Nozomi in perspective, Revisiting the causes of failure Options

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page 40

fig. I-3-1

New orbital plan for Nozomi

(here, I will have to explain, rather than translate as follows)

red: Mars
green: Earth
purple: Nozomi

(on this Earth-Mars system main character strings clockwise are)

1. 1st earth swingby: Dec 2002
2. leaving Earth gravitational field: Mars Dec 1998
3. insertion into Mars orbit: end 2003 to early 2004
4. 2nd earth swingby: June 2003

(on this page there is another Earth-Mars system in a square. The Monn is in yellows and Mars is depicted in red, with a short caption near Mars which says "into Mars orbit: Oct 1999)

end of page 40

page 41

fig I-3-2 Temp changes at temp measurement point(s?) by 1 bit communication

(Here, I have no idea as to what WANT is, but anyway)

Vertical axis is WANT temp and horizontal is the dates, from 23 July to 1 October. On the upper lef a box contains 5 character strings from top to bottom. The last one at bottom says "fitting of WANT-1".

Similarly, there are 5 character strings all pointing to the slanted line on the graph and the last one at bottom of this group of 5 character strings says "fitting of WANT-1"

The cpation of the arrow pointing vertically upward to the slanted line says "melting point under hydrazine tank pressure (2.2 deg C)"

There is another character string qualifying the same slanted line and this says "temp. increase rate per day of 0.32 deg C"

end of page 41

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page 42

(main feature of this page is a figure and a table)

Fig. II-1-1 Nozomi propulsion system outline

Most of this figure is in English. There are 5 oblong squares in dark blue. 3 of them to the left and 2 of them to the right.

Left ones from top to bottom are:

Pusher gas tank He
Fuel tank Hydrazine
Auxilliary engine RCS (mono propellant)

Right side one from top to bottm are:

NTO tank
Main engine (dual propellant) and the caption for this says "To be used for insertion into Mars transfer orbit"

In addition, there are 5 squares in light blue: They indicate the status of the valves. In this diagram all of these 5 squares carry "OPEN".

In further addition there are one red oblong square and the characters in there say: LV2: CLOSE->OPEN->CLOSE and one pale blue oblong square and the characters in there say: LV5,6: CLOSE->OPEN->CLOSE

There are two circles in this figure and one near the top and the caption for that says "Valve which developped mulfunction" and the other one near the bottom is OME.

There is a note also in the figure and it says "Valve status is all during TMI"

The qualifiers in the figure are as follows.

HLV: high pressure gas system latching valve
LV1-2, LVm: low pressure gas system latching valve
LV3-6: liquid system latching valve
RG: regulator
CV1-2: check valve
F1-3: filter
P1-4: pressure sensor

FDV1-5: inlet/outlet valve
TP1-5: test port
A&T1-4, R1&2: RCS thruster
OME: OME
FTNK-A&B: hydrazine tank
OTNK-A&B: NTO tank
GTNK: He tank

Table II-1-1 Main specs for propulsion system

Here, I will translate column by column, from left to right and from top to bottom. Sometimes, I will add row numbers so that we know where exactly we are down the columns.

Leftmost column and from top to bottom:

pressure
thruster specific impulse
thruster specific impulse
torque (9 and 10 are row numbers)
gas container or gas reservoir?
fuel tank (x2)
oxidiser tank (x2)
onborad propellant amount (20 and 21 Ditto)
effective propellant amount
propulsion system DRY mass
propulsion system WET mass

Now, second column from top to bottom:

initial pressure in the primary pressure system
initial pressure in the secondary pressure system
axial (x4)
radial (x2)
tangential (x4)
OME (x1)
RCS
OME

3rd column is as follows:

precession
spin
inner volume
MDP
destruction safety rate
inner volume
MDP
destruction safety rate
fuel (hydrazine)
oxidiser (NTO)
for RCS
for OME

the next column is nominal specs and the contents are from top to bottom (and I omit those in English):

2.3N per base
2.3N per base
2.3N per base

27.8 litter

98 litter per tank

40 litter per tank

and the last column is meant for notes and the contents are:

(=24.5 MPa)
(=1.37 MPa)

at time of pulse is given
lower or lowest limit of somekind of difference
R=1m at time of two in action
R=1m at time of two in action
CFRP/titanium alloy sphere
tatanium alloy tear drop shaped (=2.01 MPa)
titanium alloy tear drop shaped

end of page 42

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page 42

fig. II-1-2 Status at the time of failure in December 1999 (time is UTC)

(Here, most of the time line is in English. I simply suppllement those with captions in Japanese)

07:17 Start of attitude change (sun angle 60 degrees)

07:33 attitude control completed (sun angle 120 degrees)

07:41 SPIN-Up (->25 RPM) time taken is 1 minute

08:06:20 to 08:13:04 OME fired

08:32 SPIN-Down (->10 RPM) time taken is 1 minute

08:40 Start of attitude change (sun angle 120 degrees)

09:00 Attitude control completed (sun angle 43 degrees)

(character string inside this large box says):

all monitored values and status were normal except that the monitored value of NTO upstream pressure started declining as the firing started. (confirmed by reproduced TLM)

(the 1st red arrow pointing at 12:00 says): News flash from JPL that there was an insufficiency (shortfall of delta V) of about 100 m/s against the planned value of 423.22 m/s

(2nd red arrow just past 14:00 says): similar insufficiency confirmed by onboard TLM integration

end of page 42

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page 44

fig. II-1-3 Telemetry data during visible period after insertion into Mars transfer orbit (TMI)

(here, the only thing that needs translation is the caption inside a Mexican hat like area and it says):

oxidiser tank pressure P4 is low

end of page 44

page 45

fig. II-1-4 Nozomi status at time of LV2 open command (part 1)

(here, there are 9 squares in yellow and they are, from top to bottom):

P1: pressure of gas storage
P2: regulator exit pressure
P3: fuel tank pressure
P4: oxidiser tank pressure

injector temp.
OME firing duration (or time?)
delta V
LV2 status
LV2 open

(There are 3 blocks in pink and they are):

(referring to P2): transient decrease in regulator pressure due to rapid supply of He gas to oxidiser tank which was judged to be lower than normal

(referring to P4): pressure rise as LV2 is opened -> He gas is being supplied

(last small square): pressure drop is judged to be due to imperfect opening of LV2

(there are 2 more small squares in pale blue and they are):

(top square): Open
(bottom square): Close

end of page 45

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page 46

fig. II-1-5 Nozomi status at time of LV2 open command (part 2)

(caption on the left says): Shock due to LV2 opening

(caption on the right says): Vibration due to He gas flow

end of page 46

page 47

fig. II-1-6 Status of OME firing at time of insertion into Mars transfer orbit (TMI)

(here, there are 11 pale yellows areas with captions and I will go from top to bottom, then bottm to right, in this order)

P1: pressure of storage tank
P2: pressure at regulator exit
P3: fuel tank pressure
P4: oxidiser tank pressure

injector temp.
OME firing time (or duration/)
delta V
status of LV2
LV2 open (this is the bottom and I will move right from here)

OME firng start
OME firing end/LV2 close

(now lines in red)

(dotted lines in red next to P4 says): originally planned regulator level
(red solid line next to delta V says): target delta V (423.33m/s)

(there are cations in 3 pink areas. they are, from top to bottom)

Not regulated like P2, P3 -> insufficient supply of He gas

insufficient amount of delta V

status changes in response to OPEN/CLOSE command

(what remains are 2 pale blue areas and they are from top to bottom)

OPEN (top)
CLOSE (bottom)

end of page 47

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page 48

fig. II-1-7 Changes in pressure and acceleration at time of TMI

(here, left vertical axis is pressure and the right handside vertical axis is average acceleration. The horizontal axis is OME firing time (sec))

(on the graph itself, the brown curve is acceleration and inside the square the brown dot is also acceleration)

end of page 48

page 49

fig. II-1-8 Comparison of regulated pressure and propulsion

(here, the bottom line inside the square is predicted propulsion)

end of page 49

page 50

fig. II-1-9 Fuel system pressure trend

(here, inside the square we have):

P2: regulator regulated pressure
P3: fuel tank pressure
P4: oxidiser tank pressure
Pc: 500N thruster burn pressure

end of page 50

page 51

fig. II-1-10 Oxidiser system pressure trend

(captions inside the square are exactly the same as on page 50

end of page 51

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[pandaneko]

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page 52

Table II-2-1 Risks considered at time of LV2 selection

(here, I consider this table essentially to consist of 6 columns and 6 rows for ease of translation and that means tacit understanding that some of the table elements have more than one rows or columns)

(top left corner contains a caption): "Options available at time of selection"
(top right corner contains a caption): "Notes"

(top row with column numbers 3,4,5 contanis a caption): "Risks envisaged"

(hereafter I will use regular R and C numbers)

R2C3: mixture of hydrazine and NTO
R2C4: LV2 cannot be opened (valve reliability issue)
R2C5: LV2 open status cannot be monitored

R3C2: Extent of risk influence
R3C3: catastrophic
R3C4: serious
R3C5: local or localised

R4,5C1: LV2 is used
R6C1: LV2 is not used

(against these headers translated as above there are symbolic entries with either triangle, double circle, single circle and I will qualify these symbols after translating the rest of this table. Just to make sure we are using the same esignation there are triangles at R5C5 and R6C3)

R6C6: Valve is not used at all
R5C6: Valve with track records
R4C6: Valve modified to our spec

R4C2: Instruction for open/close is given
R5C2: Instruction for open/close is not given

(symbols are as follows)

◎： unthinkable from the viewpoint of principles
○： small risk (acceptable to the mission)
△： medium risk ( either acceptable to the mission or detailed assessment required)
×： too risky (unacceptable to the mission)

※Result of risk assessment

For the following reasons it was decided that we will carry LV2 and also add LVDT to go with LV2

・Vapour mixture of hydrazine and NTO

When vapour mixture takes place it will mean a very serious risk to the mission. If LV2 is used it means dual safety precaution given the role of CV2 and the risk is deemed small. However, safety precaution with CV2 only is medium in risk taking.


・LV2 cannot be opened

If LV2 is found not to open prior to TMI it will mean a very serious risk to the mission. However, by carrying out a prior checkup of LV2 the possibility of valve unopening can be reduced to a minimum, hence small risk.


・LV2 open/close status cannnot be monitored

Being unable to monitor LV2 status is not that serious and is localised. However, if we consider the burden on operators and human errors due to this burden we thought that having a monitor will reduce the risk to minimum. No monitor, then risk is deemed medimum.

end of page 52

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page 53

fig. II-2-1 Schematic of LV2 gas system latching valve

(there are 4 brown squares and these are colis)

(light blue areas are ferrite stainless steel)

(grey area in the middle is Inner piece or Inner member (presumably movable component?, P))

(to the left of above is the plug)

(incoming yellow arrow says: from He tank)

(outgoing arrow says: to oxidiser tank)

(what is seen on the extreme right is the LVDT)

Note: There is a guide with LV2 so that the inner piece is accurately centred.

end of page 53

page 54

table II-2-2 Ground test history of LV2 valve

(this is a table and I consider it to be made of 4 major columns which subdivide)


C1R1: inspection (or test)/pressurised (or loaded?, or even subjected to test?,P) items environment
C1R2: capability confirmation test
C1R3: vibration
C1R4: mechanical shock
C1R5: thermal environment
C1R6: life cycle
C1R7: oxidiser environment 1
C1R8: oxidiser environment 2

C2R1: design quality confirmation test

C21R2 (1st subcolumn of C2R2 is meant): items carried out by valve manufacturer (QT)
C22R2 (2nd subcolumn of C2R2 is meant): items carried out domestically

C2R3C1 (C1 is a subcolumn within C2, counted from left to right): function
C2R3C2: mechanical environment
C2R3C3: thermal
C2R3C4: life (or durability)
C2R3C5: immersion test

C3R1: flight model manufacturing approapriateness confirmation test

C31R2 (1st subcolumn in the main column C3 is meant): AT
C32R2: subsystem (domestic)
C33R2: at system level (domestic)

C3R3C1: items carried out (by valve manufacturer)
C3R3C2: module test or modular test
C3R3C3: subsystem test
C3R3C4: test immediately after incorporation into the system
C3R3C5: thermal test
C3R3C6: mechanical environment
C3R3C7: thermal vacuum
C3R3C8: test immediately upon arrival at launch site

C4R1: Note

C4R4: double circle is a detailed test and a single circle is a simplified test

C4R9: valve on its own (exposed 16 hours to vapour)

C4R10: valve on its own (left in running NTO for 5 hours)

end of page 54

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page 55

Table II-2-3 Number of cycles of valve open/close action

(this table, I consider it to be consisting of 6 rows)

(top row headers are from left to right)

category: status: number of cycles, in this order

C1R2: exposure to oxidiser vapour
C1R3: immersion in oxidiser liquid

(status members from top to bottom are):

(1): before exposure
(2): immediately after exposure (0.3 MPa)
(3): 16.5 hours after exposure
(4): vapour pressure reduced to 1 atmosphere
(5): after gas is purged

(6) during immersion in running liquid (differential pressure of 0.35 MPa and 5 hours continuous)
(7): after liquid is purged
(8): after cleaning and drying

end of page 55

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Please note that in what follows and in all previous translations I am always translating non alphanumeric entries only.

page 56

Table II-2-4 LV2 action history (action refers to opening and closing of the valve, P)

(before translating elements of this table I will first translate what are seen below the table. They are):

Note: Circle: valve opening/closing by autonomous commands (note 1 (actually, I cannot find this Note a anywhere on this page, P))

Square: valve is opened/closed by a command sent manually in real time

*: valve mulfunctioning during TMI was the 42nd (6th after launch) after delivery by manufacturer and the valve function had been all normal before it

*: automated command function relating to OME firing had been confirmed by ground tests. it was also verified during delta V5 in orbit.

(now, table itself and I consider this table to be consisting of 5 majot columns and 4 major rows with subdivisions)

(first, headers in the leftmost column)

C1R1: Action timing

C1R2: ground tests

C1R3: launch

C1R4: after launch

(next, headers in the top row, from left to right)

C2R1: Number of actions

C2R1 divides into 2 subcolumns and the header entry in the left subcolumn is "close->open" and the header in the right subcolumn is "open->close"

C3R1: Operation status

Here again, this divides into 2 subcolumns. Left subcolumn says "Visibility" and the right subcolumn says "Automation".

C4R1: Judgement

C5R1: Notes

(These are the headers and before translating non alphanumeric entries I will spell out some of the dates entries below. Dates in Japanese are reveresd in order. They are YEAR.MONTH.DAY, in this order, and all in numbers. For example):

97.10.21-22 : 21 to 22 October (10th month), 1997
98.2.27-3.4: 27 February (2nd month) to 4 March (3rd month) 1998
98.12.10: 10 December (12th month) 1998

(now, translations)

C3R4 divides into 5 subrows and entries in the Visibility subcolumn from top to bottom are:

Visible
Visible
Visible
invisible (orange colour highlighted)
visible

Likewise Automation subcolumn entries from top to bottom are:

square
circle
square
circle (orange colour highlighted)
square

Entries in the judgement column (major column) C4 are all "normal" except the 2nd subrow from bottom which is "abnormal" and is orange colour highlighted.

There are 16 entries in succession in C5 from top to bottom minus one. They are:

R2: delivery inspection, domestic

R3: confirmation test after pipe welding

R4: air-tightness test 1, whole propulsion system

R5: air-tightness test 2, whole propulsion system

R6: function confirmation test

R7: overall test, propulsive function

R8: overall test, preperation for environment test

R9: overall test, environment test

R10: overall test, functional air-tightness confirmation test

R11: flight operation, air-tightness test

R12: flight operation, liquid injection and primary pressurising

R13: (launch)

R14: Delta V 1

R15: Delta V 5

R16: Delta V 8

R17: Delta V 9 (TMI) and this is orange colour highlighted.

end of page 56

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page 57

Table II-2-5 FTA for LV2 mulfunction

First of all, notations belows this table.

Cross: not possible
Triangle: small possibility
Single circle: medium possibility
Double circle: large possibility

Top row headers go like:

C1R1: suspected reason
C2R1: judgement
C3R1: reason for judgement
C4R1: operational judgement

Since C1 has subcolumns I will have to de descriptive in some cases.

C1R2: mulfunction with the monitoring device

C1 leftmost subcolumn R3 to R10: mulfunction in device area (best I can translate, I am afraid..., P)

C1 righthand subcolumn R3: mulfunction with the inner piece

C1 righthand subcolumn's left subcolumn R4 to R10: mulfunction in valving action

C1 righthand subcolumn's right subcolumn's rows (and there are many and I will hereafter use R numbers only, P)

above's R4: expansion due to incompatible plug materials

above's R5: bad sliding of the plug

above's R6: plug glitching into valve opening area

above's R7: plug misallignment

above's R8: glitching of (or by) foreign material

above's R9: clearance change at sliding setion due to valve temp. change

above's R10: temporary solidification due to crystal formation (such as nitric ammonia)

(hereafter entries become regular, P)

C3R2: monitor is healthy because open/close sensor indicated that the rod for sensor moved in the same direction as the inner piece in response to the open/close command.

C3R3: inner piece movement is considered to be normal because there was a stroke large enough to change the open/close status monitor and also latching had been secured.

C3R4: mulfunction due to expansion is not possible because of the metal jacket at the sealing section and the jacket itself is resistant to NTO.

C3R5: it is thought that because the valve and the plug are independent and are activated by a differential pressure the valve body surface got roughed up by fletching wear and led to corrosion in NTO environment.

C3R6: it is thought that the valve was slightly opened during TMI. However, in this mulfunction mode the slight opening of the valve is difficult to take place.

C3R7: this must be due to bad manufacturing, but the ground tests did not give any indication.

C3R8: this possibility is low because we used a finer filter than the minimum diametrical clearance.

C3R9: the valve had functioned properly in similar environment in flight.

C3R10: propellant was charged (or injected) after dryness confirmation. Also, this phenomenon should have shown up within a few days.

(now the last column, P)

C4R5: we will leave the valve LV2 in open state because we think that slidability will worsen as time goes by.

C4R6: we will leave the valve LV2 in open state because closing it may lead to the same mulfunction with a high possibility.

C4R7: we will leave the valve LV2 in open state because closing it may lead to the same mulfunction.

C4R8: repetition of mulfunction is thought to be low in possibility because it was accidental and also the foreign material must by now have been carried downstream.

C4R10: we will leave LV2 open as closing it may lead to repetition.

(outside the table there are 5 character strings giving the degree of suspicion as the candidate for causing mulfunction. These sit side by side to Rows 5, 6, 7, 8, and 10 and carry a numerical value of 1 to 5 respectively.)

end of page 57

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page 58

Table II-2-6 History of LV2 use

(this is a simple table and I just translate the contents in the easiest way as follows. Number of days is just approx.)

Valve remained closed for :

15 days before use as LV2 CLOSE before launch (delta V1) (why delta V at all before launch beats me, P)
42 days before use during delta V1 to delta V5
80 days before use during delta V5 to delta V8
40 days before use during delat V8 to delta V9 (TMI)

end of page 58

page 59

Fig. III-1-1 Nozomi power system schematic

With this schematic I will have to be very descriptive. It all starts from the leftmost square, which is the solar battery.

To the right immediately, and effectively it is a column containing mostly power units, from P1 to P15, say. I hope you can see numbers in this column and I hope they are numerics coded with a single digit. If not you may be looking at a mess.


However, between P2 and P3 there are two more squares. One is "Beacon mode" and the other below it is "Telemetry mode". Actually, there is another square further down between P4 and P5 and that says "Attitude control system and other instruments for observation".

Now, going back to P1 power is sent down to a switch called "Temp. control circuit" which controls the "Main prop. system heater" at the extreme up and right on the schematic.

There is another switch immdeiately below a long horizontal oblong square. This oblong square says "Telemetry Command Interface (TCI)". This second switch is meant to swtich between "Beacon mode" and "Telemetry mode".

There is another square below this switch which says "Transmitter 1" (and I do not find any other transmitters on the schematic, P) and this transmitter is connected to P3 and the switcher above.

Transmitter is also connected to the receiver below it. Both transmitter and receivcer are connected to the antenna on the right (extreme right) and the receiver is receiving power from P4.

The longish square at the bottom says "Data Handling Unit (DTU)" and it has a two way power connection with the telemetry command interface. DTU also connects to the command decoder which sits between the receiver and DHU.

In addition, trhere is another strange square floating below temp. control circuit and the telemetry command interface and it says "Short cicuiting failure" and I do not know why it is sitting there, P.

end of page 59

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page 60

Table III-1-2 Connections within Common Power Supply Interface (CI-PSU) and devices/instruments related to this power supply

(here again, I will have to be descriptive, but my taks is made a lot easier than the last page in that there is a fairly recognisable regular structure in the table. I am talking about squares seen on the table. And, if you agree with me about the rough structure):

C1R1: X-band transmitter power amplifier (XPA)

C1R2: (pointing to C1R1) X-band transmitter (TMX)

C1R3: various Heaters

C1R4: (pointing to C1R3 with a thick arrow in red) Heat Control Electronics (HCE)

(Here, repetition accepted and C and R reversed or exchanged)

R4C1 (same as C1R47)

R4C2: Open/Close status monitor

R4C3: Pressure monitor

R4C4: Power for ignition

R4C5: Rocketry measurment (INS-SA)

C3R1: Ultra stable transmitter (USA)

C3R2: Data Recorder (DR)

C3R3: Timer

C3R4: S-band transmitter

C3R5: Solar Proton Monitor (SPM)

(In addition, there are two more squares in the middle area and the one above the other is):

Telemetry Command Interface

and blue dotted line connection to;

X-band transmitter
S-band transmitter
and Beacon mode/Telemetry mode switching circuit enclosed within a square formed by dotted lines

(and the other below it is):

Common Interface Power Supply Unit (CI-PSU)

including all of the red line connections emanating from tis square

Note for the title of this page (additional) is:

Red solid lines are related to power and the blue dotted lines relate to signal switching system

end of page 60

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There was a mistake on page 60. C3R1 should have been Ultra Stable Oscillater and with an abbreviation USO

page 61


Table III-1-1 CI-PSU and a list of devices connected to it

(this is a regular table with C3R12 structure. Top row from left to right is Abbreviation::Full Name::Function etc)


CI-PSU: Common Instrument Power Supply Unit: To supply power to the following 10 devices with secondary voltage of +29V, +12V, -12V, +5V

TCI:: Telemetry Command Interface :: To act as a telemetry command interface to a number of common devices

HCE:: Heater Control Electronics:: Heater ＯＮ／ＯＦＦ control and temp. measurement (Heater power is supplied directly from the bus voltage)

DR:: Data Recorder:: To keep data to be sent out to the telemetry system

SPM:: Solar Proton Monitor:: To measure solar protons (usually from 1MeV to a few tens of MeV)


IG-PS:: IGniter Power Supply:: Condensor bank type power supply to provide power to pyros

INS-SA:: INStrument-SAtellite:: Sensor only used at launch, turned OFF thereafter

EPT-SA:: Electrical Programmable Time-Satellite:: Timer circuit, only used at launch and turned OFF thereafter

P-Mon:: Pressure Monitor:: Pressure monitor for propulsive system (imported item)

LVDT:: Linear Variable Differential Transformer:: Latching valve monitor for the propulsive system (imported item)

USO:: Ultra Stable Oscillator:: For radio science measurement (imported item)

end of page 61

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page 62

fig. III-1-3 Orbital position of Nozomi on the Sun-Earth fixed system

Here, at the centre is the Sun and just to its right is where we are. The only remaining character set on this figure in 2 O'clock position says "Nozomi orbit as seen from the Earth".

End of page 62

page 63

fig. III-1-4 Operational sequence during 24 to 25 April

Note: Netted area corresponds to operational time with Usuda station in Japan. (some 10km from my mountan cottage in central Japan highland!)

(I view this time line to be consisting of 2 columns, one black and the other in red)

(Looking at the black column from top to bottom, still following the times on themain time line):

22:15 MTX_RNG_B (TLM modulation OFF)

02:00 Observation mode change

03:00 Ditto

03:25 Ditto

07:35 TLM editing mode change

07:43 Earth persuit ENA (some kind of enabling activity?, P)

09:00 Earth persuit judgement permitted

10:10 Earth persuit DIS

10:20 TLM editimg mode change

17:37 Time specification CM: TMX_TLM_MOD_ON (TLM modulation)

17:57 Time specification CM: TLM editing mode change

18:32 TMX_TLM_MOD_ON (TLM modulation ON)

18:52 DR REC->STBY

(What follows from here is the column in red, sometimes corresponding to entries in black on the left and there are 5 entries)

1. from 22:15 UDSC LOS to 07:00 is the period in which the failure (or accident) is thought to have taken place.

2. at about 09:00 No action taken* estimated from the reception level on the ground

3. at around 17:00 No action taken

4. at around 18:00 Recption despite TLM modulation being OFF

5. (against 18:32 black entry) No action taken

end of page 63

P