CN104369877B - The method for designing that a kind of deep space probe antenna points to - Google Patents

The method for designing that a kind of deep space probe antenna points to Download PDF

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CN104369877B
CN104369877B CN201410445809.5A CN201410445809A CN104369877B CN 104369877 B CN104369877 B CN 104369877B CN 201410445809 A CN201410445809 A CN 201410445809A CN 104369877 B CN104369877 B CN 104369877B
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detector
antenna
axis
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moon
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CN104369877A (en
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董捷
孙泽洲
李飞
马继楠
吴学英
张熇
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Beijing Institute of Spacecraft System Engineering
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Beijing Institute of Spacecraft System Engineering
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Abstract

The present invention provides the method for designing that a kind of deep space probe antenna points to, and concretely comprises the following steps: the expression that step one, calculating detector the earth's core orientation vector are fastened at mechanical coordinateStep 2, according to described

Description

The method for designing that a kind of deep space probe antenna points to
Technical field
The present invention relates to field of deep space exploration, be specifically related to the method for designing that a kind of deep space probe antenna points to.
Background technology
Deep space probe is during the transfer of the ground moon and circumlunar flight, under the pattern of normaling cruise and not to moon image formation state Under, generally use machinery system fixing axle (hereinafter defined as+X-axis) Direct to the sun, it is ensured that solar wing normal direction and sunlight Direction is parallel.In this case, if omnidirectional TT&C antenna is installed and is directed to parallel with ± X-axis, then detector rotates around X-axis The most do not affect the angle between antenna axis and detector-tracking telemetry and command station, thus detector cruising flight attitude is not retrained and wants Ask.Under these conditions, detector can use and revolve attitude slowly, is possible not only to avoid the concave point of antenna, moreover it is possible to utilize spinning stability Feature improves capacity of resisting disturbance.
But for having the detector of complex configuration, body surface equipment is more, makes installing space limited, need take with Detector ± X-axis has the distribution form of certain angle, blocks the impact on its gain reducing the equipment of antenna periphery as far as possible. And under this layout, if detector uses spin mode, the angle between antenna axis and detector-tracking telemetry and command station is likely to appear in Cyclically-varying in the range of 0~180 degree, ground observing and controlling system such as carries out up operation of issuing an order, and ground needs real-time judge over the ground Favourable antenna, (the usual detector total space configures 2 groups of omnidirectional antenna A and B, omnidirectional the most periodically to switch up frequency The each responsible half space of antenna A Yu B, points to difference 180 degree, and the some frequency of omnidirectional antenna A and B differs) to adapt to above-mentioned angle Change, thus add ground observing and controlling system supervision and the working strength of operation and task complexity, simultaneously in handoff procedure Up recapture will be faced, it is meant that this period cannot send up-on command, reduces emergency disposal ability.If but not Spin, find also according to analyzing, at detector+X-axis Direct to the sun, when Y, Z axis point to some specific direction, antenna axis Angle between line and detector-tracking telemetry and command station can be in 90 degree oscillate around, at this moment for detector upper and lower surfaces all the time Omnidirectional antenna gain is all minimum, the problem simultaneously still suffering from frequent switching point frequency.If ensureing that antenna points to, simply make spy Surveying device Direct to the sun axle deviation solar vector, owing to major part solar wing is not the most Two axle drive, pointing direction cannot be the suitableeest Should, make solar wing normal deviate from solar vector direction, thus affect the power supply output of solar wing;Simultaneously because sensor is being visited Survey on device be fixed installation and visual field limited, point to and be generally directed to specific spatial dimension, as the Direct to the sun axle deviation sun is vowed Amount, then may affect sun sensor normally to day capture and tracking, or make star sensor by the light disturbances such as sunlight, nothing Method normally works.
Therefore, must optimize design Y while day is pointed to by+X-axis for omnidirectional antenna, Z axis points to and (turns about the X axis Special angle), solve the problems referred to above.
For far-side of the moon landing task, owing to lander cannot realize the most directly communicating, it is necessary to use the ring moon or position Detector (i.e. relay satellite) in ground moon Lagrangian points (L2 point) realizes data and forwards, and passes through relay satellite to improve lander The real-time monitoring of the efficiency that number passes, particularly mission critical stage, needs to realize forwarding in real time, relay satellite must use over the ground and To two groups of beam antennas of the moon.Owing to directional antenna beams is narrow, it is considered to the earth, the lunar orbit change, it is generally required to use twin shaft Rotate follower realize the most over the ground and the moon is pointed to, but use rotating mechanism that weight and power consumption can be brought to increase Greatly, problems such as controlling calculating complexity is pointed to.
Therefore, a kind of relatively simple sensing control method must be designed for beam antenna and ensure long-time simultaneously to the moon Point to over the ground, and meet solar wing and power required directing constraint.
Summary of the invention
In view of this, it is an object of the invention to as overcoming the deficiencies in the prior art, it is provided that a kind of deep space probe antenna Point to method for designing, the method can be powered not affecting solar wing, sensor use under conditions of, make omnidirectional antenna around right Day orientation axes turns an angle, it is achieved the observing and controlling up-downgoing most of the time only uses one group of antenna, it is ensured that observing and controlling process is continuous, Reducing ground switching and use the operation of antenna, reduce terrestrial operation complexity, antenna is in the interval that gain is bigger simultaneously, improves Link channel surplus.
The technical solution of the present invention is as follows:
The method for designing that a kind of deep space probe antenna points to, described antenna includes omnidirectional antenna, described omnidirectional antenna pair Concretely comprising the following steps of ground sensing design:
Detector mechanical coordinate system (X, Y, Z) is defined as :+X-axis is the fixing axle for Direct to the sun, according to right-handed scale (R.H.scale) It is that principle determines+Y-axis and+Z axis;
The expression that step one, calculating detector-the earth's core orientation vector is fastened at mechanical coordinate V → 2 m = [ V → 2 mx , V → 2 my , V → 2 mz ] ;
Step 2, according to describedCalculate the angle theta between omnidirectional antenna orientation vector and detector-tracking telemetry and command station;
θ = arccos ( V → 1 · V → 2 m | V → 1 | | V → 2 m | ) Wherein, V → 1 = V 1 x V 1 y V 1 z For omnidirectional antenna on detector at detector machinery Orientation vector in coordinate system;
Step 3, when described angle theta is more than maximum allowable angle γ, make detector around the+x of detector mechanical coordinate system Axle rotates so that after rotation, the gain of omnidirectional antenna meets uplink and downlink link requirement.
Further, omnidirectional antenna of the present invention includes omnidirectional antenna A and omnidirectional antenna B, around+x in described step 3 Axle rotates to be:
Calculate with the orientation vector of omnidirectional antenna A:
(1) V is calculated1yAngle β with mechanical coordinate system+Y-axis1, calculate V2myIt is β with mechanical coordinate system+Y-axis angle2
(2) V is worked as1x·V2mxWhen >=0, now make detector after mechanical coordinate system+X-axis rotation β angle, use omnidirectional antennas Line A;
Work as V1x·V2mxDuring < 0, whether now judge the angle theta between omnidirectional antenna A orientation vector and detector-tracking telemetry and command station Meet θ≤90 °, if then making detector according to the β angle of above-mentioned calculating after+X-axis rotates, using omnidirectional antenna A, otherwise making spy Survey the device β angle according to above-mentioned calculating after+X-axis rotates, use omnidirectional antenna B.
Further, performing the inventive method is that detector is in ground moon transition phase and the stage ring moon.
Further, the detailed process of step one of the present invention is:
(a) according to currently received detector telemetry, calculating detector under the J2000 inertial coodinate system of the earth's core three Shaft position R → = R x R y R z T , Then detector-the earth's core unit vector is expressed as the earth's core J2000 inertial coodinate system V → 2 = V 2 x V 2 y V 2 z ;
V → 2 = - R → | R → |
B () calculates the earth's core J2000 inertial coodinate system and is transformed into the Matrix C of detector mechanical coordinate systemmbCbi
C () is according to described Matrix CmbCbiCalculateOrientation vector under detector mechanical coordinate system is V → 2 m = C mb C bi V → 2 .
Further, present invention detector when carried out in this manner is in the stage ring moon, and described step one calculatesWith According to the ephemeris computation moon heart-the earth's core line vector in the orientation vector of the earth's core J2000 inertial coodinate systemSubstitute.
Further, antenna of the present invention also includes that beam antenna, described beam antenna point to over the ground and point to the moon Be designed as:
(x, y, z) be defined as coordinate system :+x-axis is pointed to moon beam antenna installed surface, and+z-axis points to absolute orientation antenna peace Dress face ,+y-axis and+x-axis ,+z-axis are by right-hand rule form right angle coordinate system;
Detector points to beam antenna over the ground and uses the mounting means being fixed on detector body, and antenna points to and is positioned at over the ground The earth's core is pointed in moon normal society face;Detector to the moon point to beam antenna use Two-shaft drive mechanism install, when detector with Land device landing point line not to the moon point to beam antenna point to ± 90 degree in range envelope time, detector is around its body+z-axis Rotate 180 degree, if the lander on the far-side of the moon is in moonlit night dormancy, during without forwarding demand over the ground, cancel corresponding attitude and adjust Whole.
Beneficial effect
Under conditions of the method for the present invention can be powered not affecting solar wing, sensor uses, by around fixed to day Turn an angle to axle, it is achieved the observing and controlling up-downgoing most of the time only uses one group of antenna, it is ensured that observing and controlling process is continuous, reduce Ground switching uses the operation of antenna, reduces terrestrial operation complexity, and antenna is in the interval that gain is bigger simultaneously, improves link Channel surplus.
Detailed description of the invention
Below in conjunction with instantiation, the present invention is described in detail.
Coordinate system predefines: detector Control coordinate system is defined as inertia principal axes system.
The earth's core J2000 inertial coodinate system: zero is in earth centroid, and reference plane are J2000.0 mean equator faces, Z axis Northwards pointing to the arctic, mean equator face, X-axis points to J2000.0 mean equinox, Y-axis and X and Z axis composition right angle right-handed system.
Detector mechanical coordinate system :+X-axis is Direct to the sun axle ,+Y-axis directed towards detector one certain structural features, with+X-axis Vertically ,+Z and+X-axis and+Y-axis configuration right-handed coordinate system.
Ground moon transfer leg and the stage ring moon:
The attitude telemetry that ground passes down according to detector, calculating detector is around the anglec of rotation of+X-axis and direction, so After the result of calculating is returned to detector, detector according to passback result by adjust detector attitude control antenna Rotating, make detector-antenna vector minimum with the angle of detector-earth, the antenna gain of Optimum utilization is interval, increases observing and controlling Link channel surplus.Meanwhile, under conditions of detector+X-axis Direct to the sun, owing to solar vector is relatively slow along ecliptic change, Short period internal antenna axis is less with detector-ground variable angle in the heart, therefore periodically can calculate with separated in time And carry out back delivery operations.
A kind of deep space probe antenna points to method for designing, and described antenna includes omnidirectional antenna, and described omnidirectional antenna is over the ground Concretely comprising the following steps of sensing design:
The expression that step one, calculating detector-the earth's core orientation vector is fastened at mechanical coordinate V → 2 m = [ V → 2 mx , V → 2 my , V → 2 mz ] ;
Step 2, according to describedCalculate the angle theta between omnidirectional antenna orientation vector and detector-tracking telemetry and command station;
θ = arccos ( V → 1 · V → 2 m | V → 1 | | V → 2 m | )
I.e. try to achieve omnidirectional antenna orientation vector and detector-the earth's core orientation vector angle, wherein, V → 1 = V 1 x V 1 y V 1 z The orientation vector fastened at detector mechanical coordinate for omnidirectional antenna on detector;
Step 3, when described angle theta is more than maximum allowable angle γ, make detector rotate around+x-axis so that after rotation The gain of omnidirectional antenna meets uplink and downlink link requirement, i.e. up-downgoing can realize normally holding of certain face omnidirectional antenna correspondence frequency Continuous capture and tracking, its gain is more than another side omnidirectional antenna.
According to omni-directional antenna pattern, if the angle between antenna axis and detector-tracking telemetry and command station is within γ degree, corresponding Antenna gain nargin relatively big, uplink downlink demand can be met.The most whether adjust and turn about the X axis angle threshold based on following Principle, ground calculates θ angle (periodically calculating in conjunction with remote measurement and orbit determination data update cycle) in real time according to remote measurement and orbit determination data.This Invention is by contrasting the angle theta between the omnidirectional antenna of calculating and detector-tracking telemetry and command station with maximum allowable angle γ, if θ ≤ γ, illustrates that the gain margin of now omni-directional antenna pattern is bigger, additionally it is possible to meet the demand of uplink downlink, do not revolve Turn omnidirectional antenna, if θ > γ, illustrate that the omnidirectional antenna gain margin being now currently in use cannot meet the need of uplink downlink Ask, now rotate omnidirectional antenna so that its gain meets requirement, thus improves the reliability of detector and PERCOM peripheral communication.
Omnidirectional antenna of the present invention includes omnidirectional antenna A and omnidirectional antenna B, rotates to be around x-axis in described step 3:
Calculate with the orientation vector of omnidirectional antenna A,
(1) V is calculated1yAngle β with mechanical coordinate system+Y-axis1, calculate V2myIt is β with mechanical coordinate system+Y-axis angle2;Then
β 1 = arccos ( V 1 y V 1 y 2 + V 1 z 2 ) β 2 = arccos ( V 2 my V 2 my 2 + V 2 mz 2 )
(2) V is worked as1x·V2mx>=0, now make detector after mechanical coordinate system+X-axis rotation β angle, use omnidirectional antenna A;
Work as V1x·V2mxDuring < 0, method is identical with upper table, but need to carry out angle judgement, determines where use organizes omnidirectional antenna, I.e. judging that the angle theta between omnidirectional antenna A orientation vector and detector-tracking telemetry and command station meets whether θ≤90 ° set up, if setting up, making Detector uses omnidirectional antenna A after rotating according to the β of above-mentioned calculating, otherwise makes detector make after rotating according to the β of above-mentioned calculating Use omnidirectional antenna B.
Generally antenna is after the installation clearly of detector machinery system, V1x,V1y,V1zPositive and negative, β1Just determine that, above-mentioned Computational methods can simplify further.Can ensure after using said method that observing and controlling process is continuous, the most of the time uses one group of sky Line, reduces terrestrial operation complexity, and antenna is in the interval that gain is bigger simultaneously, improves link channel surplus.
The anglec of rotation is filled out in writing data blocks, by the computer on the up injection in ground detector, computer on device Using this value as turning about the X axis the departure of angle, control algolithm is utilized to drive actuator (thruster or momenttum wheel) to carry out Closed loop control, makes this departure be gradually decrease to zero.
If detector possesses independent navigation ability, by the autonomous calculating detector according to the method described above of computer on device around+X The anglec of rotation of axle and direction also independently perform.Unlike calculating from ground, detector-tracking telemetry and command station unit vector is in the earth's core The description of J2000 inertial coodinate systemBy on device from host computer.After detector device arrow separates from the beginning of the 2nd day,Can be near Seemingly it is expressed as the description at the earth's core J2000 inertial coodinate system of the detector-the earth's core vector, to simplify calculating.
The usual detector total space configures 2 groups of omnidirectional antennas, and (sensing of omnidirectional antenna A and omnidirectional antenna B, A and B differs 180 degree), each TT&C task being responsible for half spherical space.The present invention when at least two secondary omnidirectional antenna on detector, the most above-mentioned step Rapid two and step 3 in for the omnidirectional antenna that omnidirectional antenna is A or B.
The expression that calculating detector of the present invention-the earth's core orientation vector is fastened at mechanical coordinate's Detailed process is:
(1) according to detector attitude telemetry, T is obtained0Moment detector Control coordinate system is used to relative to the earth's core J2000 The attitude quaternion Q of property coordinate system0
(2) pose transformation matrix that detector Control coordinate system is changed to mechanical coordinate system is Cmb
(3) the generally detector total space configures 2 groups of omnidirectional antennas (sensing phase of omnidirectional antenna A and omnidirectional antenna B, A and B Differ from 180 degree), each TT&C task being responsible for half spherical space.Illustrate with omnidirectional antenna A below:
If the orientation vector of omnidirectional antenna A and mechanical coordinate system Om-XmYmZmThree axle clamp angles be (α, beta, gamma), then omnidirectional Antenna A orientation vector being expressed as in detector mechanical coordinate system V → 1 = V 1 x V 1 y V 1 z = cos α cos β cos γ .
(4) according to ground observing and controlling system orbit determination result, T is obtained0Moment detector is under the J2000 inertial coodinate system of the earth's core Three shaft positions R → = R x R y R z T , Then detector-the earth's core unit vector is expressed as the earth's core J2000 inertial coodinate system
V → 2 = - R → | R → |
Wherein, V → 2 = V 2 x V 2 y V 2 z .
(5) by the attitude quaternion Q in (1)0It is converted into pose transformation matrix Cbi(turned by the earth's core J2000 inertial coodinate system Shift to Control coordinate system), then the transition matrix that J2000 inertial coodinate system in the earth's core is changed to detector mechanical coordinate system is CmbCbi
(6)Orientation vector under detector mechanical coordinate system is
The stage ring moon:
When, after the detector rings moon, computational methods are identical with ground moon transition phase.Due to the moon heart-the earth's core line vector and detection Device-tracking telemetry and command station unit vector direction is basically identical, it is also possible to according to the ephemeris computation moon heart-the earth's core line vector at the earth's core J2000 The orientation vector of inertial coodinate systemSubstituteTo simplify calculating.
Antenna of the present invention also includes that beam antenna, described beam antenna point to over the ground and be designed as moon sensing: (x, y, z) be defined as coordinate system :+x-axis is pointed to moon beam antenna installed surface, and+z-axis points to absolute orientation antenna installed surface ,+y Axle and+x-axis ,+z-axis are by right-hand rule form right angle coordinate system;
(1) for lunar orbit detector (relay satellite), design and point to control mode as follows:
Detector points to beam antenna over the ground and uses the mounting means being fixed on detector body, and antenna points to and is positioned at over the ground Pointing to the earth's core in moon normal society face, under conditions of detector is not blocked by the moon, detector rotates around mechanical coordinate system+y-axis Can realize pointing to over the ground continuously of absolute orientation antenna, rotation period is 1 month.The moon is pointed to beam antenna and uses by detector Two-shaft drive mechanism, was affected by moon revolutions in one month, and the moon is managed longitude in periodically residing for orbital plane in touch-down zone Change.When relay satellite and lander landing point line do not point at beam antenna ± 90 degree in range envelope time, need to relay Star rotates 180 degree around its body+z-axis, and it adjusts cycle most generations four times in 1 month, when far-side of the moon lander is in Moonlit night dormancy, during without forwarding demand over the ground, can cancel corresponding pose adjustment.
Relay satellite solar wing is arranged on detector mechanical coordinate system ± Y-axis, it is possible to achieve around ± Y-axis rotation, it is considered to ecliptic Face moon moon normal society face angle little (about 5 degree), therefore solar wing at the uniform velocity rotates around Y-axis can realize with the angular velocity of about 1 °/day Direct to the sun, rotation period is 1 year.
The present invention detector (i.e. relay satellite) to supporting far-side of the moon landing task, it is also possible to power meeting solar wing Condition to attitude directing constraint, only with one group of Two-shaft drive mechanism, it is achieved the beam antenna moon over the ground and synchronization referring to over the ground To demand.
(2) for being positioned at the detector (relay satellite) of ground moon L2 point, design and point to control mode as follows:
Detector points to beam antenna over the ground and uses the mounting means being fixed on detector body, and antenna points to and is positioned at over the ground The earth's core is pointed in moon normal society face;Under conditions of detector is not blocked by the moon, detector rotates around mechanical coordinate system+y-axis Can realize pointing to over the ground continuously of absolute orientation antenna, rotation period is 1 month.Detector uses twin shaft to moon beam antenna Drive mechanism, when relay satellite and lander landing point line not the moon is pointed to that beam antenna points to ± 90 degree in range envelope Time, relay satellite rotates 180 degree around its body+z-axis, if the lander on the far-side of the moon is in moonlit night dormancy, needs without forwarding over the ground When asking, cancel corresponding pose adjustment.
The control mode of L2 point solar wing is identical with lunar orbit.Beam antenna uses above-mentioned adjustment form, permissible Make to communicate to being well between moon beam antenna and far-side of the moon lander.
In sum, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention. All within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included in the present invention's Within protection domain.

Claims (6)

1. the method for designing that deep space probe antenna points to, described deep space probe antenna includes TT&C antenna, described survey Control antenna includes omnidirectional antenna, it is characterised in that what described omnidirectional antenna pointed to over the ground concretely comprises the following steps:
The expression that step one, calculating detector-the earth's core orientation vector is fastened at mechanical coordinate
Step 2, according to describedCalculate the angle theta between omnidirectional antenna orientation vector and detector-tracking telemetry and command station;
θ = a r c c o s ( V → 1 · V → 2 m | V → 1 | | V → 2 m | )
Wherein, V → 1 = V 1 x V 1 y V 1 z The orientation vector fastened at detector mechanical coordinate for omnidirectional antenna on detector;
Step 3, when described angle theta is more than maximum allowable angle γ, make detector around detector mechanical coordinate system+x-axis rotation Turn so that after rotation, the gain of omnidirectional antenna meets uplink and downlink link requirement.
The method for designing that the most according to claim 1, deep space probe antenna points to, it is characterised in that described omnidirectional antenna bag Include omnidirectional antenna A and omnidirectional antenna B, described step 3 rotate to be around+x-axis:
Calculate with the orientation vector that omnidirectional antenna A is,
(1) V is calculated1yAngle β with mechanical coordinate system+Y-axis1, calculate V2myIt is β with mechanical coordinate system+Y-axis angle2
(2) V is worked as1x·V2mxWhen >=0, now make detector after mechanical coordinate system+X-axis rotation β angle, use omnidirectional antenna A;
Work as V1x·V2mxDuring < 0, now judge whether the angle theta between omnidirectional antenna A orientation vector and detector-tracking telemetry and command station meets θ ≤ 90 °, if then making detector according to the β angle of above-mentioned calculating after+X-axis rotates, using omnidirectional antenna A, otherwise making detector According to the β angle of above-mentioned calculating after+X-axis rotates, use omnidirectional antenna B.
The method for designing that the most according to claim 2, deep space probe antenna points to, it is characterised in that perform described design side Method is that detector is in ground moon transition phase and the stage ring moon.
4. the method for designing pointed to according to deep space probe antenna described in claim 1 or 3, it is characterised in that described step one Detailed process be:
(a) according to currently received detector telemetry, the calculating detector three axle positions under the J2000 inertial coodinate system of the earth's core Put R → = R x R y R z T , Then detector-the earth's core unit vector is expressed as the earth's core J2000 inertial coodinate system V → 2 = V 2 x V 2 y V 2 z ;
V → 2 = - R → | R → |
B () calculates the earth's core J2000 inertial coodinate system and is transformed into the Matrix C of detector mechanical coordinate systemmbCbi
C () is according to described Matrix CmbCbiCalculateOrientation vector under detector mechanical coordinate system is V → 2 m = C m b C b i V → 2 .
The method for designing that deep space probe antenna the most according to claim 1 or claim 2 points to, it is characterised in that at detector In the stage ring moon, described step one calculatesWith according to the ephemeris computation moon heart-the earth's core line vector at the earth's core J2000 inertia The orientation vector of coordinate systemSubstitute.
The method for designing that deep space probe antenna the most according to claim 1 or claim 2 points to, it is characterised in that described observing and controlling sky Line also includes that beam antenna, described beam antenna point to over the ground and be designed as moon sensing:
(x, y, z) be defined as coordinate system :+x-axis is pointed to moon beam antenna installed surface, and+z-axis is pointed to absolute orientation antenna and installed Face ,+y-axis and+x-axis ,+z-axis are by right-hand rule form right angle coordinate system;
Detector points to beam antenna over the ground and uses the mounting means being fixed on detector body, and antenna points to and is positioned at the moon over the ground The earth's core is pointed in normal society face;The moon is pointed to beam antenna and uses Two-shaft drive mechanism to install, when detector and lander by detector Landing point line not the moon is pointed to that beam antenna points to ± 90 degree in range envelope time, detector is around the rotation of its body+z-axis 180 degree, if the lander on the far-side of the moon is in moonlit night dormancy, during without forwarding demand over the ground, cancel corresponding pose adjustment.
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CN112208797B (en) * 2020-10-22 2022-07-01 上海卫星工程研究所 Attitude control method and system during calibration of two-dimensional antenna electric axis direction of deep space probe
CN112949044A (en) * 2021-02-08 2021-06-11 北京京航计算通讯研究所 Method for determining spacecraft antenna installation position and antenna pointing selection
CN113009512B (en) * 2021-02-08 2022-11-22 北京京航计算通讯研究所 System for determining spacecraft antenna installation position and antenna pointing selection
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