (t _i) and the orbital inclination - i _to a time point t _i in accordance with the mathematical relations:

,

,

, $$\vartheta (t_i)=arctg\left\{ctg\Delta \nu (t_i,t_{i+\mathrm{one}})-\frac{r_{\mathrm{to}\mathrm{about}}(t_i)[P(t_i)-r_{\mathrm{to}\mathrm{about}}(t_{i+\mathrm{one}})]}{r_{\mathrm{to}\mathrm{about}}(t_{i+\mathrm{one}})[P(t_i)-r_{\mathrm{to}\mathrm{about}}(t_i)]\sin \Delta \nu (t_i,t_{i+\mathrm{one}})}\right\}$$

,

, $$e(t_i)=\frac{P(t_i)-r_{\mathrm{to}\mathrm{about}}(t_i)}{r_{\mathrm{to}\mathrm{about}}(t_i)\cos \vartheta (t_i)}$$

,

, $$i_{\mathrm{to}\mathrm{about}}(t_i)=\arcsin \left[\frac{\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_i)}{\sin s(t_i)}\right]$$

,

Where:

; $$s(t_i)=arctg\left[\frac{\sin \Delta \nu (t_i,t_{i+\mathrm{one}})\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_i)}{\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_{i+\mathrm{one}})-\cos \Delta \nu (t_i,t_{i+\mathrm{one}})\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_i)}\right]$$

;

φ _co (t _i ) = arcsin [sinj (t _i ) sin (δz (t _i ) + δr (t _i ))];

; $$\delta z(t_i)=\arcsin \left[\frac{\sin {\varphi }_{\mathrm{to}\mathrm{but}}(t_i)}{\sin j(t_i)}\right]$$

;

j (t _i ) = arccos [cosε (t _i ) cosφ _ka (t _i )];

; $$\epsilon (t_i)=\arccos \left[\frac{\cos i_{\mathrm{to}\mathrm{but}}}{\cos {\varphi }_{\mathrm{to}\mathrm{but}}(t_i)}\right]-\beta (t_i)$$

;

r _ko (t _{i + 1} ) is the radius vector of the space object connecting the center of the Earth with the position of the space object at time t _{i + 1} ;

r _ko (t _i ) is the radius vector of the space object connecting the center of the Earth with the position of the space object at time t _i ;

µ - product of the gravitational constant by the mass of the Earth;

Δt = t _{i + 1} -t _i ;

Δν (t _i , t _{i + 1} ) is the angular distance between the positions of the space object for two successive measurement times t _i and t _{i + 1} ;

s (t _i ) - an arc lying in the plane of motion of the space object and connecting its position at time t _i and at the closest instant in time of passage of the equator;

φ _to (t _i ) is the latitude of the sub-satellite point of the space object at time t _i ;

φ _to (t _{i + 1} ) is the latitude of the sub-satellite point of the space object at time t _{i + 1} ;

j (t _i ) is the inclination of the "conditional" orbit passing through the latitudes of the satellite sub-points of the spacecraft and the space object at time t _i ;

δz (t _i ) - an arc lying in the plane of the “conditional” orbit with inclination j (t _i ) and connecting the sub-satellite point of the spacecraft at time t _i and the equator plane;

δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ;

φ _ka (t _i ) is the latitude of the sub-satellite point of the spacecraft at time t _i ;

ε (t _i ) is the heading angle for the plane of the conventional orbit passing through the latitudes of the sub-satellite points of the spacecraft, space object and the center of the Earth at time t _i ;

i _кa - inclination of the orbit of the spacecraft;

β (t _i ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _i .

The technical result of the invention is to increase the efficiency of determining the orbits of the KO motion due to the onboard processing of the optical sensors detected using the binocular system and exposed to the CCD arrays at the time t _i and t _{i + 1} images of the KO, thus obtaining the corresponding time t _i and t _{i + 1 of the} required measured angles and non-iterative calculation of the parameters of the KO orbit using the proposed mathematical dependencies.

The specified technical result is achieved by the fact that in the claimed method for determining the parameters of the orbit of a space object, which consists in determining on board the spacecraft at time t _i , where, where i = 1, 2, 3, ..., the values of the radius vector connecting the center of the Earth from the spacecraft location - r _ka (t _i), sub-satellite latitude spacecraft dots _ka -φ (t _i), values of distance between the spacecraft and space object - Δr (t _i), values of the angle between the plane of motion of the spacecraft and The direction from the spacecraft to the space object - β (t _i), it is determined at points in time t _i-board optical sensors the angle between the direction from the spacecraft to the space object and the local horizon lying in the plane formed by the provisions of a spacecraft, a space object and the center of the Earth - θ (t _i ), calculate the values of the radius vector - r _ko (t _i ) of the space object connecting the center of the Earth with the position of the space object at time t _i and the angular distance between the current positions the spacecraft and the spacecraft at time t _i - δr (t _i ) in accordance with the mathematical dependencies:

, $$r_{\mathrm{to}\mathrm{about}}(t_i)=\sqrt{r_{\mathrm{to}\mathrm{but}(t_i)}^2+\Delta r{(t_i)}^2-2r_{\mathrm{to}\mathrm{but}}(t_i)\Delta r(t_i)\cos [\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="00000015.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+\theta (t_i)]}$$

,

, $$\delta r(t_i)=\arcsin \left\{\frac{\Delta r(t_i)}{r_{\mathrm{to}\mathrm{about}}(t_i)}\sin [\frac{\mathrm{<figure-callout\; id="2"\; label="\pi "\; filenames="00000015.png"\; state="\{\{state\}\}">\pi </figure-callout>}}{2}+\theta (t_i)]\right\}$$

,

Where:

r _ka (t _i ) is the radius vector of the spacecraft connecting the center of the Earth with the position of the spacecraft at time t _i ;

Δr (t _i ) is the distance between the centers of mass of the spacecraft and the space object at time t _i ;

θ (t _i ) is the angle between the direction from the spacecraft to the space object and the local horizon lying in the plane formed by the positions of the spacecraft, space object and the center of the Earth at time t _i ;

δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ,

calculate the angular distance between the positions of the space object - Δν (t _i , t _{i + 1} ) for two successive measurement times t _i and t _{i + 1} according to the formula:

Δν (t _i , t _{i + 1} ) = arccos [cosσ (t _i ) cosδr (t _{i + 1} ) -sinσ (t _i ) sinδr (t _{i + 1} ) cosα (t _i )],

Where:

σ (t _i ) = arccos [cosδr (t _i ) cosδr _ka (t _i ) -sinδr (t _i ) sinδr _ka (t _i ) cosβ (t _i )];

α (t _i ) = π-β (t _{i + 1} ) -δ (t _i );

; $$\delta (t_i)=\arcsin \left[\sin \delta (t_i)r(t_i)\frac{\sin \beta (t_i)}{\sin \sigma (t_i)}\right]$$

;

σ (t _i ) is the angular distance between the position of the spacecraft at time t _{i + 1} and the space object at time t _i ;

δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ;

δr _кa (t _i ) is the angular distance between the positions of the spacecraft at time t _i and t _{i + 1} ;

β (t _i ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _i ;

α (t _i ) is the angle between the plane formed by the positions of the spacecraft and the space object at time t _{i + 1,} and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i ;

β (t _{i + 1} ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _{i + 1} ;

δ (t _i ) is the angle between the plane of motion of the spacecraft and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i ,

calculate the parameters of the orbit of the space object: the focal parameter is P (t _i ), the true anomaly is ϑ (t _i ), the eccentricity is e (t _i ) and the inclination of the orbit is i _ko at time t _i in accordance with the mathematical dependencies:

,

,

, $$\vartheta (t_i)=arctg\left\{ctg\Delta \nu (t_i,t_{i+\mathrm{one}})-\frac{r_{\mathrm{to}\mathrm{about}}(t_i)[P(t_i)-r_{\mathrm{to}\mathrm{about}}(t_{i+\mathrm{one}})]}{r_{\mathrm{to}\mathrm{about}}(t_{i+\mathrm{one}})[P(t_i)-r_{\mathrm{to}\mathrm{about}}(t_i)]\sin \Delta \nu (t_i,t_{i+\mathrm{one}})}\right\}$$

,

, $$e(t_i)=\frac{P(t_i)-r_{\mathrm{to}\mathrm{about}}(t_i)}{r_{\mathrm{to}\mathrm{about}}(t_i)\cos \vartheta (t_i)}$$

,

, $$i_{\mathrm{to}\mathrm{about}}(t_i)=\arcsin \left[\frac{\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_i)}{\sin s(t_i)}\right]$$

,

Where:

; $$s(t_i)=arctg\left[\frac{\sin \Delta \nu (t_i,t_{i+\mathrm{one}})\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_i)}{\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_{i+\mathrm{one}})-\cos \Delta \nu (t_i,t_{i+\mathrm{one}})\sin {\varphi }_{\mathrm{to}\mathrm{about}}(t_i)}\right]$$

;

φ _co (t _i ) = arcsin [sinj (t _i ) sin (δz (t _i ) + δr (t _i ))];

; $$\delta z(t_i)=\arcsin \left[\frac{\sin {\varphi }_{\mathrm{to}\mathrm{but}}(t_i)}{\sin j(t_i)}\right]$$

;

j (t _i ) = arccos [cosε (t _i ) cosφ _ka (t _i )];

; $$\epsilon (t_i)=\arccos \left[\frac{\cos i_{\mathrm{to}\mathrm{but}}}{\cos {\varphi }_{\mathrm{to}\mathrm{but}}(t_i)}\right]-\beta (t_i)$$

;

r _ko (t _{i + 1} ) is the radius vector of the space object connecting the center of the Earth with the position of the space object at time t _{i + 1} ;

r _ko (t _i ) is the radius vector of the space object connecting the center of the Earth with the position of the space object at time t _i ;

µ is the product of the gravitational constant by the mass of the Earth;

Δt = t _{i + 1} -t _i ;

Δν (t _i , t _{i + 1} ) is the angular distance between the positions of the space object for two successive measurement times t _i and t _{i + 1} ;

s (t _i ) - an arc lying in the plane of motion of the space object and connecting its position at time t _i and at the closest instant in time of passage of the equator;

φ _to (t _i ) is the latitude of the sub-satellite point of the space object at time t _i ;

φ _to (t _{i + 1} ) is the latitude of the sub-satellite point of the space object at time t _{i + 1} ;

j (t _i ) is the inclination of the "conditional" orbit passing through the latitudes of the satellite sub-points of the spacecraft and the space object at time t _i ;

δz (t _i ) - an arc lying in the plane of the “conditional” orbit with inclination j (t _i ) and connecting the sub-satellite point of the spacecraft at time t _i and the equator plane;

δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ;

φ _ka (t _i ) is the latitude of the sub-satellite point of the spacecraft at time t _i ;

ε (t _i ) is the heading angle for the plane of the conventional orbit passing through the latitudes of the sub-satellite points of the spacecraft, space object and the center of the Earth at time t _i ;

i _ka - the inclination of the orbit of the spacecraft;

β (t _i ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _i .

The claimed method for determining the parameters of the orbit of a space object is illustrated by the following figures:

- figure 1 shows the relative location of the spacecraft and TO,

- figure 2 shows the relative location of the planes of motion of the spacecraft and spacecraft,

- figure 3 presents the trajectory of the spacecraft and spacecraft.

In figure 1-figure 3 and in the text the following notation:

1 - the surface of the Earth,

2 - KA,

3 - the radius vector of the spacecraft, connecting the origin (center of the earth) with the position of the spacecraft on its trajectory - r _ka ,

4 - the angular distance between the current positions of the spacecraft and the space object is δr,

5 - the radius of the Earth - R,

6 - the angle between the direction from the spacecraft to the spacecraft and the local horizon lying in the plane formed by the positions of the spacecraft, spacecraft and the center of the earth - θ,

7 - the distance between the centers of mass of the spacecraft and the space object - Δr,

8 - radius - the vector of a space object connecting the origin (center of the earth) with the position of KO - r _ko ,

9 - local horizon,

10 - KO,

11 is the measurement time t _i preceding the measurement time t _{i + 1} ;

12 is the angular distance between the positions of the spacecraft at time t _i and t _{i + 1} - δr _ka ,

13 - the angle between the plane of motion of the spacecraft and the direction from the spacecraft to KO - β,

14 - the time of measurements t _{i + 1} , following the time of measurements t _i ;

15 is the angle between the plane of motion of the spacecraft and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i - δ,

16 is the angle between the plane of the large circle formed by the positions of the spacecraft and the space object at time t _{i + 1,} and the plane of the large circle formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i - α,

17 - the flight path of the spacecraft,

18 - the angular distance between the position of the spacecraft and the space object - σ,

19 is the angular distance between the positions of the space object at time t _i and t _{i + 1} - Δν,

20 - flight path KO,

21 - the equatorial plane passing through the center of the Earth perpendicular to the axis of its rotation;

22 - the angular distance between the position of the spacecraft at time t _i and the equator plane lying in the plane of the conventional orbit formed by the positions of the spacecraft and spacecraft at time t _i and the center of the Earth - δZ,

23 - inclination of the orbit of the spacecraft - i _ka ,

24 - the latitude of the satellite sub-satellite point at time t _i - φ _ka ,

25 is the heading angle for the plane of the conventional orbit passing through the latitudes of the sub-satellite points of the spacecraft, space object and the center of the Earth at time t _i - ε (t _i ),

26 - heading angle between the projection of the spacecraft velocity vector on the local horizon and the local parallel at time t _i - ε (t _i ),

27 - the inclination of the orbit of a space object - i _to ,

28 is the latitude of the sub-satellite point KO at time t _i - φ _ko (t _i ),

29 - local parallel at the latitude of the satellite sub-satellite point at time t _i ,

30 - latitude of the sub-satellite point of the TO at the time t _{i + 1} - φ _to (t _{i + 1} ).

We show the possibility of carrying out the invention, i.e. the possibility of its industrial application.

When implementing the invention from ground control points daily during a communication session, a command-program information is recorded on board the spacecraft containing data on its current orbital parameters at the time of the communication session (“Onboard spacecraft control systems”: Training manual / Brovkin A.G. ., Burdygov B.G., Gordiyko S.V. et al., Edited by Syrov A.S. M: Publishing House MAI-PRINT, 2010, p. 45-47, 56-61, 80-98) - (D6). Next, space objects are registered with onboard optical sensors, which are a binocular system of optical sensors spaced apart from each other and have parallel optical axes (D3, D4). Based on the measured parallactic displacement of the tracks of the passage of space objects fixed on the CCD matrices at the moments of time t _i and t _{i + 1} , the distance between the centers of mass of the spacecraft and the space object (Δr), as well as the angle β, is determined by method (D2) between the plane of motion of the spacecraft and the direction from the spacecraft to the space object (D6). Then, the onboard optical sensors and actuators of the spacecraft stabilization and orientation system described in (D6, p. 80-98) determine the angle θ (Fig. 1, position 6) between the direction from the spacecraft to the space object and the local horizon lying in a plane formed by the positions of the spacecraft, spacecraft and the center of the earth. Further, according to the above formulas, the orbit parameters of a space object are determined.

The procedures and technology for daily recording of command-program information containing data on the current orbital parameters of the spacecraft at the time of the communication session are shown in (D6, p. 45-47).

Registration of space objects, as well as the composition and technical capabilities of onboard optical sensors are given in (D6, p. 56-61).

The implementation of a binocular system of optical sensors spaced apart and having parallel optical axes is described in (D3, D4).

The method of measuring the parallactic displacement of the tracks of the passage of space objects fixed on CCD matrices, as well as measuring the distances between the centers of mass of the spacecraft and the space object Δr and angles β between the plane of motion of the spacecraft and the directions from the spacecraft to the space object, is carried out according to the methods given in (D2 and D3).

The interaction of onboard optical sensors and executive bodies of the spacecraft stabilization and orientation system described in (D6, p. 80-98) makes it possible to determine the angle - θ between the direction from the spacecraft to the space object and the local horizon lying in the plane formed by the spacecraft’s positions, KO and the center of the Earth.

The possibility of implementing an iterative computational on-board algorithm that refines the orbital parameters of a space object and predicts the minimum distance between the spacecraft and the space object is shown in the information sources: Guidance in Space / Richard Bettin. - M .: Engineering, 1966 - (D7), “Introduction to the theory of flight of artificial earth satellites” / Elyasberg P.E. - M .: Nauka, 1965 - (D8).

Claims (1)

The method of determining the parameters of the orbit of a space object, which consists in determining on board the spacecraft at time t _i , where i = 1, 2, 3, ..., the values of the radius vector r _ka (t _i ) connecting the center of the Earth with the location of the spacecraft, values _kA latitude φ (t _i) sub-satellite points spacecraft, Δr distance values (t _i) between the spacecraft and space object angle values β (t _i) between the plane of motion of the spacecraft and the direction of the spacecraft to a space object differs schiysya by determining at time points t _i airborne optical sensors angle θ (t _i) between the direction from the spacecraft to the space object and the local horizon lying in the plane formed by the provisions of a spacecraft, a space object and the center of the Earth radius value calculated _to the vector r (t _i) space object connecting center of the Earth to space object position at the moment of time t _i and the angular distance δr (t _i) between the current position of the spacecraft and space object at time webbings t _i in accordance with the mathematical relations:

,

,
Where:
r _ka (t _i ) is the radius vector of the spacecraft connecting the center of the Earth with the position of the spacecraft at time t _i ;
Δr (t _i ) is the distance between the centers of mass of the spacecraft and the space object at time t _i ;
θ (t _i ) is the angle between the direction from the spacecraft to the space object and the local horizon, lying in the plane formed by the positions of the spacecraft, space object and the center of the Earth at time t _i ;
δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ,
calculate the angular distance Δ v (t _i , t _{i + 1} ) between the positions of the space object for two consecutive measurement times t _i and t _{i + 1} according to the formula:
Δ v (t _i , t _{i + 1} ) = arccos [cosσ (t _i ) cosδr (t _{i + 1} ) -sinσ (t _i ) sinδr (t _{i + 1} ) cosα (t _i )],
Where:
σ (t _i ) = arccos [cosδr (t _i ) cosδr _ka (t _i ) -sinδr (t _i ) sinδr _ka (t _i ) cosβ (t _i )];
α (t _i ) = π-β (t _{i + 1} ) -δ (t _i );

;
σ (t _i ) is the angular distance between the position of the spacecraft at time t _{i + 1} and the space object at time t _i ;
δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ;
_Single δr (t _i) - the angular distance between the positions of the spacecraft at instants t _i and t _{i + 1;}
β (t _i ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _i ;
α (t _i ) is the angle between the plane formed by the positions of the spacecraft and the space object at time t _{i + 1} , and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i ;
β (t _{i + 1} ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _{i + 1} ;
δ (t _i ) is the angle between the plane of motion of the spacecraft and the plane formed by the positions of the spacecraft at time t _{i + 1} and the space object at time t _i ,
calculate the parameters of the orbit of the space object: the focal parameter P (t _i ), the true anomaly ϑ (t _i ), the eccentricity e (t _i ) and the inclination of the orbit i _ko at time t _i in accordance with the mathematical dependencies:

,

,

,

,
Where:

;
φ _co (t _i ) = arcsin [sinj (t _i ) sin (δz (t _i ) + δr (t _i ))];

;
j (t _i ) = arccos [cosε (t _i ) cosφ _ka (t _i )];

;
r _ko ( _{i + 1} ) is the radius vector of the space object connecting the center of the Earth with the position of the space object at time t _{i + 1} ;
r _ko (t _i ) is the radius vector of the space object connecting the center of the Earth with the position of the space object at time t _i ;
µ is the product of the gravitational constant by the mass of the Earth;
Δt = t _{i + 1} -t _i;
Δ v (t _i , t _{i + 1} ) is the angular distance between the positions of the space object for two successive measurement times t _i and t _{i + 1} ;
s (t _i ) - an arc lying in the plane of motion of the space object and connecting its position at time t _i and at the closest instant in time of passage of the equator;
φ _to (t _i ) is the latitude of the sub-satellite point of the space object at time t _i ;
φ _to (t _{i + 1} ) is the latitude of the sub-satellite point of the space object at time t _{i + 1} ;
j (t _i ) is the inclination of the "conditional" orbit passing through the latitudes of the satellite sub-points of the spacecraft and the space object at time t _i ;
δz (t _i ) - an arc lying in the plane of the “conditional” orbit with inclination j (t _i ) and connecting the sub-satellite point of the spacecraft at time t _i and the equator plane;
δr (t _i ) is the angular distance between the current positions of the spacecraft and the space object at time t _i ;
φ _ka (t _i ) is the latitude of the sub-satellite point of the spacecraft at time t _i ;
ε (t _i ) is the heading angle for the plane of the conventional orbit passing through the latitudes of the sub-satellite points of the spacecraft, space object and the center of the Earth at time t _i ;
i _ka - the inclination of the orbit of the spacecraft;
β (t _i ) is the angle between the plane of motion of the spacecraft and the direction from the spacecraft to the space object at time t _i .

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