astronautics lecture12

8/13/2019 Astronautics Lecture12

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Introduction to Astronautics

Sissejuhatus kosmonautikasse

Vladislav Pustnski

2009

Tallinn University of Technology


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Navigation, guidance & steering of rockets

The thrust produced by the engines is applied to the rocket in points different from the centerof mass. According to the laws of mechanics, it gives rise to torques(moments of force) inthe general case. These torques try to rotate the rocket around its center of mass faster andfaster. There are no torques only if the center of mass lies on the line of the resultant force.The rocket should move along the path defined by the flight profile, so the rotations of its

body are predefined as well; these rotations should be provided by the guidance system. Thismeans that torque should be controlled and the guidance system should be able to change it.

However, steering is unavoidable in the simplest case as well, when the rocket should flyalong a straight line (for example, performing an orbital change maneuver). The problem isthat a rocket device is unstable in the general case. Even with a fixed-mass device it isimpossible to ensure that the center of mass lies exactlyon the line of the resultant force.Tolerances at installation of engines and other devices would necessarily create some momentarm. The real situation is even worse, since the forces and the position of the center of masschange in flight. During the flight in the atmosphere, varying lift forces act to the body of therocket, and the mass of the rocket changes along the trajectory. The level of the propellantdrops, large amounts of liquids in the tanks wave, the propellant sloshes, the body of therocket is subject to various oscillations, separation of parts like nose fairings and interstagesoccurs, etc. These factors lead to quick shifts of the center of mass.

Stabilization and steering

The rocket is a device that should deliver its payload to the target. It should follow the rightpath, often guided by its own systems, and should maintain stability so that it do not wanderoff its trajectory. Let us look in detail how these issues are addressed.


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Rocket rotationsThe angular motion of a rocket may be represented as rotation about three independent axeswhich are mutually perpendicular (as for each 3-dimensional body). The choice of these axesis natural for a launch vehicle, since it has a nose and a tail, and it is also possible todistinguish up and down (although sometimes it is done by convenience only, since the

Due to these factors the rocket body is subject to variable torques, so its flight would beunstable without steering. A popular misconception exists that rockets are unstable since theircenter of mass is placed in front of their engines, and the forces are applied in the tail. EvenGoddard built his first rockets so that the engines were placed in front of their center of mass.This misconception arises from the wrong analogy of such rocket (with engines in front) with

a suspended pencil which is stable, while a standing pencil (analogous to a rocket withengines in the tail) is unstable. However, a suspended pencil is stable due to the reaction of thesuspension: small angular deviation from the equilibrium position gives rise to the reactionforce that returns the pencil to the equilibrium. In the case of a standing pencil, the reaction ofthe support forces the pencil to deviate more and more from the equilibrium. As for a rocket,the reaction force of exhaust gases does not depend on the rocket attitude, so small rotationsdo not lead to appearance of any change of this reaction. That means that the rocket is

indifferent to angular deviations: they are not amplified nor dampen, and the rocket simplycontinues to rotate if there is some torque. By the same reason, a rocket with multiple enginesin the back is not more stable in the least than a rocket with one engine, as one may thinktaking as an analogy a one-legged and a four-legged chair. It is the support reaction force thatmakes a four-legged chair stable, since if the chair is inclined, the reaction of the support onthe lower side increases and returns the chair to stability. No reaction force changes in the case

of an inclined rocket, thus it does not become stable if it has more engines in the back.


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Stabil ization & steer ing methodsThe above-mentioned arguments demonstrate that rocket devices need stabilization for anormal flight. Rockets may be compared to a pencil on the finger tip: it may stand only if thehand reacts to each deviation from the equilibrium and returns it back to its unstableequilibrium position. In general, rockets should by stabilized by all three axes. Yaw and pitchstabilizations are unavoidable since otherwise the rocket would deviate from its path.However, in some cases roll stabilization may be avoided. This is the case of spin stabilization(when the rocket is intentionally wound round the roll axis, see further) or if rolling motion isslow enough not to destabilize the rocket by other two axes (body rotation is described byEulers equations, rotation around one axis may give rise to complicated angular motionaround another axes). There is a number of practical methods used for stabilization. They maybe divided into passiveand activemethods.

Passive methods include aerodynamic stabilizationand spin stabilization.Aerodynamicstabilizationis realized by placing finsin the tail part of the rocket, so that

rocket may be axisymmetric or have nothing to distinguish the upper and the lower side).For a satellite distinguishing between the nose and the tail, the up and the down maybe even more conventional, but it is always done someway.

A natural choice of axes is nose tail, up down and left right. The nose-tail axisis called the roll axis, the up-down axis is called the yaw axisand the left-right axis is called

the pitch axis. The corresponding rotations are called rolling motion, yaw motionand pitchmotion, or simply roll, yawand pitch. These are so-called Tait-Bryan rotations. Thepositive direction of rotation is clockwise if looked from the tail, from the downside and fromthe left side.


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aerodynamic pressure could orient the rocket axis along the air flow. For that, the center ofpressureshould be placed behind the center of mass, and the area of the fins should besufficient for aerodynamic forces to overcome perturbational torques. This method is feasibleonly for the first stages of rockets which fly in dense atmospheric layers. Upper stages fly invery rarified atmosphere or nearly in vacuum and cannot be aerodynamically stabilized.

Aerodynamic stabilization is also limited by the rocket size. The rocket mass grows as cube ofits linear dimensions, so does the thrust. However, aerodynamic forces, being proportional tothe area of the rocket, grow as square of the linear dimensions, thus efficiency of aerodynamicstabilization drops off with linear dimensions of the rocket, and the fins become too large anddrastically increase the weight of the stage. The problem of this method is also that most oflaunch vehicles are aerodynamically unstable. They have heavy first stages with high meandensity (due to kerosene and/or solid propellants), while the upper stages are ordinarily of

lower mean density due to hydrogen fuel and voluminous nose fairing under which thepayload is placed. These factors place the center of mass of the launch vehicle quite low, andit is generally below the center of pressure. To shift the center of pressure below the center ofmass, large fins would be required. In the early era of rocketry, aerodynamic stabilization wasthe only stabilization method. The first ballistic missile V-2also had large fins. Nowadayspassive aerodynamic stabilization is rarely used on launch vehicles, since it mostly should be

aided with other steering methods (to provide motion along the predefined curved path) andbecause of large weight of aerodynamic surfaces; however, even giant Saturn Vhad smallfins to make the rocket a little bit more stable. However, the smallest launch vehicle, the firstJapanese Lamda-4Srocket, had a fully aerodynamically stabilized first stage.

Another passive stabilization method is spin stabilization. The idea of this method is thatthe rocket is stabilized by rotation around the roll axis. If the rocket rotates quickly enough,


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pitch and yaw torques try to incline the rocket in different directions in different moments oftime, so the resultant deviation averages to zero. This method is often applied on small solidupper stages of launch vehicles because of its simplicity. A stage may be wound before launchon the launch vehicle, in this case the stage sits on a special spin tablemounted on a bearingon the lower stage, like it was done on the Juno Iand on the Payload Assist Module (PAM)

based on the Star 48solid rocket motor on the Space Shuttle, theDeltaand the Titanlaunchvehicles (rotation frequency is about 60 rpm). A stage or a spacecraft may be also spun bymotors, the thrust of whis is directing out of the plane of the roll axis (like historical Halerocketsin the 18thcentury). After launch the spacecraft rotates with the spin-stabilized stageand may need to be de-spun. Motors may be used, but enother mechanism known as yo-yode-spinis also applied if the rotation frequency is too high and the attitude control systemcannot cope with it. To cables with weights (yo-weights) are wound round the payload and

fixed. For de-spin they are released. Angular momentum transfers to unwinding weights andspinning slows down. Sometimes only one yo-weight is used. Its release forces the spent stageto tumble, and the impulse of aftereffect (that may cause the spent stage slam into thepayload) averages over different directions, so the stage cannot come closer to the payload.Spinning of a spacecraft may play other roles as well, like uniform exposition to the Sun toavoid excessive heating and/or uniform illumination of the solar cells placed around the

spacecraft. For instance, the Apollo CSM had a roll rotation of about one rpmfor uniformheating during its flight to the Moon and back, the Pioneer 6, 7, 8, 9probes had solar cellsaround their cylindrical body that needed uniform illumination.

Active stabilization methodsare quite diverse, they are based on active steering and areoften used not only to keep the attitude of the rocket, but to change it. Most of the launchvehicles follow their paths thanks to continuous attitude control. Let us take a closer look tothese methods.


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(along the axis of the rocket) diminishes due to appearance of a non-axial component.

Gimbal is effective only if the engine is far from the center of mass and so can create asignificant moment arm. This condition is satisfied for most launch vehicles, but on spacecraftit should not necessarily be so. For example, in the Ascent Stageof the Apollo LunarModulethe engine was very close to the center, thus gimbal would have been useless; this

stage was steered only by small attitude control motors. The engines were gimbaled on allother stages of theApollospacecraft.

Stabilization and steering with special vernier engines (or steering nozzles) is also one ofthe most wide-spread methods. Small engines (or, more generally, nozzles) the thrust vector ofwhich do not pass through the center of mass create controlling torques and rotate the rocketabout its axes. To vary controlling interventions, the nozzles may be gimbaled or,

alternatively, their thrust may vary. Verniers may be organized in different ways. These maybe small separate engines consuming the same components as the main engine and evenorganized with it in a common assembly, as it is done on the RD-107/108 engines of theSoyuz rocket, where steereing nozzles were installed (2 and 4 respectively). Another reasonfor using verniers on the R-7, the predecessor of the Soyuz, was to diminish the effects of theimpulse of aftereffect: the main engines had been cut off shourtly before the required velocitycount was intergrated, and the steering engines continued to work until the required velocity

was achieved. Verniers may be a stand-alone assembly, as the vernier engine for steering inthe roll channel of the futureAres Iaunch vehicle. Sometimes verniers are organized inspecial assemblies, as it was on theApollospacecraft (both CSMand theLunar Module; theverniers of theLMhad separate tanks but also took some propellant from the main tanks oftheAscent Stage). In some cases no there are no special vernier engines provided, and gasfrom the turbine of the turbopump is used for steering, it is directed to special gimbaling


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Guidance and navigation systems of rocketsTo keep the rocket on its predefined trajectory during launch (or performing other maneuversin space), the rocket should be actively steered. First of all, its attitude should be stabilizedand controlled to keep the rocket on the required path. In the previous section we have got anoverview of the steering methods, now let us look systems and instruments used for guidance

and navigation.There are three essential conceptions related to the issue: navigation, guidanceand

control.Navigationis a group of methods to define the position and the attitude of the rocket,guidanceuses navigation data and other information (following the target, for instance) tokeep the rocket on its path, controlis realization of commands issued by the guidance systemto reactions of the actuators.

vernier nozzles. Such design was used, for example, on the Luna-16/17and other E-8lunarprobes. If separate engines are used as verniers, their mass and the mass of their propellantincrease the mass of the structure.

One of the rarely used methods of steering (possible only on multi-engine rockets) isthrust differentiation, when control torques are provided by varying thrusts of the opposite

engines. This method was applied on the Soviet lunar rocket N1 (probably it was the onlylaunch vehicle where it was used; however, later vernier engines were also added for betterroll control). Nearly no losses are related to this method. Its greatest problem is that thereshould be enough engines on the rocket and their distance from the rocket axis should not besmall, so that the moment arm were sufficient. It is also useless with solid rocket motors.

Other attitude control methods used on spacecraft will be discussed in the further lectures.


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All launch vehicles and most of spacecraft are provided with autonomous navigation.That means that on-board devices are able to determine the attitude of the rocket, its velocityand accelerations. However, frequently additional outer sources of data are used. These maybe commands form the Earth, stellar navigation(on many interplanetary probes, but also onsatellites, manned spacecraft and also ICBMs), GPSdata, horizon finding system, radar or

other location of the surface (at landing on a celestial body), etc.Nowadays the autonomous navigation is mostly based on the properties of gyroscopestokeep the initial preset direction for long periods of time. The attitude of the rocket may bemeasured with gyros by determination of angles between the preset position of the gyro andthe position of its suspension fixed relative to the rocket. It is also possible to measure angularvelocities with the aid of gyros. Accelerometersmake it possible to find accelerations of therocket, their working principle is measuring spring deformation by a mass, or some equivalent

method. Since the working principle of gyros and accelerometers is directly related to inertia,navigation systems based on such devices are called inertial navigation systems (INS), orinertial guidance systems. These systems are based on the so-called inertial measurementunits (IMUs), which contain the corresponding set of gyros and accelerometers. Togetherwith the computer (digital or analog) which process the data and sends signals to the guidancesystem they form the inertial reference platform.

Gyros provide information on angular velocities of the rocket, while accelerometers givelinear accelerations. Integration of the angular velocities gives the attitude of the rocketrelative to the fixed axes, integration of the accelerations gives the linear velocities and doubleintegration of the accelerations gives coordinates. So the position and the attitude of the rocketrelative to the external reference frame may be determined independently.

However, data from the inertial reference platform contain errors which appear due to


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limited precision of the instruments and tend to accumulate. It is also important to point outthat inertial navigation does not account for gravitational accelerations, since mechanicalphenomena onboard the rocket are independent (with high degree of precision) of gravityfields. Thus, all phenomena onboard the rocket falling in the gravity field of a planet are thesame as they would be if the rocket were in deep space. By these reasons other data are often

used for navigation together with INS data, specially in long flights. Space probes takeinformation about their attitude from the solar sensorsand stellar sensors. Ground linktelemetry was used to correct trajectory of the first ICBMs. Positions of satellites are definedusing GPS signals. Action sequences of probes performing planetary landings are based ondata gathered by optical observations of the surface, radar location data, sometimes laserlocation, gamma-ray sensors etc. Crews of manned spacecraft are often also present in thecontrol loop. For instance, precision of the inertial guidance platform of theApollospacecraft

was such that it needed human interventions from time to time: the crew oriented thespacecraft manually using stellar observations.

Besides the navigation tasks, the stabilization problem should be solved as well (since, aswe have already seen, rockets are generally unstable). If the rocket is not passively stabilized,stabilization data is issued by similar (or same) instruments and sensors as navigation data.Often the stabilization and the navigation system are actually a single system, both tasks are

performed by the same devices.Gyros, accelerometers, sensors are the measuring instruments of a rocket. Their signals

should be processed and corresponding control commands should be issued and sent toactuators of the devices described above. Theguidance systemis responsible for this task.This system is based on a computer, which is an analog or digital device. The first suchcomputers were, of course, analog and they appeared in the beginning of the 20thcentury on


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torpedoes. They became much more sophisticated, but remained analog till mid 1960th, whendigital computers became compact enough to be placed onboard ICBMs and launch vehicles.However, even nowadays some simplest systems are still analog.

The most simple guidance system had, obviously, the first JapaneseLabda-4Srocket,where the first three stages were unguided: the first stage was aerodynamically stabilized and

the next two stages were spin-stabilized. Only the fourth stage was oriented relative to theattitude of the only gyro, the stage was spun for stabilization and the instrumental unit wasseparated before the engine of the fouths stage was fired. The guidance system of theJuno Iwas also simple, only the first stage was guided. Some rockets are not controlled in all threechannels. For instance, the Luna E-8probes were not controlled in the roll channel. For thesake of simplicity and reliability, simplified guidance methods may be realized. The Soyuzlaunch vehicle up to the latest modernizations is put on the correct azimuth by rotation of thelaunch pad, since its guidance system is not designed to control azimuth autonomously. TheLuna E-6probes (Luna-9/13) had simplified landing sequence: thanks to the properties oftheir trajectories, it was possible not to determine the attitude of the probe relative to theMoon and so not to measure and cancel separately the vertical and the horizontal velocities.Instead, at a certain moment the probe oriented itself along the local vertical line and latercould begin the decelerating burn (by a signal of the radio altimeter) without any change of its

attitude. Thus, there was no need to continuously control the attitude and the position alongthe trajectory, it was enough to keep the attitude. A similar method was used on the returnrockets of the Luna E-8-5sample probes (Luna-16/20/24). Before launch from the Moon, thelocal vertical direction was determined by a pendulum system in the instrument unit of thedescent stage, the gyro on the ascent stage memorized this direction and during the ascent theguidance system only had to keep the rocket on this straight path. The engine was cut off by a


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rocket. Thus, the output is fed back into the input through the rocket attitude, and the controlloop is closed through the body of the rocket.

A different concept is open-loop navigation. While controlpoints the rocket to thedesired direction, navigationdetermines the path where to point. Open-loop navigation is thesimplest approach. It means that if some deviation from the preset path occurs, the system

tries to return the rocket to that path. For instance, if the attitude of the rocket changes, thesystem simply commands to restore the attitude, not taking care if the new trajectory (shiftedfrom the initial, since the rocket has flown with a wrong attitude for a while) is optimal or not.The close-loop navigationis a more sophisticated strategy. If applied, the system will notnecessarily re-establish the initial attitude. It will compute in the real time a new optimal pathand will send the rocket to this path. Implementation of this strategy needs more complexalgorithms and quicker computers. The example is the Saturn V, where this strategy wasimplemented on the second and the third stages. However, an open-loop navigation wasimplemented on the first stage. This is because the first stage works when the rocket passesthrough dense air layers and is subject to intensive aerodynamic loads. Thus, the main task forthe rocket at that time is to fly directly into the wind, not allowing any tilt relative to itsvelocity vector; otherwise the rocket may break. So it flies with a preprogrammed tilt angle tosafely leave the dense atmosphere. The path of the rocket may deviate from the correct one

due to winds and errors, but these trajectory imperfections are corrected by the second stage.On the very last seconds of the orbital injection the Saturn Valso switched to an open-loopnavigation and flied at a preprogrammed tilt angle. This is because residual errors at this pointare so small that their elimination would cost more than the imperfections themselves.

The navigation and guidance systems of a launch vehicle are usually confined in one unitthat is placed on the upper stage. Besides instruments and electronics, this unit include power


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supply batteries, antennas for ground link, etc. Electric wiring connects this system with theactuators on all stages, vents, pyrotechnic devices etc., and also with sensors inside the tanks(they signal propellant levels), interstages and nose fairings (they signal the stages and thefairing separation) and others. The radio transmitter send telemetry to the ground link. If theupper stage of a launch vehicle is different in different flights (or may be absent in other

flights), the upper stage may be provided with a separate instrument unit, the example is theProton. Satellites and spacecraft have their own control systems independent of that of theirlaunch vehicles.


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End of the Lecture 12


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Stable and unstable systems

Stick is unstable, any deviation

from equilibrium should be

met by a corresponding shift of

the hand so that the stick could

stand (By source)

Suspended body is stable, any

deviation from equilibrium

gives rise to a force that

returns it to the equilibrium

position (By source)
http://fiziks.org.ua/fizicheskie-igrushki-ustojchivoe-ravnovesie/http://fiziks.org.ua/fizicheskie-igrushki-ustojchivoe-ravnovesie/http://fiziks.org.ua/fizicheskie-igrushki-ustojchivoe-ravnovesie/http://fiziks.org.ua/fizicheskie-igrushki-ustojchivoe-ravnovesie/


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Body axes (Tait-Bryan) rotations

(By source)
http://exploration.grc.nasa.gov/education/rocket/rotations.htmlhttp://exploration.grc.nasa.gov/education/rocket/rotations.html


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Lambda-4S

The first stage of Japanese Lambda-4S

was aerodynamically stabilized (By source)

(By source)
http://upload.wikimedia.org/wikipedia/commons/9/98/L-4S-5_rocket.jpghttp://www.astronaut.ru/bookcase/books/afanasiev3/foto/18-7.jpghttp://www.astronaut.ru/bookcase/books/afanasiev3/foto/18-7.jpghttp://upload.wikimedia.org/wikipedia/commons/9/98/L-4S-5_rocket.jpg


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Spin-stabilized spacecrafts

Pioneer 6 Sun orbiter (By source) SBS-3 satellite with a PAM

module released from the

Shuttle cargo bay (By source)

Apollo 16 CSM on orbit

around the Moon (By source)
http://pagesperso-orange.fr/pierre.boyer2/astronautique/pioneer6.jpghttp://upload.wikimedia.org/wikipedia/commons/0/04/SBS-3_with_PAM-D_stage.jpghttp://taylor.typepad.com/.a/6a00d83452444369e2010536e8e133970b-500wihttp://taylor.typepad.com/.a/6a00d83452444369e2010536e8e133970b-500wihttp://upload.wikimedia.org/wikipedia/commons/0/04/SBS-3_with_PAM-D_stage.jpghttp://pagesperso-orange.fr/pierre.boyer2/astronautique/pioneer6.jpg


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Movable air vanes

(By source)

Fins with movable

rudders of the Redstone

launch vehicle (By source)

Launch of a

Redstone (By source)
http://exploration.grc.nasa.gov/education/rocket/rktcontrl.htmlhttp://www.fas.org/nuke/guide/usa/theater/us_missile_redstone_08.jpghttp://www.daviddarling.info/images/Redstone_liftoff.jpghttp://www.daviddarling.info/images/Redstone_liftoff.jpghttp://www.fas.org/nuke/guide/usa/theater/us_missile_redstone_08.jpghttp://exploration.grc.nasa.gov/education/rocket/rktcontrl.html


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(By source)

Jet vanes

Scheme of the launch vehicle Kosmos, view

from side and from tail.

1) Jet vane supprot

2) Fin

3) Jet vane

(By source)
http://exploration.grc.nasa.gov/education/rocket/rktcontrl.htmlhttp://epizodsspace.narod.ru/bibl/afan/r12/01.htmlhttp://epizodsspace.narod.ru/bibl/afan/r12/01.htmlhttp://exploration.grc.nasa.gov/education/rocket/rktcontrl.html


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Gas pass-by from the chamber to the nozzle (By V.I.Feodosjev,

osnovy tehniki raketnogo poleta.)

External flow injection into the nozzle


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(By source)

Gimbaled engines

Scheme of the Aestus, the upper stage engine

of the Arian V. Gimbal unit is seen (By source)
http://exploration.grc.nasa.gov/education/rocket/rktcontrl.htmlhttp://cs.astrium.eads.net/sp/LauncherPropulsion/images/Aestus-Fig.gifhttp://cs.astrium.eads.net/sp/LauncherPropulsion/images/Aestus-Fig.gifhttp://exploration.grc.nasa.gov/education/rocket/rktcontrl.html


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(By source)

Vernier engines

Soyuz launch

vehicle, the 1stand

the 2ndstages.

Small vernier

engines are seen(By source)
http://exploration.grc.nasa.gov/education/rocket/rktcontrl.htmlhttp://farm4.static.flickr.com/3590/3378374405_a61b6e8f15_b.jpghttp://farm4.static.flickr.com/3590/3378374405_a61b6e8f15_b.jpghttp://exploration.grc.nasa.gov/education/rocket/rktcontrl.html


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INS of Minuteman III ICBM (Bysource)

Inertial navigation system

(By source)
http://www.techbastard.com/missile/minuteman/images/guidance-system.jpghttp://collections.nasm.si.edu/media/full/A19770995000d3.jpghttp://collections.nasm.si.edu/media/full/A19770995000d3.jpghttp://www.techbastard.com/missile/minuteman/images/guidance-system.jpg


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IMU of the Peacekeeper

ICBM (By source)

Inertial measurement unit
http://upload.wikimedia.org/wikipedia/commons/1/12/Peacekeeper_ICBM_Inertial_Measurement_Unit.jpghttp://upload.wikimedia.org/wikipedia/commons/1/12/Peacekeeper_ICBM_Inertial_Measurement_Unit.jpg


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Gyrostabilized platform of Minuteman III ICBM (By source)

Gyrostabilized platform
http://www.techbastard.com/missile/minuteman/images/gyro.jpghttp://www.techbastard.com/missile/minuteman/images/gyro.jpg


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Due to simplified guidance system

of the ascent rocket, all landing

sites of E-8-5 are near the Eastern

side of the lunar disk (By source)

Luna E-8-5

Luna-16 on the surface of the

Moon (By source)
http://www.ast.cam.ac.uk/~ipswich/Miscellaneous/Fecunditatis.gifhttp://3.bp.blogspot.com/_VRIPUQofXu8/Sa3iSjZ9AiI/AAAAAAAAFKw/5i7Ck4E5-4k/s320/7011a.jpghttp://3.bp.blogspot.com/_VRIPUQofXu8/Sa3iSjZ9AiI/AAAAAAAAFKw/5i7Ck4E5-4k/s320/7011a.jpghttp://www.ast.cam.ac.uk/~ipswich/Miscellaneous/Fecunditatis.gif

astronautics lecture12

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