CN102679945A - Satellite pointing and attitude measuring method and device based on three-point reflecting cooperation - Google Patents

Abstract

The invention discloses a satellite pointing and attitude measuring method and a satellite pointing and attitude measuring device based on three-point reflecting cooperation, and belong to an angle measurement technology in the field of measurement. According to the device, three cube-corner prisms are arranged on a small satellite to be measured; the three cube-corner prisms form a right triangle of which the normal vector does not change along with the rotation of the small satellite to be measured; a laser of a reference small satellite is dead against the midpoint of hypotenuse of the right triangle formed by the three cube-corner prisms; and constructing a mathematic relation of the distance between the two cube-corner prisms on the small satellite to be measured, which are positioned on the right-angle sides, and the projection distance of the two cube-corner prisms on the reference small satellite. According to the method, the reference line deflection angle and spatial attitude angle of the small satellite to be measured relative to the reference small satellite are measured. By adoption of the device and the method, the pointing and spatial attitude of the small satellite to be measured relative to the reference small satellite can be indirectly acquired only by measuring the angle of the small satellite to be measured relative to the reference small satellite; the measurement device is simple, and the measurement result is accurate.

Description

Satellite sensing and attitude measurement method and device based on three point reflection cooperations

Technical field

The invention belongs to the measurement of angle technology in the field tests of measuring, relate generally in a kind of moonlet formation technology, come to obtain indirectly measuring method and the device of moonlet to be measured with respect to benchmark moonlet position and distance through measurement of angle.

Background technology

Along with rapid development of science and technology, the Small Satellite Formation Flying technology receives the great attention of various countries.Small Satellite Formation Flying is meant that a Small Satellite Group a bit is a benchmark with certain, keeps a given shape, orbits the earth with the identical orbital period.Tasks such as signal Processing, communication and useful load are born in the mutual collaborative work of each of formation flight moonlet jointly.The Small Satellite Group of formation flight not only can substitute traditional large satellite of single identical function with lower cost, higher reliability and viability; Can also break through the size restrictions of traditional large satellite; The application and the performance of expansion large satellite; Comprise earth observation, three-dimensional imaging, accurate location, atmospheric exploration, astronomical sight and geophysical observatory etc., have huge military value and civilian value.

Though the Small Satellite Formation Flying technology has broad application prospects, be faced with the challenge of supertech difficulty.Because being the accurate control through base measurement between high-precision star and formation satellite formation, the superiority of the moonlet of formation flight realizes; And the measuring accuracy to baseline requires to reach a centimetre magnitude; Even the millimeter magnitude, pointing accuracy and attitude measurement accuracy all require to reach a rad magnitude, therefore; Embody the superiority of Small Satellite Formation Flying, at first will carry out high-acruracy survey formation moonlet state.

Quantity of state comprises flying speed, height and the rotational angle of every moonlet, and the measurement of quantity of state is divided into the absolute status measurement again and relative status is measured.Compare with the absolute status measurement; The relative status surveying party realizes that moonlet formation autonomous flight, formation maintenance and control etc. have prior meaning, in numerous relative status amounts, and the position of moonlet relative datum moonlet to be measured; Comprising angle and distance, is the basis that keeps satellite communication.

In space flight intersection field; Like in January, 2008; No. 1 publish an article " based on the measuring method of relative position and attitude between the spacecraft of binocular vision " of aerospace journal the 29th volume; In March, 2010 and for example; Optical technology the 36th volume is delivered " based on relative pose Measurement Algorithm between the spacecraft of the monocular vision " article of etc.ing No. 2, and all extensively a kind of method of employing is respectively according to the attitude of benchmark moonlet and the attitude of moonlet to be measured, sets up the three-dimensional coordinate of benchmark moonlet and the three-dimensional coordinate of moonlet to be measured; And moonlet three-dimensional coordinate to be measured is rotated with translation and can overlaps with benchmark moonlet three-dimensional coordinate, and rotation amount and translational movement can obtain through matrix operation.This method proposes for the docking technique that solves in the space flight intersection field; Though can accurately measure moonlet to be measured with respect to benchmark moonlet direction of living in and attitude, the shortcoming of this method is the distance that can't measure between moonlet to be measured and the benchmark moonlet.

In laser ranging field, like Chinese patent publication number CN101349757A, open day on January 21st, 2009; Invention " active collaboration type phase laser distance measuring method and device "; Disclose a kind of laser distance measurement method, this method is utilized twin-beam one way cooperation measurement pattern, and the attenuated form that makes measuring system light echo energy is the quadratic power attenuation function; Therefore can increase system's light echo energy and signal to noise ratio (S/N ratio) to a great extent, be fit to long-range range finding.This method is applied to formation moonlet relative status measures, can accurately obtain two distances between the moonlet, yet the maximum shortcoming of this method is to measure the angle of moonlet relative datum moonlet to be measured.

Summary of the invention

The present invention is directed to the problem that exists in the above-mentioned prior art, designed a kind ofly, can obtain moonlet to be measured simultaneously with respect to the sensing of benchmark moonlet and the measuring method and the device of spatial attitude only through measurement of angle.

The objective of the invention is to realize like this:

Satellite based on three point reflection cooperations points to and attitude measurement method, may further comprise the steps:

A, first constantly; Laser instrument emitted laser bundle is through the Amici prism transmission; By behind first prism of corner cube, second prism of corner cube, the pyrometric cone prismatic reflection, Yan Yuanlu returns again, reflects through Amici prism for the second time after the telescope imaging; And by the imageing sensor collection, and view data is flowed to computing machine handle; Through mathematical operation, obtain first prism of corner cube under the situation of not considering magnification of telescope and second prism of corner cube with the laser beam vertical direction on projector distance d ₁With second prism of corner cube and pyrometric cone prism with the laser beam vertical direction on projector distance d ₂

B, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, on the moonlet to be measured between first prism of corner cube and second prism of corner cube apart from l ₁, utilize first prism of corner cube that a step obtains and second prism of corner cube with the laser beam vertical direction on projector distance d ₁, use calculating formula:

$d_1=l_1\frac{r_1-r_2\cos \mathrm{\α}}{\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}$

Try to achieve the angle of the benchmark moonlet radius of gyration and the moonlet radius of gyration to be measured;

C, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, on the moonlet to be measured between second prism of corner cube and the pyrometric cone prism apart from l ₂, utilize second prism of corner cube that a step obtains and pyrometric cone prism with the laser beam vertical direction on projector distance d ₂, and the benchmark moonlet radius of gyration that obtains of b step and the angle of the moonlet radius of gyration to be measured, and the coordinate of establishing the benchmark moonlet is (r ₁, 0,0), use calculating formula:

$h=\frac{\sqrt{l_2^2-d_2^2}\sqrt{r_1^2{r}_2^2-2r_1{r}_2\cos \mathrm{\α}}}{d_2}$

Try to achieve the distance h of benchmark moonlet place rotational plane and moonlet to be measured place rotational plane, the coordinate of moonlet to be measured is (r ₂Cos α, r ₂Sin α, h);

D, second constantly; Laser instrument emitted laser bundle is through the Amici prism transmission; Again by behind first prism of corner cube, second prism of corner cube, the pyrometric cone prismatic reflection; Return along former road, for the second time through the Amici prism reflection after telescope imaging and by the imageing sensor collection, and view data flowed to computing machine handle; Through mathematical operation, obtain first prism of corner cube and second prism of corner cube with the laser beam vertical direction on projector distance d ' ₁

E, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, on the moonlet to be measured between first prism of corner cube and the second pyramid rib apart from l ₁, between the second pyramid rib and the pyrometric cone rib apart from l ₂, utilize first prism of corner cube that a step obtains and second prism of corner cube with the laser beam vertical direction on projector distance d ₁, the benchmark moonlet radius of gyration that b step obtains and the angle of the moonlet radius of gyration to be measured, d go on foot first prism of corner cube that obtains and second prism of corner cube with the laser beam vertical direction on projector distance d ' ₁, use calculating formula:

$\mathrm{\β}=\arcsin \frac{l_1{d}_1^{\′}(r_1-r_2\cos \mathrm{\α})}{l_2{d}_1\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}-\arcsin \frac{r_1-r_2\cos \mathrm{\α}}{\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}$

Try to achieve relative first constantly, the angle that benchmark moonlet and moonlet to be measured are turned over, and the coordinate that obtains benchmark moonlet this moment is (r ₁Cos β, r ₁Sin β, 0), the coordinate of moonlet to be measured is (r ₂Cos (alpha+beta), r ₂Sin (alpha+beta), h);

F, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, utilize the benchmark moonlet radius of gyration and the angle of the moonlet radius of gyration to be measured that b step obtains, and the benchmark moonlet place rotational plane that obtains of c step and the moonlet to be measured distance h that belongs to rotational plane, use calculating formula:

$d=\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}+h^2}$

Obtain between benchmark moonlet and the moonlet to be measured apart from d.

Satellite based on three point reflection cooperations points to and attitude measuring; Be included in and dispose laser instrument, Amici prism, telescope, imageing sensor and computing machine on the benchmark moonlet; Amici prism is positioned on the emitting light path of laser instrument; Telescope and imageing sensor are positioned on the reflected light path of Amici prism, and computing machine is communicated with imageing sensor; Configuration first prism of corner cube, second prism of corner cube, pyrometric cone prism on moonlet to be measured; The laser instrument emitted laser bundle of benchmark moonlet is through the Amici prism transmission; Again by behind first prism of corner cube, second prism of corner cube, the pyrometric cone prismatic reflection; Return along former road, for the second time through the Amici prism reflection after telescope imaging and by the imageing sensor collection, and view data flowed to computing machine handle; First prism of corner cube, second prism of corner cube, the pyrometric cone prism triangular arrangement that on moonlet to be measured, meets at right angles; Wherein second prism of corner cube is positioned at place, summit, right angle, and first prism of corner cube and second prism of corner cube place straight line and second prism of corner cube and pyrometric cone prism place straight line are orthogonal; The normal vector direction on first prism of corner cube, second prism of corner cube and plane, pyrometric cone prism place is constant; Laser instrument emitted laser bundle on the benchmark moonlet is through the Amici prism transmission, and the direction of transmitted light beam is pointed to the mid point of moonlet first prism of corner cube to be measured and pyrometric cone prism line.

Characteristics of the present invention are:

1. on moonlet to be measured, disposed three prism of corner cubes, and let planar form right angle triangle of these three prism of corner cubes, this is one of the present invention's essential characteristic of being different from existing method and apparatus;

2. the normal vector direction that guarantees plane, three prism of corner cube places is constant, and just prism of corner cube does not rotate with moonlet to be measured, and this is that the present invention is different from one of essential characteristic that has method and apparatus now;

3. the laser instrument that remains the benchmark moonlet faces the hypotenuse point midway that three prism of corner cubes constitute, and this is that the present invention is different from one of essential characteristic that has method and apparatus now;

Above-mentioned three characteristics can guarantee to be on the moonlet to be measured the mathematical relation that distance and their projector distances on the benchmark moonlet between two prism of corner cubes on the right-angle side become to confirm.Utilize the pairing mathematical relation of device according to the invention, can measure the angle of moonlet relative datum moonlet to be measured.

The beneficial effect that These characteristics is brought is: only through the angle of moonlet relative datum moonlet to be measured is measured, just can obtain moonlet to be measured indirectly with respect to benchmark moonlet position and distance, measurement mechanism is simple, and measurement result is accurate.

Description of drawings

Fig. 1 is that the formation Small Satellite Group is rotated synoptic diagram around the earth

The satellite that Fig. 2 is based on three point reflection cooperations points to and the attitude measuring structural representation

Fig. 3 is the moonlet relative position synoptic diagram of forming into columns in first moment

Fig. 4 is the moonlet relative position synoptic diagram of forming into columns in second moment

Piece number explanation among the figure: 1 laser instrument, 2 Amici prisms, 3 telescopes, 4 imageing sensors, 5 computing machines, 6 first prism of corner cubes, 7 second prism of corner cubes, 8 pyrometric cone prisms.

Embodiment

Below in conjunction with accompanying drawing the specific embodiment of the invention is described in detail.

Satellite based on three point reflection cooperations points to and attitude measuring; Be included in configuration laser instrument 1, Amici prism 2, telescope 3, imageing sensor 4 and computing machine 5 on the benchmark moonlet; Amici prism 2 is positioned on the emitting light path of laser instrument 1; Telescope 3 is positioned on the reflected light path of Amici prism 2 with imageing sensor 4, and computing machine 5 is communicated with imageing sensor 4; Configuration first prism of corner cube 6, second prism of corner cube 7, pyrometric cone prism 8 on moonlet to be measured; The laser instrument 1 emitted laser bundle of benchmark moonlet is through Amici prism 2 transmissions; Again by after first prism of corner cube 6, second prism of corner cube 7,8 reflections of pyrometric cone prism; Return along former road, for the second time through Amici prism 2 reflections after telescope 3 imagings and gather by imageing sensor 4, and view data flowed to computing machine 5 handle; First prism of corner cube 6, second prism of corner cube 7, pyrometric cone prism 8 triangular arrangement that on moonlet to be measured, meets at right angles; Wherein second prism of corner cube 7 is positioned at place, summit, right angle, and first prism of corner cube 6 and second prism of corner cube, 7 place straight lines and second prism of corner cube 7 and pyrometric cone prism 8 place straight lines are orthogonal; The normal vector direction on first prism of corner cube 6, second prism of corner cube 7 and plane, pyrometric cone prism 8 place is constant; Laser instrument 1 emitted laser bundle on the benchmark moonlet is through Amici prism 2 transmissions, and the direction of transmitted light beam is pointed to the mid point of moonlet first prism of corner cube 6 to be measured and pyrometric cone prism 8 lines.

Satellite based on three point reflection cooperations points to and attitude measurement method, may further comprise the steps:

A, first constantly; Laser instrument 1 emitted laser bundle is through Amici prism 2 transmissions; Again by after first prism of corner cube 6, second prism of corner cube 7,8 reflections of pyrometric cone prism; Return along former road, for the second time through Amici prism 2 reflections after telescope 3 imagings and gather by imageing sensor 4, and view data flowed to computing machine 5 handle; Through mathematical operation, obtain under the situation of not considering telescope 3 magnifications, first prism of corner cube 6 and second prism of corner cube 7 with the laser beam vertical direction on projector distance d ₁=86.6mm, second prism of corner cube 7 and pyrometric cone prism 8 with the laser beam vertical direction on projector distance d ₂=65.5mm, this moonlet relative position of forming into columns constantly is as shown in Figure 2;

B, according to the orbit radius r of benchmark moonlet ₁=10km, the orbit radius r of moonlet to be measured ₂=10km, on the moonlet to be measured between first prism of corner cube 6 and second prism of corner cube 7 apart from l ₁=100mm, utilize first prism of corner cube 6 that a step obtains and second prism of corner cube 7 with the laser beam vertical direction on projector distance d ₁=86.6mm, use calculating formula:

$d_1=l_1\frac{r_1-r_2\cos \mathrm{\α}}{\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}$

$86.6\×{10}^{-3}=100\×{10}^{-3}\×\frac{10\×{10}^3-10\×{10}^3\cos \mathrm{\α}}{\sqrt{{(10\×{10}^3)}^2+{(10\×{10}^3)}^2-2\×(10\×{10}^3)(10\×{10}^3)\cos \mathrm{\α}}}$

Can be in the hope of angle=120 of the benchmark moonlet radius of gyration and the moonlet radius of gyration to be measured °;

C, according to the orbit radius r of benchmark moonlet ₁=10km, the orbit radius r of moonlet to be measured ₂=10km, on the moonlet to be measured between second prism of corner cube 7 and the pyrometric cone prism 8 apart from l ₂=100mm, utilize second prism of corner cube 7 that a step obtains and pyrometric cone prism 8 with the laser beam vertical direction on projector distance d ₂=65.5mm, and angle=120 of the benchmark moonlet radius of gyration that obtains of b step and the moonlet radius of gyration to be measured °, use calculating formula:

$h=\frac{\sqrt{l_2^2-d_2^2}\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}{d_2}$

$h=\frac{\sqrt{{(100\×{10}^{-3})}^2-{(65.5\×{10}^{-3})}^2}\sqrt{{(10\×{10}^3)}^2+{(10\×{10}^3)}^2-2\×(10\×{10}^3)\×\cos \left(\frac{2\mathrm{\π}}{3}\right)}}{65.5\×{10}^{-3}}$

Can be in the hope of the distance h=20km of benchmark moonlet place rotational plane with moonlet to be measured place rotational plane, and if the coordinate that can access the benchmark moonlet be (10,0,0), then the coordinate of moonlet to be measured is (5,8.66,20), the km of unit;

D, second constantly; Laser instrument 1 emitted laser bundle is through Amici prism 2 transmissions; Again by after first prism of corner cube 6, second prism of corner cube 7,8 reflections of pyrometric cone prism; Return along former road, for the second time through Amici prism 2 reflections after telescope 3 imagings and gather by imageing sensor 4, and view data flowed to computing machine 5 handle; Through mathematical operation, obtain first prism of corner cube 6 and second prism of corner cube 7 with the laser beam vertical direction on projector distance d ' ₁=100mm, this moonlet relative position of forming into columns constantly is as shown in 3;

E, according to the orbit radius r of benchmark moonlet ₁=10km, the orbit radius r of moonlet to be measured ₂=10km, on the moonlet to be measured between first prism of corner cube 6 and second prism of corner cube 7 apart from l ₁=100mm, between second prism of corner cube 7 and the pyrometric cone prism 8 apart from l ₂=100mm, utilize first prism of corner cube 6 that a step obtains and second prism of corner cube 7 with the laser beam vertical direction on projector distance d ₁=86.6mm, the benchmark moonlet radius of gyration that b step obtains and angle=120 of the moonlet radius of gyration to be measured °, d go on foot first prism of corner cube 6 that obtains and second prism of corner cube 7 with the laser beam vertical direction on projector distance d ' ₁=100mm, use calculating formula:

$\mathrm{\β}=\arcsin \frac{l_1{d}_1^{\′}(r_1-r_2\cos \mathrm{\α})}{l_2{d}_1\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}-\arcsin \frac{r_1-r_2\cos \mathrm{\α}}{\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}$

$\mathrm{\β}=\arcsin \frac{100\×{10}^{-3}\×100\×{10}^{-3}\×(10\×{10}^3-10\×{10}^3\×\cos \left(\frac{2\mathrm{\π}}{3}\right))}{100\×{10}^{-3}\×86.6\×{10}^{-3}\×\sqrt{{(10\×{10}^3)}^2+{(10\×{10}^3)}^2-2\×(10\×{10}^3)\×(10\×{10}^3)\×\cos \left(\frac{2\mathrm{\π}}{3}\right)}}$

$-\arcsin \frac{10\×{10}^3-10\×{10}^3\×\cos \left(\frac{2\mathrm{\π}}{3}\right)}{\sqrt{{(10\×{10}^3)}^2+{(10\×{10}^3)}^2-2\×(10\×{10}^3)\×(10\×{10}^3)\×\cos \left(\frac{2\mathrm{\π}}{3}\right)}}$

Can be in the hope of relative first constantly, the angle that benchmark moonlet and moonlet to be measured are turned over, and the coordinate that can access benchmark moonlet this moment is (8.66,5,0), the coordinate of moonlet to be measured is (8.66,5,20), the km of unit;

F, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, utilize angle=120 ° of the benchmark moonlet radius of gyration that b step obtains and the moonlet radius of gyration to be measured, and the benchmark moonlet place rotational plane that obtains of c step and moonlet to be measured distance h=20km of belonging to rotational plane, use calculating formula:

$d=\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}+h^2}$

$d=\sqrt{{(10\×{10}^3)}^2+{(10\×{10}^3)}^2-2\×(10\×{10}^3)\×(10\×{10}^3)\×\cos \frac{2\mathrm{\π}}{3}+{(20\×{10}^3)}^2}=26.458\mathrm{km}$

The distance that can try to achieve between benchmark moonlet and the moonlet to be measured is 26.458km.

Claims (2)

1. the satellite based on three point reflection cooperations points to and attitude measurement method, it is characterized in that may further comprise the steps:

A, first constantly; Laser instrument emitted laser bundle is through the Amici prism transmission; By behind first prism of corner cube, second prism of corner cube, the pyrometric cone prismatic reflection, Yan Yuanlu returns again, reflects through Amici prism for the second time after the telescope imaging; And by the imageing sensor collection, and view data is flowed to computing machine handle; Through mathematical operation, obtain first prism of corner cube under the situation of not considering magnification of telescope and second prism of corner cube with the laser beam vertical direction on projector distance d ₁With second prism of corner cube and pyrometric cone prism with the laser beam vertical direction on projector distance d ₂

B, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, on the moonlet to be measured between first prism of corner cube and second prism of corner cube apart from l ₁, utilize first prism of corner cube that a step obtains and second prism of corner cube with the laser beam vertical direction on projector distance d ₁, use calculating formula:

$d_1=l_1\frac{r_1-r_2\cos \mathrm{\α}}{\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}$

Try to achieve the angle of the benchmark moonlet radius of gyration and the moonlet radius of gyration to be measured;

C, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, on the moonlet to be measured between second prism of corner cube and the pyrometric cone prism apart from l ₂, utilize second prism of corner cube that a step obtains and pyrometric cone prism with the laser beam vertical direction on projector distance d ₂, and the benchmark moonlet radius of gyration that obtains of b step and the angle of the moonlet radius of gyration to be measured, and the coordinate of establishing the benchmark moonlet is (r ₁, 0,0), use calculating formula:

$h=\frac{\sqrt{l_2^2-d_2^2}\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}{d_2}$

Try to achieve the distance h of benchmark moonlet place rotational plane and moonlet to be measured place rotational plane, the coordinate of moonlet to be measured is (r ₂Cos α, r ₂Sin α, h);

D, second constantly; Laser instrument emitted laser bundle is through the Amici prism transmission; Again by behind first prism of corner cube, second prism of corner cube, the pyrometric cone prismatic reflection; Return along former road, for the second time through the Amici prism reflection after telescope imaging and by the imageing sensor collection, and view data flowed to computing machine handle; Through mathematical operation, obtain first prism of corner cube and second prism of corner cube with the laser beam vertical direction on projector distance d ' ₁

E, according to the orbit radius r of benchmark moonlet ₁, moonlet to be measured orbit radius r ₂, on the moonlet to be measured between first prism of corner cube and the second pyramid rib apart from l ₁, between the second pyramid rib and the pyrometric cone rib apart from l ₂, utilize first prism of corner cube that a step obtains and second prism of corner cube with the laser beam vertical direction on projector distance d ₁, the benchmark moonlet radius of gyration that b step obtains and the angle of the moonlet radius of gyration to be measured, d go on foot first prism of corner cube that obtains and second prism of corner cube with the laser beam vertical direction on projector distance d ' ₁, use calculating formula:

$\mathrm{\β}=\arcsin \frac{l_1{d}_1^{\′}(r_1-r_2\cos \mathrm{\α})}{l_2{d}_1\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}-\arcsin \frac{r_1-r_2\cos \mathrm{\α}}{\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}}}$

Try to achieve relative first constantly, the angle that benchmark moonlet and moonlet to be measured are turned over, and the coordinate that obtains benchmark moonlet this moment is (r ₁Cos β, r ₁Sin β, 0), the coordinate of moonlet to be measured is (r ₂Cos (alpha+beta), r ₂Sin (alpha+beta), h);

F, according to the orbit radius r of benchmark moonlet ₁, the orbit radius r of moonlet to be measured ₂, utilize the benchmark moonlet radius of gyration and the angle of the moonlet radius of gyration to be measured that b step obtains, and the benchmark moonlet place rotational plane that obtains of c step and the moonlet to be measured distance h that belongs to rotational plane, use calculating formula:

$d=\sqrt{r_1^2+r_2^2-2r_1{r}_2\cos \mathrm{\α}+h^2}$

Obtain between benchmark moonlet and the moonlet to be measured apart from d.

2. the satellite based on three point reflection cooperations points to and attitude measuring; Be included in and dispose laser instrument (1), Amici prism (2), telescope (3), imageing sensor (4) and computing machine (5) on the benchmark moonlet; Amici prism (2) is positioned on the emitting light path of laser instrument (1); Telescope (3) and imageing sensor (4) are positioned on the reflected light path of Amici prism (2), and computing machine (5) is communicated with imageing sensor (4); Configuration first prism of corner cube (6), second prism of corner cube (7), pyrometric cone prism (8) on moonlet to be measured; The laser instrument of benchmark moonlet (1) emitted laser bundle is through Amici prism (2) transmission; Again by after first prism of corner cube (6), second prism of corner cube (7), pyrometric cone prism (8) reflection; Return along former road, for the second time through Amici prism (2) reflection after telescope (3) imaging and gather by imageing sensor (4), and view data flowed to computing machine (5) handle; It is characterized in that: first prism of corner cube (6), second prism of corner cube (7), pyrometric cone prism (8) triangular arrangement that on moonlet to be measured, meets at right angles; Wherein second prism of corner cube (7) is positioned at place, summit, right angle, and first prism of corner cube (6) and second prism of corner cube (7) place straight line and second prism of corner cube (7) and pyrometric cone prism (8) place straight line are orthogonal; The normal vector direction on first prism of corner cube (6), second prism of corner cube (7) and plane, pyrometric cone prism (8) place is constant; Laser instrument on the benchmark moonlet (1) emitted laser bundle is through Amici prism (2) transmission, and the direction of transmitted light beam is pointed to the mid point of moonlet first prism of corner cube to be measured (6) and pyrometric cone prism (8) line.

Images