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DOCUMENTNO. D5-15560-6
TITLE APOLLO/SATURN V POSTFLIGHT TRAJECTORY - AS-506
MODEL NO. SATURN V CONTRACTNO. NAS8-5608, Schedule II,Part IIA,
Task 8.1.6,Item 42
October 6, 1969
S. C. Krausse, ManagerFLIGHT SYSTEMS ANALYSIS
ISSUE NO. ISSUED TO
THE _IP_'_/_'_'_I#'G COMPANY SPACE DIVISION LAUNCH SYSTEMS
BRANCH
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D5-15560-6
REV I S IONS
DESCR I PT ION DATE A PPROVEDREV.SYM
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ABSTRACTAND LIST OF KEY WORDS
This document presents the postflight trajectory for the
Apollo/Saturn V AS-506 flight. Included is an analysis of the
orbitaland powered flight trajectories of the launch vehicle, the
freeflight trajectories of the expended S-IC and S-II stages,
andthe slingshot trajectory of the S-IVB/IU. Trajectory
dependentparameters are provided in earth-fixed launch site,
launchvehicle navigation, and geographic polar coordinate
systems.The time history of the trajectory parameters for the
launchvehicle is presented from guidance reference release to
Command/Service Module (CSM) separation.
Tables of engine cutoff, stage separation, parking orbit
in-sertion, and translunar injection conditions are included inthis
document. The heliocentric parameters of the S-IVB/IUare given.
Figures of such parameters as altitude, surfaceand cross ranges,
and magnitudes of total velocity and accel-eration as a function of
range time for the powered flighttrajectories are presented.
The following is a list of key words for use in indexing
thisdocument for data retrieval:
Apollo/Saturn VAS-506Postflight TrajectoryPowered Flight
TrajectoryOrbital TrajectorySpent Stage TrajectorySlingshot
Trajectory
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CONTENTS
PARAGRAPH
REVISIONSABSTRACTAND
LISTCONTENTSILLUSTRATIONSTABLESREFERENCESACKNOWLEDGEMENTSOURCEDATA
PAGE
OF KEY WORDS
SECTION 1 - SUMMARYAND INTRODUCTION
SECTION 2 - COORDINATESYSTEMSAND LAUNCHPARAMETERS
SECTION 3 - POWEREDFLIGHT TRAJECTORYRECONSTRUCTION
3.13.1 .I3.1.23.1.33.23.2.13.2.23.33.3.13.3.2
POWEREDFLIGHT TRAJECTORYAscent PhaseSecond Burn PhaseTargeting
ParametersDATA SOURCESAscent PhaseSecond Burn
PhaseTRAJECTORYRECONSTRUCTIONAscent PhaseSecond Burn Phase
SECTION 4 - ORBITAL TRAJECTORYRECONSTRUCTION
4.14.24.2.14,2.24.34.3.14,3.24.4
ORBITAL TRAJECTORIESORBITAL DATA SOURCESOrbital Tracking
DataOrbital Venting Acceleration
DataTRAJECTORYRECONSTRUCTIONParking Orbit Insertion
ConditionsTranslunar Injection ConditionsORBITAL TRACKING
ANALYSlS
SECTION 5 - TRAJECTORYERRORANALYSIS
5,15.1 .I5.1.25.1.3
5.1.45,2
ERRORANALYSISQuantity of Tracking DataQuality of Tracking
DataConsistency Between TrackingVelocity DataContinuity Between
TrajectoryTRAJECTORYUNCERTAINTIES
and Guidance
Segments
PAGE
iiiii
iv
vivii
viiiix
X
I-I
2-I
3-I
3-I3-I3-I3-23-23-23-43-43-43-6
4-I
4-I4-24-24-24-24-24-34-3
5-I
5-I5-I5-I
5-25-25-3
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PARAGRAPH
CONTENTS (Continued)
SECTION 6 - SPENT STAGE TRAJECTORIES
S-IC SPENT STAGE TRAJECTORYS-II SPENT STAGE TRAJECTORY
SECTION 7 - S-IVB/IU SLINGSHOT TRAJECTORY
APPENDIX A - DEFINITIONS OF TRAJECTORYSYMBOLS AND COORDINATE
SYSTEMS
APPENDIX B - TIME HISTORY OF TRAJECTORYPARAMETERS - METRIC
UNITS
APPENDIX C - TIME HISTORY OF TRAJECTORYPARAMETERS - ENGLISH
UNITS
PAGE
6-I
6-I6-I
7-I
A-I
B-I
C-I
V
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FIGURE
ILLUSTRATIONS
3-I Ground Track and Tracking Stations - AscentPhase
3-2 Altitude - Ascent Phase
3-3 Surface Range Ascent Phase3-4 Cross Range - Ascent Phase3-5
Space-Fixed Velocity and Flight Path Angle
Ascent Phase3-6 Total Inertial Acceleration - Ascent Phase
3-7 Mach Number and Dynamic Pressure - S-IC Phase3-8 Altitude -
Second Burn Phase
3-9 Space-Fixed Velocity and Flight Path Angle -Second Burn
Phase
3-I0 Total Inertial Acceleration - Second BurnPhase
PAGE
3-73-83-9
3-I0
3-113-123-133-14
3-15
3-16
3-11 Available Tracking Data - Ascent Phase 3-173-12 Antenna
Locations and Center of Gravity 3-18
3-13 Azimuth Angle Tracking Comparison - AscentPhase 3-19
3-14 Elevation Angle Tracking Comparison -Ascent Phase 3-20
3-15 Slant Range Tracking Comparison - AscentPhase 3-21
4-I Orbital Acceleration Due to Venting 4-44-2 Ground Track
4-5
5-I Estimated Trajectory Uncertainty - AscentPhase 5-4
6-I Ground Tracks for S-IC and S-II Spent Stages 6-2
7-I Slingshot Maneuver Longitudinal VelocityIncrease 7-2
7-2 Trajectory Conditions Resulting from Sling-shot Maneuver
Velocity Increment 7-3
7-3 S-IVB/IU Velocity Relative to Earth Distance 7-4
7-4 S-IVB/IU and Spacecraft Relative Trajectories 7-5
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TABLES
TABLE
3-I3-113-1113-1V3-V3-VI
4-I
4-114-1114-1V4-V4-VI4-VII5-I5-115-1116-I6-117-1
7-11
7-111
Times of Significant EventsSignificant Trajectory
ParametersEngine Cutoff ConditionsStage Separation
ConditionsTargeting ParametersAvailable Tracking Data - Powered
FlightTrajectorySummary of Orbital C-Band Tracking
DataAvailable
Orbital Venting Acceleration PolynomialsParking Orbit Insertion
ConditionsTranslunar Injection ConditionsCSM Separation
ConditionsParking Orbit Tracking Utilization SummaryPost TLI
Tracking Utilization SummaryTracking Data Spread Ascent
PhaseTracking Data Spread - Parking Orbit PhaseTracking Data Spread
- Post TLI PhaseS-IC Spent Stage Trajectory ParametersS-II Spent
Stage Trajectory ParametersComparison of Slingshot Maneuver
VelocityIncrement
Comparison of Lunar Closest ApproachParametersHeliocentric Orbit
Parameters
PAGE
3 -223 -233-243 -253-26
3-27
4-64-74-84-9
4-104-114-12
5-55-65-76-36-4
7-6
7-77-8
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REFERENCES
•
•
•
•
NASA Document SE 008-001-I, "Project Apollo CoordinateSystem
Standards," June, 1965.
NASA Document M-D E 8020.008B, "Natural Environment andPhysical
Standards for the Apollo Program," April, 1965.
NASA Document MFT-I-69, "AS-506 G Mission Launch
VehicleOperational Trajectory," July 14, 1969.
Lockheed Document TM 54/30-150, "Manual for the GATEProgram,"
September, 1967.
viii
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ACKNOWLEDGEMENT
The analyses presented in this document were conducted bythe
following Boeing personnel:
G. EngelsJ. GrahamJ. JaapJ. Liu
The analysis presented in Section 7 of this document was
con-ducted by the following MSFC personnel of the
S&E-AERO-MDivision and is included for completeness in terms of
spentstage trajectories:
D. McFaddenC. Varnado
Questions concerning the information presented in this
documentshould be directed to the technical supervisor:
R. D. McCurdy, AG-13The Boeing CompanyHuntsville, Alabama
35807
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SOURCE DATA PAGE
The following listed government-furnished documentation wasused
in the preparation of this document:
Exhibit FFLine Item DateNumber GFD Title Received
R-AERO-P-#35c OMPT Format 6/16/69R-AERO-P-#17 Tracking and
Network Specifica-
tions 7/9/69R-AERO-P-#35b Transponder Locations 7/9/69
N/A Operational Trajectory CertifiedData (MSFC supplied)
7/18/69
l-MO-#4a Insertion Point and/or OrbitalElements 7/17/69
l-MO-#4c Six Seconds Raw Radar 7/17/69l-MO-#4f Meteorological
Data (Final) 7/25/69I-MO-#6 IP Raw MP 7/17/69I-MO-#9 Pulse Radar
7/25/69l-MO-#17c Final Significant Time of Events 7/25/69l-MO-#18a
Preliminary Guidance Velocities 7/18/69l-MO-#18c Orbital Venting
Accelerations
Data Cards 9/8/69
X
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SECTION 1
SUMMARY AND INTRODUCTION
The Apollo/Saturn V AS-506 vehicle was launched from Launch
Complex 39, Pad A at the Kennedy Space Center on July 16,
1969,at 8:32:00 A.M. Eastern Standard Time (Range Time Zero) at
anazimuth of 90 degrees east of north. Range time, which
isreferenced to Range Time Zero, is used throughout this
documentunless otherwise specified. Guidance reference release
(GRR)was established to have occurred at -16.968 seconds.
Firstmotion occurred at 0.3 second. At 13.2 seconds, a roll
maneuverwas initiated, orienting the vehicle to a flight azimuth
of72.058 degrees east of north. This flight azimuth, dependenton
the launch time, launch day and month, is calculated
usingpolynomial coefficients taken from the guidance presettings
inorder to achieve the desired translunar targeting parameters.The
translunar targeting parameters are functions of the moonposition,
earth parking orbit inclination, earth-moon distance,and moon
travel rate.
The vehicle performed with only minor deviations throughout
theentire flight. The vehicle was inserted into a parking orbitat
709.33 seconds at an altitude of 191.1 km (103.2 n mi) and atotal
space-fixed velocity of 7,793.1 m/s (25,567.9 ft/s). Thevehicle
remained in orbit for approximately one and one-halfrevolutions.
The S-IVB stage was restarted during the secondrevolution
approximately midway between Australia and Hawaii,at 9,856.2
seconds.
At 10,213.03 seconds, the vehicle was injected onto a
circum-lunar trajectory at an altitude of 334.4 km (180.6 n mi) and
atotal space-fixed velocity of 10,834.3 m/s (35,545.6 ft/s).
At11,723 seconds, the CSM separated from the launch vehicle at
analtitude of 7,065.7 km (3,815.2 n mi) and a total
space-fixedvelocity of 7,608.6 m/s (24,962.6 ft/s). Following LM
extrac-tion, the launch vehicle maneuvered to a slingshot
attitudefixed relative to local horizontal. The retrograde
velocityto achieve S-IVB/IU lunar slingshot was accomplished by a
LOX
dump, APS burn, and LH_ venting. The S-IVB/IU closest approachof
3,379 km (1,825 n ml) to the lunar surface occurred at78.70 hours
into the mission.
The impact location of the expended S-IC stage was determinedto
be 30.212 degrees north latitude and 74.038 degrees westlongitude
at 543.7 seconds. The impact location of the ex-pended S-II stage
was determined to be 31.535 degrees northlatitude and 34.844
degrees west longitude at 1,213.7 seconds.
Section 2 of this document defines the coordinate systems
andlaunch parameters used for the postflight trajectory
analysis.
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SECTION 1 (Continued)
The postflight mass point trajectory related parameters
andanalytical procedures are presented in Sections 3 through 7.The
trajectory is divided into six phases:
a
bC
de
f
Ascent PhaseOrbital PhaseSecond Burn PhasePost TLI Phase
Free Flight PhaseSlingshot Phase
The ascent phase, covering the portion of flight from
guidancereference release to orbital insertion (709.33 seconds),
isdiscussed in Section 3. This trajectory was established fromdata
provided by external C-band radars and telemetered on-board data
obtained from the ST-124M inertial platform.
The second burn phase, discussed in Section 3, covers theportion
of flight from S-IVB restart preparations to trans-lunar injection
(10,213.03 seconds). This trajectory wasestablished by integrating
the ST-124M platform telemeteredguidance velocities between
constraining state vectors ob-tained from the orbital and post TLI
trajectory phases.
The orbital phase, discussed in Section 4, covers the portionof
flight from orbital insertion to S-IVB restart preparations(9,278.2
seconds). The orbital trajectory was establishedfrom data provided
by the C-band radars of the Manned SpaceFlight Network.
The post translunar injection (TLI) phase, discussed in
Section4, covers the portion of flight from the translunar
injectionto CSM separation (11,723 seconds). This trajectory
wasestablished from data provided by the C-band radars of theManned
Space Flight Network.
The error analysis of the reconstructed trajectory is
discussedin Section 5. The criteria for error analysis are included
andtrajectory uncertainty limits are assigned to the boost,
parkingorbit, second burn, and post TLI phases.
The free flight phase, discussed in Section 6, covers
thetrajectories of the expended S-IC and S-II stages.
Thesetrajectories are based on initial conditions obtained from
thepostflight trajectory at separation. The nominal
separationimpulses for both stages were used in the simulation.
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SECTION 1 (Continued)
The slingshot phase, discussed in Section 7, covers the
tra-jectory of the S-IVB/IU after it was separated from the
CSM/LM.This trajectory was produced by integrating orbital
modelequations forward from a state vector at 21.58 hours GMT,July
16, 1969, which was established by Goddard Space FlightCenter from
Unified S-band (USB) tracking data.
Appendix A provides a detailed definition of the
symbols,nomenclature, and coordinate systems used throughout
thedocument.
Appendix B tabulates the time history of the
trajectoryparameters in metric units.
Appendix C tabulates the time history of the
trajectoryparameters in English units.
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SECTION 2
COORDINATESYSTEMSAND LAUNCHPARAMETERS
The time history of Observed Mass Point Trajectory parametersin
both metric and English units is tabulated in Appendices Band C,
respectively. These tabulations are in earth-fixedlaunch site,
launch vehicle navigation, and geographic polarcoordinate systems.
These coordinate systems are defined inReference I, "Project Apollo
Coordinate System Standards,"(PACSS) and are designated PACSSIO,
PACSSI, and PACSSI3, re-spectively. The trajectory symbols and
terminology used inthis document are defined in Appendix A.
The Fischer Ellipsoid of 1960 (Reference 2) is used as
therepresentative model for the earth and its gravitational
field.All latitude and longitude coordinates are defined with
respectto this ellipsoid.
The geographic coordinates for Launch Complex 39, Pad A, atthe
Kennedy Space Center are as follows:
Geodetic LatitudeLongitude
28.608422 degrees north80.604133 degrees west
The height of the center of gravity of the launch vehicleabove
the reference ellipsoid is 59.4 m (194.9 ft).
The azimuth alignments are as follows:
Launch AzimuthFlight AzimuthST-124M Platform Azimuth
90.0 degrees east of north72.058 degrees east of north72.058
degrees east of north
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SECTION 3
POWEREDFLIGHT TRAJECTORYRECONSTRUCTION
3.1 POWEREDFLIGHT TRAJECTORY
3.1.1 Ascent Phase
A comparison of actual and nominal times for significant
flightevents is presented in Table 3-I. The nominal times for
theseevents are taken from Reference 3.
The tracking stations and the vehicle ground track for theascent
phase are shown in Figure 3-I.
The actual altitude, surface range, and cross range are shownin
Figures 3-2 through 3-4, respectively, for the entire
ascenttrajectory. The magnitude of the total space-fixed
velocityvector and the associated flight path angle are shown in
Figure3-5. The magnitude of the total inertial acceleration
vectoris shown in Figure 3-6. Mach number and dynamic pressure
areshown during the S-IC phase of the ascent trajectory in
Figure3-7.
Various trajectory parameters, such as altitude, velocity,
andacceleration are given at some significant event times inTable
3-11.
Engine cutoff and stage separation conditions are given inTables
3-111 and 3-1V, respectively.
The ascent trajectory, from guidance reference release toparking
orbit insertion, is tabulated in Tables B-I throughB-Ill in metric
units, and in Tables C-I through C-Ill inEnglish units. These
tables present the trajectory in theearth-fixed launch site
(PACSSIO), launch vehicle navigation(PACSSI3), and geographic polar
(PACSSl) coordinate systems.The definitions pertaining to the
trajectory symbols and thecoordinate systems are given in Appendix
A.
3.1.2 Second Burn Phase
A comparison of actual and nominal times for significant
flight events pertaining to the second burn phase is includedin
Table 3-I.
The actual altitude is shown in Figure 3-8. The magnitude ofthe
total space-fixed velocity vector and the associated flightpath
angle are shown in Figure 3-9. The magnitude of the totalinertial
acceleration vector is shown in Figure 3-10. Themaximum total
inertial acceleration and earth-fixed velocityare shown in Table
3-11.
3-IPRECEDING PAGE BLANK NOT FILMED
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3.1 .2 (Continued)
The second burn trajectory, from the time of S-IVB
restartpreparations to CSM separation, is tabulated in Tables
B-Vthrough B-VII in metric units, and in Tables C-V throughC-VII in
English units. These tables present the trajectoryin the
earth-fixed launch site (PACSSIO), launch vehiclenavigation
(PACSSI3), and geographic polar (PACSSI) coordinatesystems. The
definitions pertaining to the trajectory symbolsand the coordinate
systems are given in Appendix A.
3.1.3 Targeting Parameters
The actual and nominal targeting parameters are given in
Table3-V. These nominal parameters are used in the guidance
com-puter as terminal conditions for the powered flight phases.The
actual targeting parameters were close to nominal.
3.2 DATA SOURCES
3.2.1 Ascent Phase
Tracking data and telemetered guidance velocity data
werereceived during the period from first motion through
orbitalinsertion. The time periods for which tracking system
coveragewas available are shown in Figure 3-11 and itemized in
Table3-VI. The geographic locations of the tracking stations andthe
ground track for the ascent trajectory are shown in Figure3-I. The
antenna locations for the tracking system and thevehicle center of
gravity are shown in Figure 3-12.
Considerable C-Band tracking data were furnished by the
sta-tions located at Cape Kennedy, Patrick Air Force Base,
MerrittIsland, Grand Turk Island, and Bermuda Island. These
trackingdata were provided as measured parameters in azimuth
angle,elevation angle, and slant range. These measurements
aredefined in Reference 1 and designated as PACSS3a.
Comparisons between these data and the ascent trajectory
werecalculated in PACSS3a. The position components of the
ascenttrajectory in PACSSIO were corrected for the differences
be-tween the center of gravity and the transponder location.
Thecorrected position components were transformed into the
meas-ured parameters of PACSS3a. Differences or deviations
(track-ing data minus corresponding parameters derived from the
ascenttrajectory) were calculated, smoothed, and plotted as
functionsof time, and are shown in Figures 3-13 through 3-15.
Cape Kennedy (1.16) radar provided tracking data from 25 to400
seconds. The azimuth angle measurements were noisythroughout the
time span of tracking, and oscillated about
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3.2.1 (Continued)
the trajectory up to about 175 seconds. After 175 seconds,
the azimuth angle measurements agree favorably with the tra-
jectory with maximum deviation of 0.016 degree. The
elevation
angle measurements were noisy throughout the tracking period
with maximum deviation of 0.037 degree from the trajectory.
The slant range measurements contained little noise
throughout
the tracking period with maximum deviation of 48 m (157 ft)from
the trajectory.
Patrick (0.18) radar provided tracking data from 25 to
500seconds. The azimuth angle measurements contained little
noise
throughout the tracking period. They deviated considerably
from the trajectory up to about 225 seconds, but agree
excel-
lently thereafter with maximum deviation of 0.008 degree.
The
elevation angle measurements were noisy during the early
por-tion (25 to 75 seconds) and the later portion (465 to 500
seconds) of tracking. The elevation angle measurements also
deviated considerably from the trajectory up to about lO0
seconds, and agree favorably with the trajectory in the timespan
from lO0 to 465 seconds with maximum deviation of 0.028
degree. The slant range measurements contained little noise
throughout the tracking period with maximum deviation of 32
m(I05 ft) from the trajectory.
Merritt Island (19.18) radar furnished data from 80 to 425
seconds. The azimuth angle measurements were of good quality
except in the time spans of 80-120 and 165-200 seconds,
where
the data were erratic. The azimuth angle measurements
reached
a maximum deviation of 0.059 degree at ll5 seconds, and
de-creased rapidly thereafter with near zero deviation after
300
seconds. The elevation angle measurements were of good
quality
and deviated a maximum of 0.030 degree from the trajectory.The
slant range measurements were of good quality except inthe time
span of 170-200 seconds, where the data were erratic.
The slant range measurements had a discontinuity at about
390
seconds, indicating a switch from beacon to skin tracking.
Themaximum deviation of slant range measurements from the
trajec-
tory amounted to 35 m (ll5 ft).
Grand Turk (7.18) radar supplied data from 230 to 520
seconds.
The azimuth and elevation angle measurements were noisy and
erratic throughout the tracking period. Although the slantrange
measurements contained little noise and deviated reason-
ably from the ascent trajectory, the data were considered as
invalid and were not used in the trajectory reconstruction.
Bermuda (67.16) radar provided data from 275 to 710 seconds.The
azimuth angle measurements contained little noise through-
3-3
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3.2.1 (Continued)
out the tracking period. Except for a characteristic
deviationfrom 500 to 600 seconds, the azimuth angle measurements
werein good agreement with the trajectory with maximum deviationof
0.012 degree. The elevation angle measurements were noisyat the
beginning (275 to 330 seconds) of tracking. A char-acteristic
deviation occurred from 500 to 625 seconds. Theelevation angle
measurements were in good agreement with thetrajectory near the end
of trackina with a deviation of 0.022degree at parking orbit
insertion (709.33 seconds). The slantrange measurements contained
little noise throughout thetracking period; however, a large
deviation occurred in theinterval 375 to 575 seconds. Approaching
the end of thetracking period, the deviation in the slant ranae
measurementsdecreased rapidly with a deviation of 48 m (157 ft) at
parkingorbit insertion.
Bermuda (67.18) radar provided data from 250 to 710 seconds.The
azimuth angle measurements contained little noise throughoutthe
tracking period. As with the 67.16 radar, a characteristicdeviation
was evident from 500 to 600 seconds. Otherwise, theazimuth angle
measurements were in good agreement with the tra-jectory with
maximum deviation of 0.024 degree. The elevationangle measurements
were noisy at the beginning (250 to 330seconds) of tracking. A
characteristic deviation occurred from500 to 625 seconds. The
elevation angle measurements were ingood agreement with the
trajectory near the end of trackingwith a deviation of 0.030 degree
at parking orbit insertion.The slant range measurements contained
little noise throughoutthe tracking period; however, a large
deviation occurred from400 to 575 seconds. Approaching the end of
the tracking period,the deviation in the slant range measurements
decreased rapidlywith a deviation of 20 m (66 ft) at parking orbit
insertion.
3.2.2 Second Burn Phase
Telemetered guidance velocity data during the S-IVB second
burnperiod were received. Also, C-band radar tracking data
wereobtained from the Redstone Ship from 9,726 to 10,098
seconds.These tracking data were found to be invalid and were not
usedin the trajectory reconstruction.
3.3 TRAJECTORY RECONSTRUCTION
3.3.1 Ascent Phase
The ascent trajectory from guidance reference release to
orbitalinsertion was established by a composite solution of
availabletracking data and telemetered onboard guidance velocity
data.
3-4
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3.3.1 (Continued)
Before the data were used in the trajectory solution, one ormore
of the following processing steps was performed:
a .
b.C.
d.eo
f.
Inspecting for format and parity errorsTime editingData editing
and filteringRefraction correction
ReformattingCoordinate transformation
The position components of the tracking point of the vehiclein
PACSSIO were established by merging the launch phase andascent
phase trajectory segments.
The launch phase (from first motion to 20 seconds) was
estab-lished by integrating the telemetered guidance
accelerometerdata and by constraining it to the early portion of
the ascentphase trajectory. The ascent phase (from 20 seconds to
orbitalinsertion at 709.33 seconds) was based on a composite fit
ofexternal tracking data and telemetered onboard guidance
velocitydata. The ascent phase was constrained to the insertion
vectorobtained from the orbital analysis of Section 4. The
outputdata were transformed to the vehicle center of gravity.
A computer program (GATE), which uses a guidance error model,was
utilized. The telemetered guidance velocity data wereused as the
generating paramete_ and error coefficients wereestimated to best
fit the tracking observations. The Kalmanrecursive method was used
for the estimation. Reference 4gives a theoretical discussion of
the GATE program.
The position components, in PACSSIO, were filtered and
differ-entiated to obtain vehicle velocity and acceleration
components.Since numerical differentiators tend to distort the
datathrough the transient areas (engine cutoffs), the
guidancevelocity data were integrated and used to fill in these
areas.
The trajectory data in PACSSIO were then transformed to
severalcoordinate systems. Various trajectory parameters were
alsocalculated and are presented in Appendices B and C. In
cal-culating the Mach number and dynamic pressure, measured
meteoro-logical data were used up to an altitude of 56.0 km (30.2 n
mi).Above this altitude the measured data were merged into the
U.S.Standard Reference Atmosphere.
3-5
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3.3.2 Second Burn Phase
The second burn trajectory was established by combining
anorbital trajectory segment and a powered flight
trajectorysegment.
The orbital trajectory segment covers the 9ortion of flightfrom
the beginning of S-IVB restart preparations (9,278.2seconds) to
9,715 seconds. This trajectory segment was ob-tained from the
orbital solution as described in Section 4.
The powered flight trajectory segment covers the time spanfrom
9,715 seconds to translunar injection (10,213.03 seconds).This
trajectory segment was established by integrating thetelemetered
guidance velocity data forward from the statevector at 9,715
seconds and constraining the end point to thetranslunar injection
vector (obtained from the post TLI tra-jectory of Section 4). The
GATE program was utilized forthe solution.
The Redstone Ship tracking data during the second burn phasewere
noisy and erratic. These tracking data were not utilizedin the
trajectory reconstruction.
The position components, in PACSSIO, were filtered,
differen-tiated, shaped, and transformed in the same manner as
describedin Paragraph 3.3.1.
3-6
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D5-15560-6
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D5-15560-6
TABLE 3-I. TIMES
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EVENT
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Guidance Reference Release
First Motion
Start of Ttme Base 1
Mach l
Maximum Dynamic Pressure
S-IC Center Engine Cutoff
S-IC Outboard Engine Cutoff
S-IG/S-II Separation Command
S-II Center Engine Cutoff
S-ll Outboard Engine Cutoff
S-II/S-IVB Separation Command
S-IVB Ist Guidance Cutoff
Parking Orbit Insertion
Begin S-IVB Restart Prepa-rations
S-IVB Engine Relgnltlon
(STDV Open)
S-IVB 2nd Guidance Cutoff
Translunar Injection
CSM Separation
Begin Slingshot Maneuver
OF SIGNIFICANT EVENTS
RANGE TIME, SEC
ACTUAL
-16.968
0.3
0.6
66.3
83.0
135.20
161.63
162.3
460.62
548.22
549.0
699.33
709.33
9,278.2
9,856.2
10,203.03
10,213.03
11,723
17,467.7
NOMINAL
-16.987
0.3
0.7
65.6
81 .3
135.26
161 .08
161.8
460.08
551.65
552.4
699.49
709.49
9,277.3
9,855.5
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10,214.06
11,704
17,404.4
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1.7
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0.55
0.5
0.54
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0.9
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19
63.3
3-22
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D5-15660-6
TABLE 3-11. SIGNIFICANT TRAJECTORY PARAMETERS
EVENT
i
First Notion
Math 1
Maximum Dynamic Pressure
Maximum Total |nerttalAcceleration: S-IC
S-II
S-IVB 1st Burn
S-IVB 2nd Burn
Maxtmum Earth-FixedVelocity: S-IC
S-II
S-IVB Ist Burn
S-IVB 2nd Burn
PARAMETER
Range Time, sec
Total Inertlal Acceleratfon, m/s 2
(ftls2)
(g)
Range Time, sec
Altitude, km(n ml)
Range Time, sec
Dynamic Pressured N/cm 2
(Ibf/ft 2 )
Altitude, kmin ml)
Range Time, sec
Acceleration, m/s 2
(ftls 2 )
(1)
Range Time, sec
Acceleration, m/s 2
(ft/s2)(g)
Range Time, sac
Acceleration, m/s 2
(¢t/s 2)
(g)
Range Time, sec
Acceleration, m/s 2
(ftls 2 )
(g)
Range Ttme, sec
Velocity, m/s
(ft/s)
Range Time, sec
Velocity, m/s
(ft/s)
Range Time, sec
Velocity, m/s
(ft/s)
Range Time, sec
Velocity, m/s
(ftls)
VALUE
0.3
10.47
(34.35)
(i .07)
66.3
7.8
(4.2)
83.0
3.52
(735.2)
13.6(7.3)
161.71
38.61
(126.67)
(3.94)
460.70
17.84
(58.53)
(1.82)
69g.41
6.73
(22.08)
(0.69)
10.203.11
14.22
(A6.65)
(1.45)
162.30
2,402.7
(7,882.9)
549.00
6,515.7
(21,377.0)
70g,33
7.389,5
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10,203.50
10,433.4
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3-23
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D5-15560-6
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D5-15560-6
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PARAMETER
Range Time, sec
Altitude, km(n mi)
Surface Range kmIn mi)
Space-Fixed Velocity,
Flight Path Angle,
Heading Angle, deg
Cross Range, km(n mi)
m/s(ft/s)
deg
S-lC/S-IISEPARATIONCOMMAND
162.3
66.7(36.0)
95.1(51 .3)
2,773.9(9,100.7)
19.020
75.436
0.5(0.3)
Cross Range Velocity, m/s(ft/s)
Geodetic Latitude, deg N
Longitude, deg E
12.8(42.0)
28.865
-79.676
S-II/S-IVBSEPARATIONCOMMAND
549.0
187.4(lOl .2)
l ,623.4
(876.6)
6,918.8
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O.611
82.426
27.5
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174.7(573.2)
31 .883
-64.147
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D5-15560-6
THIS PAGE INTENTIONALLY LEFT BLANK.
3-28
-
D5-15560-6
SECTION 4
ORBITAL TRAJECTORYRECONSTRUCTION
4.1 ORBITAL TRAJECTORIES
The S-IVB/LM/CSM was inserted into a circular parking orbit
at709.33 seconds. While in parking orbit, vehicle subsystemcheckout
was carried out from the tracking stations and MissionControl
Center at Houston. During the second revolution,approximately
midway between Australia and Hawaii, the S-IVBstage was restarted
and the vehicle was placed onto a circum-lunar trajectory.
The parking orbit insertion conditions were close to nominal.The
space-fixed velocity at insertion was equal to nominal, andthe
flight path angle was 0.013 degree greater than nominal.The
eccentricity was 0.00001 less than nominal. The apogeeand perigee
were 0.5 km (0.3 n mi) and 0.6 km (0.3 n mi) lessthan nominal,
respectively.
The translunar injection (TLI) conditions were also close
tonominal. The eccentricity was 0.00029 greater than nominal,the
inclination was 0.004 degree greater than nominal, thenode was
0.019 deqree lower than nominal, and C3 was 16,877m2/s2 (181,663
ft2/s 2) greater than nominal. The space-fixedvelocity was 3.2 m/s
(10.5 ft/s) greater than nominal, and thealtitude was 3.1 km (I.6 n
mi) less than nominal.
The parking orbit trajectory spans the interval from insertionto
begin S-IVB restart preparations (9,278.2 seconds). Thepost TLI
trajectory covers the period from translunar injection(10,213.03
seconds) to CSM separation (11,723 seconds). Thesetwo orbital
trajectories were established by the integrationof the orbital
model equations using the insertion/injectionvector as the initial
conditions.
The insertion/injection conditions, as determined by theOrbital
Correction Program (OCP), were obtained by a differ-ential
correction procedure which adjusted the
estimatedinsertion/injection conditions to fit the C-band radar
trackingdata in accordance with the weights assigned to the
data.After all available C-band radar tracking data were
analyzed,the stations and passes providing the better quality data
wereused in the determination of the insertion/injection
conditions.
4-1 PRECEDING PAGE BLANK NOT FILMED
-
D5-15560-6
4.2 ORBITAL DATA SOURCES
4.2.1 Orbital Tracking Data
Orbital tracking was conducted by the NASA Manned Space
FlightNetwork (MSFN). A summary of the C-band tracking data isgiven
in Table 4-I. There were also considerable UnifiedS-band (USB)
tracking data available during these periods offlight which were
not used due to the abundance of C-bandradar data.
4.2.2 Orbital Venting Acceleration Data
During the orbit, no major thrusting occurred; however, theorbit
was continuously perturbed by low-level LH2 ventingthrust. To
accurately model the orbit of the vehicle, thisperturbation was
taken into account. The venting model wasderived from telemetered
guidance velocity data from theST-124M guidance platform. The
guidance velocity data werefitted in segments by polynomials in
time. These polynomialswere analytically differentiated to obtain
the accelerationcomponents measured by the guidance platform. Table
4-11lists the acceleration polynomials derived by this
method.Figure 4-I reflects the best estimate of the total
ventingacceleration (RSS of components) after atmospheric
effectsand biases have been removed.
4.3 TRAJECTORY RECONSTRUCTION
4.3.1 Parking Orbit Insertion Conditions
The Orbital Correction Program (OCP) was used to solve for
theparking orbit insertion conditions utilizing C-band trackingdata
and the above-mentioned vent model. The insertion condi-tions are
given in Table 4-111. The parking orbit solutionwas based on a
composite fit of the two Bermuda stations atinsertion, pass one of
Carnarvon, pass two of Patrick, andpass two of Carnarvon. This
combination of trackers is geo-metrically spaced to insure adequate
coverage of the parkingorbit. The Bermuda data at insertion were
also used in thetrajectory reconstruction of the ascent phase. The
use ofBermuda data in the ascent phase solution and also in
theorbital phase solution aids in assuring the continuity of
thetrajectory. The orbital solution, with the exception of
theFPS-16M Bermuda radar, is based on the higher quality
FPO-6radars. The ground track from parking orbit insertion to
CSMseparation is given in Figure 4-2. The parking orbit trajec-tory
in PACSSI is given in Tables B-IV and C-IV.
4-2
-
D5-15560-6
4.3.2 Translunar Injection Conditions
The translunar injection (TLI) conditions were determined bythe
Orbital Correction Program (OCP) utilizing the post injec-tion
C-band tracking data. The TLI conditions are given inTable 4-1V.
The TLI state vector obtained by the GATE programfrom the
integration of guidance velocity data agreed favorablywith the OCP
determined TLI vector. The post TLI trajectoryis included in Tables
B-V through B-Vll in metric units andTables C-V through C-VII in
English units. The CSM separationconditions are given in Table
4-V.
4.4 ORBITAL TRACKING ANALYSIS
The stations used to obtain the parking orbit insertion
condi-tions and translunar injection conditions are given by
Tables4-VI and 4-VII, respectively. These two tables also
includethe number of data points and the Root-Mean-Square
(RMS)errors of the residuals for each data type. These RMS
errorsrepresent the difference between the actual radar
observationsand the calculated observations based on the orbital
ephemerisdefined by the initial conditions. The RMS residual errors
include high frequency errors (assumed Gaussian), systematicerrors
due to instrumentation biases, mathematical model error,and errors
in the correction for atmospheric refraction.
The maximum RMS error of the radar residuals for the
parkingorbit was 18 m (59 ft) in slant range, 0.030 degree in
elevationangle, and 0.015 degree in azimuth angle. The maximum RMS
errorof the radar residuals for the post TLI trajectory was 18 m(59
ft) in slant range, 0.025 degree in elevation angle, and0.020 in
azimuth angle. The magnitudes of these RMS errors arereasonable and
indicate the validity of the parking orbit andpost TLI
trajectory.
4-3
-
D5-15560-6
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4-4
-
D5-15560-6
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-
D5-15560-6
TABLE 4-I. SUMMARYOF ORBITAL C-BAND TRACKING DATA AVAILABLE
STATIONi l
Bermuda
Bermuda
Tananarive
Carnarvon
California
Patrick
Grand Turk
Redstone Ship
Hawaii
Antigua
Ascension
TYPE OF RADARS
71r
FPS-16M
FPQ -6
FPS-16M
FPQ-6
TPQ-18
FPQ-6
TPQ-18
FPS-16M
FPS-16M
FPQ-6
TPQ-18
REV 1
X
X
X
X
X
REV 2
X
X
X
POST TL I
X
4-6
-
D5-15560-6
TABLE 4-11. ORBITAL VENTING ACCELERATIONPOLYNOMIALS*
X**
Tb 710 1 ,483 9,535Te 1 ,483 9,535 9,840CO -0.29883288xi0 -5
-0.12140570xi0 -5 -0.61607689xi0 -6
C1 0.19159214xi0 -7 -0.25510786xi0 "9 0.49930034xi0 -7
C2 -0.46780418xi0 "I0 0.13961048xi0 -II -0.39763102xi0 -9
C3 0.34343775xi0 -13 -0.59877535xi0 -15 0.86249576xi0 -12
C4 0 0.89589398xi0 -19 0
C5 0 -0.44624259xi 0-23 0
Tb 710Te 9,840
CO 0.13272155xi0 -7
C1 0.601 77901xi0 -II
C2 0C3 0
C4 0
C5 0°,
ZT b 710 1 ,483 9,535
T e 1 ,483 9,535 9,840
CO 0.54491435xi0 -5 0.39339382xi0 -6 -0.26517094xi0
C 1 -0.37627287xi0 °7 -0.24289009xi0 -8 0.I0419636xi0
C2 0.86370452xi0 "I0 0.15008060xi0 -II -0.92767644xi0
C3 -0.61633706xi0 -13 -0.30356055xi0 -15 0.22408258xi0
C4 0 0.20894634xi0 -19 0
C5 0 -0.21112472xi0 -24 0
-6
-7
-I0
-12
t3+C4t4+C t 5* Polynomials are of the form a=Co+Clt+C2t2+C 3
5
where a is the acceleration component (km/s2) and t = T-T bwhere
TbST
-
D5-15560-6
TABLE 4-111. PARKING ORBIT INSERTION CONDITIONS
PARAMETER
Range Time, sec
Altitude, km(n mi)
Space-Fixed Velocity, m/s(ft/s)
VALUE
709.33
191 .I(103.2)
7,793.1(25,567.9)
Flight Path Angle, deg
Heading Angle, deg
Inclination, deg
Descending Node, deg
Eccentricity
Apogee*, km(n mi)
Perigee*, km(n mi)
Period, min
Geodetic Latitude, deg N
Longitude, deg E
0.012
88.848
32.521
123.088
0.00021
186.0(100.4)
183.2(98.9)
88.18
32.672
-52.694
*Based on a spherical earth of radius 6,378.165 km(3,443.934 n
mi)
4-8
-
D5-15560-6
TABLE 4-1V. TRANSLUNARINJECTION CONDITIONS
PARAMETER VALUE
Range Time, sec
Altitude, km
(n mi)
Space-Fixed Velocity, m/s(ft/s)
Flight Path Angle, deg
10,213.03
334.4(180.6)
10,834.3(35,545.6)
7.367
Heading Angle, deg
Inclination, deg
Descending Node, deg
Eccentricity
C3", m2/s 2
(ft2/s 2 )
Geodetic Latitude, deg N
Longitude, deg E
60.073
31 .383
121 .847
0.97696
-1,391,607
(-14,979,133)
9.983
-164.837
* Twice the specific energy of orbit
C3 = V2 _
where V = Inertial Velocity
!J : Gravitational ConstantR = Radius vector from center of
earth
4-9
-
D5-15560-6
TABLE 4-V. CSM SEPARATION CONDITIONS
PARAMETER VALUE,,
Range Time, sec
Altitude, km(n mi)
Space-Fixed Velocity, m/s(ftls)
11 ,723
7,065.7(3,815.2)
7,608.6(24,962.6)
Flight Path Angle, deg
Heading Angle, deg
Geodetic Latitude, deg N
Longitude, deg E
45.148
93.758
31.246
-90.622
4-10
-
D5-15560-6
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4-12
-
D5-15560-6
SECTION 5
TRAJECTORYERRORANALYSIS
5.1 ERRORANALYSIS
The confidence level or uncertainty one may assign to a
recon-structed trajectory depends on the degree of fulfillment of
thefollowing criteria:
a. Quantity of Tracking Datab. Quality of Tracking Datac.
Consistency between Tracking and Guidance Velocity Datad.
Continuity between Trajectory Segments
These criteria vary from flight to flight. Therefore, a
rig-orous statistical error analysis of the reconstructed
trajec-tory is difficult to obtain. The following paragraphs
summarizethe results for this flight, and lead to the position and
ve-locity uncertainties for the reconstructed trajectory.
5.1.1 Quantity of Tracking Data
The available tracking data for the powered flight phases
aregiven in Figure 3-11 and Table 3-VI. The tracking coveragesfor
the parking orbit and post TLI phases are given in Table4-I.
The tracking stations for the ascent and post TLI phases
pro-vided extensive redundant coverages. The available trackingdata
during parking orbit provided adequate coverage. TheRedstone Ship
C-band tracking data were available for a portionof the second burn
phase.
5.1.2 Quality of Tracking Data
The tracking data were generally of good quality. The Grand
Turk (7.18) radar data for the ascent phase and the Redstone
Ship radar data for the second burn phase were found to be
invalid. However, the tracking data furnished before and
after the second burn phase were of good quality.
Comparisons of the tracking data in measured parameters
(PACSS3a)
with the ascent trajectory are shown in Figures 3-13 throuQh
3-15. These plots indicated that the tracking data from the
different stations were mutually consistent. Except for
thecharacteristic data deviations from the Bermuda stations
occur-
ring approximately in the time span 400-600 seconds, the
track-
ing data deviations were of acceptable magnitude. The
tracking
data obtained during the parking orbit and post TLI phases
were
5-I
-
D5-15560-6
5.1.2 (Continued)
of good quality. The RMS errors of residuals for each data
type are given in Tables 4-Vl and 4-VII, respectively.
The tracking data were transformed into the earth-fixed
launchsite coordinate system (PACSSIO) and differenced with the
re-constructed trajectory to provide a more direct indication ofthe
spread of the tracking data. The tracking data spreadsfor the
ascent, parking orbit, and post TLI phases are givenin Tables 5-I
through 5-111, respectively.
5.1.3 Consistency Between Tracking and Guidance Velocity
Data
The consistency between tracking and guidance velocity datacan
be obtained by examining the guidance velocity error plotsduring
powered flight trajectory segments. These error plotsgive the
differences between the guidance velocities from theST-124M
platform and those derived from the reconstructed tra-jectory.
The guidance velocity error plots for the ascent phase
hadreasonable shapes and magnitudes. The maximum error amountedto
1.5 m/s (4.9 ft/s) in the X-direction, 2.8 m/s (9.2 ft/s)in the
Y-direction, and 0.7 m/s (2.3 ft/s) in the Z-direction,referenced
to launch vehicle platform-accelerometer coordinatesystem
(PACSSI2).
The guidance velocity error plots for the second burn phase
had reasonable shapes and magnitudes. The maximum error
amounted to 1.2 m/s (3.9 ft/s) in the X-direction, 1.7 m/s
(5.6 ft/s) in the Y-direction, and 0.9 m/s (3.0 ft/s) in the
Z-direction, referenced to PACSSI2.
5.1.4 Continuity Between Trajectory Segments
The continuity between trajectory segments can be obtained
byexamining the spread of solutions at parking orbit insertionand
translunar injection before the trajectory segments weremerged
together.
Comparisons of the spread of solutions at the parking
orbitinsertion obtained independently by the powered flight
andorbital analyses yielded good agreement. The position
andvelocity components of the solutions had a spread of 70 m(230
ft) and 0.3 m/s (I.0 ft/s) in the downrange direction,170 m (558
ft) and 0.8 m/s (2.6 ft/s) in the vertical direction,and 130 m (427
ft) and 1.7 m/s (5.6 ft/s) in the crossrangedirection, referenced
to the earth-fixed launch site coordinatesystem (PACSSlO).
5-2
-
D5-15560-6
5.1.4 (Continued)
Comparisons of the TLI vectors determined independently fromthe
powered flight and orbital analyses yielded good agreement.The TLI
vector from the powered flight analysis was obtained bypropagating
forward the state vector at 9,715 seconds (fromparking orbit
analysis) to 10,213.03 seconds. The TLI vectorfrom the orbital
analysis was determined separately by usingthe post TLI tracking
data. The position and velocity compon-ents of the two solutions
had respectively a spread of 90 m(295 ft) and 0.3 m/s (I.0 ft/s) in
the X-direction, 80 m(262 ft) and 1.2 m/s (3.9 ft/s) in the
Y-direction, and 430 m(1,411 ft) and 1.4 m/s (4.6 ft/s) in the
Z-direction, refer-enced to the earth-fixed launch site coordinate
system (PAC_SIO).
A dispersion analysis was performed for the parking orbit
tra-jectory. Three solutions were obtained by judiciouslyselecting
various tracking data combinations. The parking orbitinsertion
vectors had a spread in position and velocity compon-ents
respectively of 60 m (197 ft) and 0.3 m/s (I.0 ft/s) indownrange
(Z), 275 m (902 ft) and 0.I m/s (0.3 ft/s) in vertical(X), and 80 m
(262 ft) and 0.2 m/s (0.7 ft/s) in crossrange(Y), referenced to the
earth-fixed launch site coordinatesystem (PACSSIO).
5.2 TRAJECTORY UNCERTAINTIES
Based on the information of Paragraph 5.1, past experience,
andengineering judgment, the trajectory uncertainties were
esti-mated.
The trajectory uncertainties for the ascent phase are shown
inFigure 5-I. At S-IC OECO, the uncertainties in position
andvelocity components in PACSSIO are ±60 m (±197 ft) and ±0.4
m/s(±1.3 ft/s), respectively. At S-II OECO, the uncertainties
inposition and velocity components in PACSSIO are ±350 m (±1,148ft)
and ±0.7 m/s (±2.3 ft/s), respectively. At insertion andthroughout
the parking orbit, the uncertainties in positionand velocity
components in PACSSIO are ±500 m (±1,640 ft) and±I.0 m/s (±3.3
ft/s), respectively. The trajectory uncertain-ties increased to
±750 m (±2,461 ft) in position componentsand ±1.5 m/s (±4.9 ft/s)
in velocity components at TLI. Thetrajectory uncertainties at CSM
separation are ±1,500 m(±4,921 ft) in position components and ±2.0
m/s (±6.6 ft/s)in velocity components.
5-3
-
D5-15560-6
0 0-0
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5-4
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D5-15560-6
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D5-1 5560-6
THIS PAGE INTENTIONALLY LEFT BLANK.
5-8
-
D5-15560-6
SECTION 6
SPENT STAGE TRAJECTORIES
6.1 S-IC SPENT STAGE TRAJECTORY
Postflight predictions of earth surface impact parameters forthe
spent S-IC stage were computed using a mass point trajec-tory
simulation computer program. S-IC postflight burnoutposition and
velocity data were combined with nominal mainpropulsion system
decay performance and nominal retro rocketperformance to initialize
the simulation program.
Three separate theoretical trajectories were computed for
the
spent S-IC stage. These three trajectories represent the
fol-
lowing booster atmospheric entry conditions:
a. Zero-degree angle-of-attack entryb. Ninety-degree
angle-of-attack entryc. Tumbling entry
The tumbling booster case is considered to define actual
caseimpact conditions although no tracking coverage was
availablefor confirmation.
Results of the three computed S-IC spent stage trajectories
are summarized in Table 6-I. The ground track is shown in
Figure 6-I.
6,2 S-II SPENT STAGE TRAJECTORY
Three separate theoretical trajectories, corresponding to
thezero-degree, ninety-degree, and tumbling case
trajectoriescomputed for the S-IC stage, were computed for the
spent S-IIstage.
The computed results, assuming a tumbling stage, were
consideredto define stage impact conditions since no tracking
coverageof the spent S-II stage was available.
Results of the three computed S-II spent stage trajectoriesare
summarized in Table 6-11. The ground track is shown inFigure
6-I.
PRECEDING PAGE BLANK NOT FILMED6-1
-
D5-15560-6
0
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N g33_1930 - 3(]fllllVl
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6-2
-
D5-15560-6
TABLE 6-1. S-IC SPENT STAGE TRAJECTORY PARAMETERS
EVENT
Impact: Tumbling Case
Impact: 0 ° Angle-of-Attack
Impact: 90 ° Angle-of-Attack
Apex: Tumbling Case
PARAMETER
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Altitude, km(n mi)
Surface Range, km(n mi)
VALUE
543.7
30.212
-74.038
661.4(357.1)
503.5
30.231
-73.942
671.0(362.3)
577.8
30.198
-74.105
554.9(353.6)
269.1
115.0(62.1)
327.4(176.8)
6-3
-
D5-15560-6
TABLE 6-11. S-II SPENT STAGE TRAJECTORY PARAMETERS
EVENT
Impact: Tumbling Case
Impact: 0 ° Angle-of-Attack
Impact: 90 ° Angle-of-Attack
Apex: Tumbling Case
PARAMETER
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Altitude, km(n mi)
Surface Range, km(n mi)
VALUE
1,213.7
31.535
-34.844
4,392.5(2,371.8)
1,179.9
31.497
-34.582
4,417.8(2,385.4)
1,252.7
31.573
35.113
4,366.7(2,357.8)
587.0
188.8(I01 .9)
l ,862.9(l,OO5.9)
6-4
-
D5-15560-6
SECTION 7
S-IVB/IU SLINGSHOT TRAJECTORY
Following LM extraction, the S-IVB/IU was placed on a
lunarslingshot trajectory. This was accomplished by slowino downthe
S-IVB/IU to make it pass by the trailino edge of the moonand obtain
sufficient energy to continue to a solar orbit.The velocity
increase was achieved by a combination of 108-second LOX dump,
280-second APS burn, and LH 2 vent. A timehistory of the vehicle
longitudinal velocity increase for theslingshot maneuver is
presented in Figure 7-I. Table 7-Ipresents a comparison of the
actual and nominal velocityincrease due to the various phases of
the maneuver. The majorerror contribution in total velocity
increase is the resulting7.3 m/s (24.0 ft/s) from the continuous
venting system (CVS)as compared to 3.5 m/s (11.5 ft/s) for the
predicted value.Figure 7-2 presents the resultant conditions for
variousvelocity increases at the given attitude of the vehicle
forthe maneuver.
The S-IVB/IU closest approach of 3,379 kilometers (1,825 n
mi)above the lunar surface occurred at 78.70 hours into the
mis-
sion. The trajectory parameters were obtained by
integratingforward a vector furnished by Goddard Space Flight
Center(GSFC) which was obtained from USB tracking data during
theactive lifetime of the S-IVB/IU. The actual and
nominalconditions at closest approach are presented in Table
7-11.Figure 7-3 illustrates the influence of the moon on the
S-IVB/IUenergy (velocity) relative to the earth and shows that
theS-IVB/IU escaped as a result of the lunar encounter. Figure7-4
illustrates the relationship between the S-IVB/IU and thespacecraft
in the lunar vicinity, with all paths shown in thespacecraft's
orbital plane. The spacecraft had completed onelunar revolution
prior to S-IVB/spacecraft close approach, atwhich time the two
vehicles were approximately 3,500 km (1,890n mi) apart. Some of the
heliocentric orbit parameters of theS-IVB/IU are presented in Table
7-111. The same parametersfor the orbit of the earth are also
presented for comparison.
7-I
-
D5-15560-6
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TABLE 7-I. COMPARISON OF SLINGSHOT MANEUVER
VELOCITYINCREMENT
PARAMETER ACTUAL NOMINAL
Longitudinal Velocity Increase, m/s(ft/s)
LOX Dump_ mls(ft/s)
APS Burn, m/s
(ft/s)
Continuous Vent System*, m/s(ftls)
36.3(I19.1)
17.0(55.8)
12.0(39.4)
7.3(24.0)
31 .5(103.3)
16.0(52.5)
12.0(39.4)
3.5(II .5)
* Latched open at 17,468 seconds
7-6z
-
D5-15560-6
TABLE 7-II. COMPARISON OF LUNAR CLOSEST APPROACHPARAMETERS
PARAMETER ACTUAL NOMINAL
Selenocentric DistanCelnkm mi)
Altitude Above Lunar Surface, km(n mi)
Time from Launch, hr
Velocity Increase Relative toEarth from Lunar Encounter,
km/s
(n mi/s)
5,117(2,763)
3,379
(l ,825)
78.7
0.680(0.367)
3,700(I ,998)
1 ,962(I ,059)
78.4
0.860(0.464)
7-7
-
D5-15560-6
TABLE 7-111. HELIOCENTRIC ORBIT PARAMETERS
PARAMETER
Semimajor Axis, 106 km
(106 n mi)
Aphelion, 106 km
(106 n mi)
Perihelion, 106 km
(106 n mi)
Inclination,* deg
Period, days
S-IVB/IU
143.08
(77.26)
151.86
(82.OO)
134.30
(72.52)
0.3836
342
EARTH
149.00
(80.45)
151 .15
(81 .61)
146.84
(79.29)
0.0000
365
* Measured with respect to the ecliptic plane
7-8
-
D5-15560-6
APPENDIX A
DEFINITIONS OF TRAJECTORY SYMBOLS AND COORDINATE SYSTEMS
SYMBOL
XE, YE, ZEDXE, DYE, DZEDDXE, DDYE, DDZE
XS, YS, ZSDXS, DYS, DZSDDXS, DDYS, DDZS
GC DISTGC LATGD LATLONG
DEFINITION
Position, velocity, and acceleration compo-nents of _tehicle
center of gravity in Earth-Fixed Launch Site Coordinate System.
Theorigin of this system is at the intersectionof Fischer Ellipsoid
(1960) and the normalto it which passes through the launch site.The
X axis coincides with the ellipsoidnormal passing through the site,
positiveupward. The Z axis is parallel to theearth-fixed flight
azimuth, defined atguidance reference release time, and ispositive
down range. The Y axis completesa right-handed system. This
coordinatesystem is identical to Standard CoordinateSystem I0 of
Project Apollo Coordinate SystemStandards, abbreviated as
PACSSIO.
Position, velocity, and acceleration compo-nents of vehicle
center of gravity in LaunchVehicle Navigation Coordinate System.
Theorigin of this system is at the center ofthe earth. The X axis
is parallel to FischerEllipsoid normal through the launch
site,positive upward. The Z axis is parallel tothe flight azimuth,
positive downrange.The Y axis completes a right-handed system.The
direction of the coordinate axes remainsfixed in space at guidance
reference release.This coordinate system is identical toStandard
Coordinate System 13 of ProjectApollo Coordinate System Standards,
abbrevi-ated as PACSSI3.
Position components of vehicle center ofgravity in Geographic
Polar CoordinateSystem. Position in this system is definedby the
geocentric distance (GC DIST), geo-centric latitude (GC LAT),
geodetic latitude(GD LAT), and longitude (LONG). Geocentricdistance
is the distance from the geocenterto vehicle center of gravity.
Geocentriclatitude is the angle between the radiusvector of the
subvehicle point and the equa-torial plane, positive north of the
equa-torial plane. Geodetic latitude is the
A-I
-
D5-15560-6
SYMBOL
EF VELVEL-AZVEL-EL
SF VEL
FLT-PATH
HEAD
APPENDIX A (Continued)
DEFINITION
angle between the normal to the Fischer
Ellipsoid through the subvehicle point and
the equatorial plane, positive north of theequatorial plane.
Longitude is the angle
between the projection of the radius vector
into the equatorial plane and the Greenwichmeridian, positive
east of the Greenwich
meridian. This coordinate system is iden-
tical to Standard Coordinate System l of
Project Apollo Coordinate System Standards,abbreviated as
PACSSI.
Earth-fixed velocity of vehicle center of
gravity in Geographic Polar Coordinate
System. Velocity in this system is givenin terms of azimuth
(VEL-AZ), elevation
(VEL-EL), and magnitude of the velocity
vector (EF VEL). Azimuth is the angle be-
tween the projection of the velocity vector
into the local horizontal plane and the
north direction in this plane, positive
east of north. Elevation is the angle be-
tween the velocity vector and the local
horizontal plane, positive above the hori-
zontal plane. This coordinate system isidentical to Standard
Coordinate System l
of Project Apollo Coordinate System Stand-
ards, abbreviated as PACSSI.
Space-fixed velocity of vehicle center of
gravity in Geographic Polar Coordinate
System. Velocity in this system is givenin terms of heading
angle (HEAD), flight
path angle (FLT-PATH), and magnitude of
velocity vector (SF VEL). Heading angle is
the angle between the projection of thevelocity vector into the
local horizontal
plane and the north direction in this plane,
positive east of north. Flight path angle
is the angle between the velocity vector
and the local horizontal.plane, positiveabove the horizontal
plane. This coordi-
nate system is identical to Standard Co-
ordinate System l of Project Apollo
Coordinate System Standards, abbreviatedas PACSSIo
A-2
-
D5-15560-6
SYMBOL
ALTITUDE
RANGE
TIME
APPENDIX A (Continued)
DEFINITION
Perpendicular distance from vehicle __nterof gravity to Fischer
Ellipsoid, positiveabove Fischer Ellipsoid.
Surface range, measured along Fischer Ellip-soid from the launch
site to the subvehiclepoint.
Range time, referenced to nearest integersecond before IU
umbilical disconnect.
A-3
-
D5-15560-6
THIS PAGE INTENTIONALLY LEFT BLANK,
A-4
-
D5-15560-6
APPENDIX B
TIME HISTORY OF TRAJECTORYPARAMETERS- METRIC UNITS
The postflight trajectory, from guidance reference release toCSM
separation,is tabulated in metric units in Tables B-Ithrough
B-VII.
Table B-I gives the earth-fixed launch site position,
velocity,and acceleration components for the ascent phase of the
flight.
Table B-II gives the launch vehicle navigation
position,velocity, and acceleration components for the ascent phase
ofthe flight.
Table B-Ill gives the geographic polar coordinates for theascent
phase of flight.
Table B-IV gives the geographic polar coordinates for theparking
orbit phase of flight.
Table B-V gives the earth-fixed launch site position,
velocity,and acceleration components for the second burn phase of
theflight.
Table B-VI gives the launch vehicle navigation
position,velocity, and acceleration components for the second
burnphase of flight.
Table B-VII gives the geographic polar coordinates for thesecond
burn phase of flight.
B-IPRECEDINGPAGE BLANK NOT RLMED
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