apol lo guidance

8/14/2019 Apol Lo Guidance

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Ob ectivesOb ectives

Describe coordinate systems

Prime: PGNCS IMU Management Backu : CSM SCS/LM AGS Attitude Mana ement

Identify state vector determination techniques Prime: PGNCS Coastin Fli ht Navi ation Prime: PGNCS Powered Flight Navigation Backup: LM AGS Navigation


3/89

Review of Basic N avi ation Conce tsReview of Basic N avi ation Conce ts

Navigation: Where am I?


4/89


Navigation: Where am I? Vehicle maintains internal

representation of where it iswith respect to some external

State vector (position andvelocity vectors)


5/89





Attitude


6/89





Attitude To maintain accuracy, this

internal representation must beupdated periodically using

some source o ex erna rudata (sensor measurements)


7/89

Coordinate S stemsCoordinate S stemsPlanet-Fixed Coordinates

--

Basic Reference Coordinates

Lunar ephemeris Earth rotation

Stable Member Coordinates

REFSMMAT

Navigation Base Coordinates

Nav base location

Vehicle Coordinates

Bod Coordinates

c.m. location

Vehicle-Fixed Coordinates


8/89

Basic Reference Coordinate S stemBasic Reference Coordinate S stem

All nav stars and lunar/solar ephemerides

All vehicle state vectors referenced to this

powered flight

Simplified inertial-to-Earth-fixed computations


9/89


Origin at center of Earthor center o moon


10/89


Origin at center of Earthor center o moon Command and Service

Module (CSM) navigation Lunar Sphere of Influence(r=64373.76 km,

between Earth and mooncentered when crossing the

moons Sphere of Influence

34759.05 nmi)


11/89


Origin at center of Earthor center o moon Command and Service

Module (CSM) navigation Lunar Sphere of Influence(r=64373.76 km)

Ecliptic Plane



Axes: X-axis pointed to First Point

of Aries

Equatorial Plane

X


12/89


Origin at center of Earth Zor center o moon Command and Service


Ecliptic Plane




of Aries

Equatorial Plane

X

Z axis parallel to Earthmean north pole


13/89


Origin at center of Earth Zor center o moon Command and Service


Ecliptic Plane



Y


of Aries

Equatorial Plane

X

Z axis parallel to Earthmean north pole

Y axis completed right-


14/89

IM U Stable Member Coordinate S stemIM U Stable Member Coordinate S stem

Inertial coordinate

Stable Member +X-AXIS

system Defined relative to

Stable Member +Z-AXIS

y erenceto Stable Member

STABLEMEMBER Many possible

alignments during a IMU CASE(CUTAWAY) Stable Member +Y-AXISmission (discussedlater)


15/89

CSM Vehicle Coordinate S stemCSM Vehicle Coordinate S stem

Rotating coordinate Egress Hatch (-Z)system, xe tobody

Origin along vehiclecen er ne, . min) behind Command

Module (CM) heat shield + +X forward along

longitudinal axis

.

+X


16/89



Origin along vehiclecen er ne, . min) behind Command


longitudinal axis

+Z

feet when in couches.

+X

+Z


17/89



Origin along vehicle+Ycen er ne, . m

in) behind Command


longitudinal axis

+Z

feet when in couches +Y starboard completed

right-handed system

.

+X

+Z


18/89


19/89

LM Vehicle Coordinate S stemLM Vehicle Coordinate S stem

Rotatin coordinate

system, fixed to LM body Origin along vehiclecen er ne, . min) below LM ascentstage base

Axes: +X up through top hatch

+ orwar rougegress hatch +X 5.08 m (200)

+Z out of screen


20/89

LM Vehicle Coordinate S stemLM Vehicle Coordinate S stem

Rotatin coordinate

system, fixed to LM body Origin along vehiclecen er ne, . min) below LM ascentstage base

Axes: +X up through top hatch

+ orwar rougegress hatch +Y starboard completed

+X 5.08 m (200)

r g - an e sys em +Z out of screen


21/89

CSM / LM Bod Coordinate S stemsCSM / LM Bod Coordinate S stems

Origin at vehicle center of mass

+X

+Y+Y

+X+Z


22/89

Navi ation Base Coordinate S stemNavi ation Base Coordinate S stem

Rotatin coordinate

+XNB

system, fixed tonavigation base+ZNB

the transformation between

stable member coordinates

Origin at center ofnavigation base

+XNB LM+X Axis

IMUOuter

Gimbal

Axes parallel to vehiclebody axes

+ZNB

LM+Z AxisIMU

MiddleGimbal

+YNB

IMUInner

Gimbal


23/89

EarthEarth- -f ixed Coordinate S stemfixed Coordinate S stem

Rotating coordinate +Zsystem, xe to art All Earth landmarks,

including launch site +XGreenwich

Meridian

,system

Origin at center of Earth

Equator

+Z along true north pole


24/89




Meridian

+X

,system


Equator

+Z along true north pole +X along true Greenwich

meridian at equator


25/89




Meridian

+Y

+X

,system


Equator

+Z along true north pole +X along true Greenwich

meridian at equator

+Y in equatorial plane,completed right-handedsystem


26/89

MoonMoon--f ixed Coordinate S stemfixed Coordinate S stem

Rotating coordinate +Zsystem, xe to moon All lunar landmarks,

including landing site,

system Origin at center of moon

+Z along true north pole

Moon as viewed from Earth


27/89




system Origin at center of moon +X out of screen

+Z along true north pole +X along zero longitude at

equator (center of moon

v s e sc

Moon as viewed from Earth


28/89




system Origin at center of moon

+Y

+X out of screen

+Z along true north pole +X along zero longitude at

equator (center of moon

v s e sc +Y completed right-handedsystem (trailing moon inits orbit around the Earth) Moon as viewed from Earth


29/89


Describe coordinate systems

Prime: PGNCS IMU Management

Backu : CSM SCS/LM AGS Attitude Mana ement Identify state vector determination techniques

Prime: PGNCS Coastin Fli ht Navi ation Prime: PGNCS Powered Flight Navigation Backup: LM AGS Navigation


30/89

P GN CS I M U M ana ementP GN CS I M U M ana ement

Apollo used three-gimbal IMU-

gimbal IMU, but vulnerable to gimbal

lock when all three gimbals in sameplane Spacecraft attitudes operationally

constrained to avoid gimbal lock Apollo Flight Director Attitude Indicator

(FDAI) driven directly by IMU gimbalangles rather than computer

Allowed IMU to operate independentlyof com uter Gimbal Lock Allowed gimbal lock region to be

graphically depicted as red circles onFDAI ball

Periodic IMU aligns to different

Accommodate variety of missionattitudes while avoiding gimbal lock Provide meaningful FDAI attitude

display to crew


31/89

Common REFSMM ATsCommon REFSMM ATs

Nominal (LVLH) aunc a on y

Landing Site Liftoff Entry (CM only)


32/89

P referred REFSMM ATP referred REFSMM AT

Used for major burns +X aligned with V vector

at Time of Ignition (TIG) V

+X

R


33/89



at Time of Ignition (TIG) +Y er endicular to both

V+X

V vector and positionvector at TIG Direction could be defined -

up or heads-down burnattitude

R

+Y into screen (heads-up) -


34/89



at Time of Ignition (TIG) +Y er endicular to both

V+X

+Z (heads-down)

V vector and positionvector at TIG Direction could be defined

+Z (heads-up)

-up or heads-down burnattitude

+Z com leted ri htR

handed system FDAI read 0,0,0 when in

burn attitude at TIG +Y into screen (heads-up) -


35/89

Nominal REFSMM ATNominal REFSMM AT

Aligned with Local Vertical/Local

of alignment

Used for coasting orbital flight +Z aligned with radius vector (+Rbar)

at time of align

V

+Z

R


36/89



of alignment


at time of align

V

+Y aligned with negative orbitalmomentum vector (-Hbar) at time ofalign +Y out of screen

+Z

R


37/89



of alignment


at time of align

V

+Y aligned with negative orbitalmomentum vector (-Hbar) at time ofalign

+X in orbit plane in direction of velocity

+X

+Y out of screen+Z

FDAI read 0,0,0 when in airplaneattitude at time of align

Note that this was an inertialorientation aligned with LVLH only at

R

one po n n me Inertial pitch angle diverged from LVLH

pitch angle at orbital rate Crew used Orbital Rate Display Earth

and Lunar (ORDEAL) to bias FDAIp c ang e o sp ay a u e


38/89

Launch Pad REFSMM ATLaunch Pad REFSMM AT

CSM onlNorth

+Z aligned with radiusvector (+Rbar) at liftoffme

+

East

from above


39/89


CSM onlNorth

Launch Azimuth(typ. 72 at window open)

+Z aligned with radiusvector (+Rbar) at liftoff+Xme

+X aligned with flightazimuth at liftoff time +

East

from above


40/89


CSM onlNorth

Launch Azimuth(typ. 72 at window open)

+Z aligned with radiusvector (+Rbar) at liftoff+Xme

+X aligned with flightazimuth at liftoff time +

East

+Y

from above

+Y completed right-

handed systemFDAI roll 162

At liftoff, FDAI read pitch90, yaw 0, roll 90 plus


41/89

Landin Si te and Liftoff REFSMMATsLandin Si te and Liftoff REFSMMATs

+X aligned with positionvector at p anne an ngtime

+X

R


42/89


+X aligned with positionvector at p anne an ng

time +Z pointed forwardpara e o or

plane) +X+Z

R


43/89


+X aligned with positionvector at p anne an ng

time +Z pointed forwardpara e o or

plane)

+Y completed right-

+X

+ +Z LM FDAI read 0,0,0 at

landingR

oidentical except definedat planned lunar liftoff


44/89

P TC REFSMM ATP TC REFSMM AT

Used for passive thermalcontrol (barbecue roll) during

translunar/transearth coast +X in ecliptic plane-

line+X


45/89




line +Z perpendicular to ecliptic

lane directed south

+X

+Z


46/89





lane directed south

+X+Y

+Z

+Y completed right-handedsystem


47/89





lane directed south

+X+Y

+Z

+Y completed right-handedsystem

PTC roll initiated from 90 deg

pitch attitude to place CSM/LMstack perpendicular to ecliptic(and hence, line of sight to


48/89

Entr REFSM MATEntr REFSM MAT

Ali ned with LVLH atpredicted time of EntryInterface (EI), 122 km400 kft altitude

FDAI read pitch 180, 0, 0in heads-down heat-

+X

EI

Note that nominal EI+Y into screen

+Z

degrees above localhorizontal


49/89

I MU Ali nment Techni uesI MU Ali nment Techni ues

Two vectors re uiredto uniquely defineorientation of one

another First vector fixes a line

of sight (LOS) butleaves one degree offreedom rotation

about LOS)


50/89

I MU Ali nment Techni uesI MU Ali nment Techni ues

Two vectors re uiredto uniquely defineorientation of one

another First vector fixes a line

of sight (LOS) butleaves one degree offreedom rotation

about LOS) Second vector fixes


51/89

CSM I M U Ali nmentCSM I M U Ali nment

Crew marked on two stars (or other

SXTSCT

sextant (SXT) or scanning telescope(SCT)

Auto optics modes allowed SXT/SCTshaft and trunnion to be pointed

computer Manual optics modes allowed

tweaking of SXT/SCT shaft/trunnionusing optics controller

Minimum Impulse Controller (MIC)could be used to tweak CSM attitude

Crewman Optical Alignment Sight(COAS) could be used as backup

Not attached to navigation base calibration required prior to use

Minimum ImpulseController (MIC)

OpticsController

MARK andMARK REJECT

pushbuttons


52/89

LM Docked IMU Ali nmentLM Docked IMU Ali nment

Initial coarse alignment usedCM gimbal angles

Docking mechanism did nottightly constrain relative roll rew recor e oc ng ang e

(R c) from index marks ontunnel during initial LM

activation Required LM gimbal anglescomputed manually from CMgimbal angles as follows:

LM = c - CMIGALM = 180+ IGA CM

MGALM = 360- MGA CM


53/89

LM Orbital IMU Ali nmentLM Orbital IMU Ali nment

Crew marked on two stars (or

using the alignment optical

telescope (AOT) AOT had six detent positions;,

could be used while docked toCSM

Rendezvous Radar (RR) antennare uired to be ositioned out ofAOT field-of-view

Crew entered detent position codeand star code manually intocomputer

COAS could be used as backup(same calibration restrictions asCSM)


54/89

LM AOT Usa eLM AOT Usa e

X-line and Y-line on AOTret c e use or n- g t

alignment Crew allowed star to driftacross e -o -v ew

X line

Y line


55/89




Crew pressed [MARK Y]

when star crossed Y-line

[MARK Y]


56/89




Crew pressed [MARK Y]

when star crossed Y-line Crew pressed [MARK X]when star crossed X-line

Marks could be taken ine er or er

Crew pressed [MARKREJECT] if bad mark

[MARK X]


57/89

LM Lunar Surface IMU Ali nmentLM Lunar Surface IMU Ali nment

Not always possible to sight on


58/89



For first surface alignment,local gravity vector (asmeasured by IMUaccelerometers) could besubstituted for one of the starsightings

g


59/89




Present orientation of LM Y

+Z

and Z axes stored in moon-fixed coordinates at conclusionof each alignment


60/89




Present orientation of LM Yand Z axes stored in moon-fixed coordinates at conclusionof each alignment

alignments, could use eithergravity vector and present Zaxis, or present Y and Z axes


61/89

LM AOT Surface Usa eLM AOT Surface Usa e

Stars may never cross AOT X

LM in fixed attitude Moon rotates very slowly Different markin techni ue

required AOT reticle had two additional

markings

Cursor

Archimedean spiral (radius

increases linearly with angle) AOT reticle rotated to allow

superimposed on star Reticle angle displayed oncounter, manually entered via

Spiral


62/89


Stars may never cross AOT X Shaft angle (A S)



markings Archimedean spiral (radius


superimposed on star Reticle angle displayed oncounter, manually entered via


63/89


Stars may never cross AOT X



markings Archimedean spiral (radius


superimposed on star Angle displayed on counter,manually entered via DSKY

Reticle angle (A R)


64/89

CSM SCS Atti tude Mana ementCSM SCS Atti tude Mana ement

Stabilization and Control System (SCS) served asac up contro system or t e r mary u ance,

Navigation, and Control System (PGNCS) Attitude reference provided by two Gyro Assembliess , eac o w c con a ne ree o y oun e

Attitude Gyros (BMAGs) GA2 BMAGs measure attitude rate GA1 BMAGs nominally measure attitude change from

reference attitude but could be configured to measurerates as backup to GA2

dd


65/89

CSM SCS Atti tude Mana ementCSM SCS Atti tude Mana ement

G ro Dis la Cou ler(GDC) combined GA1

attitude difference withreference attitude toproduce total attitude fordisplay to crew

current IMU attitude onAttitude Set Control Panel

,

aligned to reference BMAGs were more

LM AGS A i d MLM AGS A i d M


66/89

LM AGS Attitude Mana ementLM AGS Attitude Mana ement

Abort Sensor Assembl ASA was stra downinertial navigation system for the Abort GuidanceSystem (AGS)

a access to own st ata v atelemetry link

ASA to IMU

AGS could also calibrate ASA

gyro/accelerometer biases using IMU asreference

Ob tiOb ti


67/89


Review basic navi ation conce ts Describe coordinate systems Identif attitude determination techni ues

Prime: PGNCS IMU Management Backup: CSM SCS/LM AGS Attitude Management

ent y state vector eterm nat ontechniques

Prime: PGNCS Powered Flight Navigation Backup: LM AGS Navigation

Coastin I nte rationCoastin I nte ration


68/89


Enckes Method Use current state vector

and gravity of primary bodyto com ute a referenceconic



69/89




Sum all other accelerations

to ro a ate aposition/velocity deviancefrom the reference conic



70/89




Sum all other accelerations

to ro a ate aposition/velocity deviancefrom the reference conic

When deviances exceed

threshold, compute newreference conic and zerothe deviations (rectification)


71/89

Perturb in AccelerationsPerturb in Accelerations


72/89

Perturb in AccelerationsPerturb in Accelerations

Earth or lunar orbit: non-spherical gravity

Translunar/transearth coast: Earth, lunar,an so ar grav y sp er ca erms on y

No drag

No IMU acceleration

Measurement Incor orationMeasurement Incor oration


73/89

Measurement Incor orationMeasurement Incor oration

programs available,not all on both

Program CSM LM Prime

vehicles MCC prime for most

en ezvous n oar

forms of navigation;onboard capability Cislunar- MCC

- -comm backup

Lunar Surface MCC

LM Rendezvous Navi ationLM Rendezvous Navi ation


74/89


Actual

Navigated

Coasting

=vr xr

r

r

ass ve e c e r

+

Coasting

c ve e c e r

+

=vr x r

r

r

Integration Integration

The state vectors for both vehicles arepropagated to the current time



75/89


Actual

Navigated

Coasting

=vr xr

r

r

ass ve e c e r

+

Coasting

c ve e c e r

+

=vr x r

r

r


Q

The LM RR takes a measurement (range, range

Measurement

rate, shaft, or trunnion angle) of the CSM



76/89

Actual

Navigated

Coasting

=vr xr

r

r

ass ve e c e r

+

Coasting

c ve e c e r

+

= vr x r

r

r

br


MeasurementGeometry

QRR Measurement

Estimate

Q

Q

+

- Residual

The navigation software computes an estimate of the RR measurementbased on the current state vectors, and a measurement geometry vector

Measurement

The navigation software computes the difference (residual) between theactual RR measurement and the estimated measurement



77/89

Actual

Navigated

Coasting

=vr xr

r

r

ass ve e c e r

+

Coasting

c ve e c e r

+

= vr x rr

r

br

r


MeasurementGeometry Weighting

Vector Q

RR MeasurementEstimate

Computation

MeasurementQ

Q

r

+

- Residual

The navigation software computes a weighting vector

Measurement Incorporation

,vector, and predefined sensor variances



78/89

Actual

Navigated

Coasting

=vr xr

r

r

ass ve e c e r

+

Coasting

c ve e c e r

+

= vr

x r

r

r

br

r



Vector r

r

Q


Computation

Measurement

Q r

Q

Q

=iasb

v xr

rr

r

+

- ResidualSV Update

The navigation software computes an update to the state


vector and the measurement residual



79/89

Actual

Navigated

Coasting

=vr xr

r

r

ass ve e c e r

+

Coasting

c ve e c e r

+

= vr

x r

r

r

br

r


v

r r

r


Vector

r r

Q


Computation

Measurement

State Vector Alarm Test

CrewAction

Pass

Fail

Accept

RejectQ

r

Q

Q

=iasb

v xr

rr

r

iasbr

+

- ResidualSV Update

The state vector update is tested against a predefined threshold If the test passes, the state vector and RR biases are updated

Measurement Incorporation Pass

Accept

Otherwise, alarm annunciated and crew either accepts or rejects the update



80/89

Actual

Navigated

V+

V+

UpdateMode

Coasting

=vr xr

r

r

ass ve e c e r

M a n e u v e r

++

Coasting

c ve e c e r

M a n e u v e r

++

= vr

x r

r

r

br

r


v

r r

r


Vector

r r

Q


Computation

Measurement


CrewAction

Pass

Fail

Accept

RejectQ

r

Q

Q

=iasb

v xr

rr

r

iasbr

+

- ResidualSV Update

State vector update can be applied to either vehicle (usually the active vehicle, LM) If CSM performs maneuver, maneuver V should be externally applied to CSM vector

Measurement Incorporation PassAccept

I f it uacks like oneI f it uacks like one


81/89

Apollo navigation software initial development by Battinwas concurrent w t an n epen ent o a man s woron recursive estimators (later named Kalman filters) Early Apollo documents didnt use Kalmans nomenclature

a n scovere a man s wor ur ng eve opmen Apollo navigation software contained several

simplifications/differences from orthodox Kalman filter -

Square root of covariance: [E] = [W][W] T Eliminating negative numbers from matrix improved convergence

One measurement incor oration at a time Reduced a lot of matrix-vector math to vector-scalar math

Measurement edit test used state vector update rather than ratio Ratio test incorporates covariance, becomes more stringent as state

CSM Rendezvous Navi ationCSM Rendezvous Navi ation


82/89

V+

V+

UpdateMode

Coasting

=vr xr

r

r

ass ve e c e r

M a n e u v e r

++

Coasting

c ve e c e r

M a n e u v e r

++

= vr

x r

r

r

br

r


v

r r

r


Vector r r

QVHF/SXT

MeasurementEstimate

Computation

Measurement


CrewAction

Pass

Fail

Accept

RejectQ

r

Q

Q

r

+

-

=v

xr

r

CSM rendezvous measurements are performed using


Sensor biases are not propagated

LM Lunar Surface Navi ationLM Lunar Surface Navi ation


83/89

+

Coasting

=vr xr

r

r

e c e r

+

PlanetaryInertial

e c e a e

= vr

x r

r

r

br

r

Integration Orientation

v

r r

r


Vector r r

Q


Computation

Measurement


CrewAction

Pass

Fail

Accept

RejectQ

r

Q

Q

=v

xr

r

r

+

-

The LM vehicle state is stored in Moon-Fixed Coordinates and updated by transforming to inertialcoordinates


Only RR range and range rate are incorporated, not angles RR biases are not propagated

CSM Orbital Navi ationCSM Orbital Navi ation


84/89

Coasting

=vr xr

r

r

e c e r

+

Landmark

br

r

Integration

v

r r

r


Vector

r r

Position

lr r

Q

SCT MeasurementEstimate

Computation

Measurement

CrewAction

Accept(known

landmark)

RejectQ

r

Q

Q

=

lr

v xr

rr

r

lr r

+

-

Only the CSM state vector is propagated Measurements are SCT shaft and trunnion angles on a landmark on the Earth or lunar surface

Measurement Incorporation (unknown

landmark)

Landmark may be known (update CSM state vector) or unknown (update landmark position) Sensor biases are not propagated

CSM CislunarCSM Cislunar- -Midcourse Navi ationMidcourse Navi ation


85/89

Coasting

=vr x r

r

r

e c e r

+

Star Direction,Landmark

SXTlandmark

line of sight(LLOS)

SXTstar

line of sightSLOS

br

r

Integration

v

r r

r

MeasurementGeometry WeightingVector

Position

Q

SXT MeasurementEstimate

Computation

SXTStar-Landmark/ Measurement

CrewAction

Accept

RejectQ

r

Q

Q

r

+

-

=

v

r x

r

r

r

Only the CSM state vector is propagated Measurements are SXT marks on a star and either a landmark or Earth/moon horizon

HorizonMeasurement

Incorporation

View throughSXT reticle

All updates must be accepted or rejected by the crew Sensor biases are not propagated

P ow ered Fli ht Navi ationP ow ered Fli ht Navi ation


86/89

Both CSM and LM used Average-G algorithm for state vector propagation

Used IMU accumulated V over one guidance cycle (2 seconds)

Used average gravitational acceleration over one cycle, primary body only Earth gravity model: spherical and J2 (equatorial bulge) terms only

Estimated vehicle mass updated based on IMU sensed V No measurement incorporation for CSM LM Average-G incorporated Landing Radar (LR) measurements only

. Velocity data available starting at 10.6 km (35 kft) altitude Both range and velocity subjected to simple independent reasonableness checks All data inhibited at 15.2 m (50 ft) altitude

Basic Reference coordinates) during powered descent, ascent, and aborts Since IMU aligned to landing/liftoff REFSMMAT, sometimes referred to as

landing site coordinates -

LM AGS N avi ationLM AGS N avi ation


87/89

AGS state vectors initialized from PGNS telemetry linkupon crew comman

AGS state vectors could also be initialized via manualkeyboard entries of vectors voiced up from MCC AGS propagated CSM/LM state vectors from last

initialized data using acceleration data from ASA If LM under PGNS control, AGS acquired rendezvous

radar (RR) data (range, range rate, and angles)automatically from PGNS

If LM under AGS control, AGS acquired rendezvousra ar a a v a manua en r es Range and range rate only Crew manually pointed LM +Z axis at CSM to zero RR angles

SummarSummar


88/89

Coordinate Systems Prime: PGNCS IMU Management

Backu : CSM SCS/LM AGS Attitude Mana ement State Vector Determination

Prime: PGNCS Coastin Fli ht Navi ation

Prime: PGNCS Powered Flight Navigation Backup: LM AGS Navigation

ReferencesReferences


89/89

Apollo Operations Handbook, Block II Spacecraft, Volume I: Spacecraft Description . SM2A-03-Block II- 1 15 Januar 1970.

Apollo Operations Handbook, Lunar Module, LM 10 and Subsequent, Volume I: Subsystems Data . LMA790-3-LM 10, 1 April 1971.

Guidance System Operations Plan for Manned LM Earth Orbital and Lunar Missions using Program Luminary 1C (LM131 rev. 1), Section 5: Guidance Equations (rev. 8) . MIT Charles StarkDraper Laboratory R-567, April 1970.

Guidance System Operations Plan for Manned CM Earth Orbital and Lunar Missions using Program Colossus 3, Section 5: Guidance Equations (rev. 14) . MIT Charles Stark DraperLaboratory R-577, March 1971.

Space Navigation Guidance and Control, Volume 1 of 2 . MIT Instrumentation Laboratory R-500,June 1965.

po o 15 rogram escr pt on . e co ectron cs, 1971. Project Apollo Coordinate System Standards . NASA SE 008-001-1, June 1965. Apollo Training: Guidance and Control Systems - Block II S/C 101 , 15 September 1967. Apollo Experience Report Guidance and Control Systems. NASA TN D-8249, June 1976. A ollo Ex erience Re ort Onboard Navi ational and Ali nment Software . NASA TN D-6741

March 1972.

Apollo Experience Report: Very-High-Frequency Ranging System . NASA TN D-6851, June 1972. Apollo Experience Report Guidance and Control Systems: Orbital-Rate Drive Electronics for the Apollo Command Module and Lunar Module . NASA TN D-7784, September 1974.

A ollo Guidance Com uter Histor Pro ect Interview with R. Battin MIT 30 Se tember 2002(http://authors.library.caltech.edu/5456/01/hrst.mit.edu/hrs/apollo/public/interviews/battin.htm).

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