P3D Launch Sequence Study (Part I)
Started: September 1, 1996 
Last Update: December 5, 1996
Viktor Kudielka (ÖVSV P3D Mission Analysis
Project)
Introduction
This document is intended as a base for discussion of alternative
launch sequences of P3D.
Start Data
 Start date: Ariane flight AR502, mid April 1997
 Launch window/actual start time: Ariane Standard Launch Window,
first perigee at 23:40 UT (+/ 00:40)
 GTO data:
 mean motion: 2.243458 orbits/day
 eccentricity: .7160
 inclination: 7.0 degrees
 argument of perigee: 178.0 degrees
 longitude of ascending node(RAAN): depending on start date and time, 200
degrees assumed
 Satellite Data:
 dry mass: 200 kg nominal, 250 kg actual ??
 start mass: 400 kg nominal, 500 kg actual ??
 arc jet propellant(NH3): 52 kg max., ?? kg actual
 bipropellant(MNH+N2O4): 220 kg max., ??? kg actual
 arc jet velocity: 4750 m/s
 arc jet mass flow: 25 10^6 kg/sec
 400 N motor velocity: 3000 m/s
 bipropellant mass flow: .1333 kg/sec
Nominal DeltaV
 Assumptions:
 dry mass: 200 kg
 start mass: 400 kg
 arcjet propellant: 50 kg
 bipropellant: 150 kg
 arc jet velocity: 4750 m/s
 400 N motor velocity: 3000 m/s
 Efficiency: .9
 Arcjet first: 4750 .9 ln(400/350) + 3000 .9 ln(350/200) = 571 + 1511 =
2082 m/s
 Biprop first: 3000 .9 ln(400/250) + 4750 .9 ln(250/200) = 1269 + 954 =
2223 m/s
 1/2 arcjet, 1 biprop, 1/2 arcjet: 4750 .9 ln(400/375) +
3000 .9 ln(375/225) + 4750 .9 ln(225/200) = 276 + 1379 + 503 = 2158 m/s
Scenario A
Motto: ``Gut Ding braucht Weile'' ==
``Rome wasn't built in a day''
This scenario represents a first attempt to design a proper sequence of
orbital manoeuvers for achieving a satellite lifetime of 20 years and longer.
The major challenge is to properly use the two very different propulsion
systems for achieving this goal.
First Drift Phase
Without any major manoeuver (i.e. change of inclination)
the perigee of the initial GTO will drift from its initial value of
178° through 180° and further on to 360°, with a rate
of about 0.77°/day.
We want to arrive at an orbit with a 16 hour period, an inclination of
60°(+/3° depending on the
then current longitude of the ascending node (RAAN))
and an argument of perigee (ArgP) of about 315°(see
``Drifting P3D Orbits: Perigee at 225° or 315°?'').
A major inclination change can be done with a minimum of deltaV only at
apogee, that is,
when the perigee is near 0° or 180°, and the orbital period
as well as
the eccentricity are as high as possible. Since an ArgP of 180° will
be reached already within a few days after start, there will be not enough
time to do orbit and attitude determination, checking all
mechanical and electronic systems, adjusting attitude and
spinning up the satellite. Consequently the inclination change has to be
done near an ArgP of 0°/360°
The final goal of ArgP=315° can be reached now faster,
although with a higher total deltaV, than from an ArgP of 180°.
Until ArgP=360° is reached, the orbital period
can be increased in a stepwise fashion with the arcjet. But with a major
restriction. The sun angle of the satellite (with the solar panels still
in the initial position) must be low enough for recharging the batteries.
The example presented in this chapter relies on the following assumption:
 A sun angle (with panels folded to the satellite frame)
of less than 45° is sufficient to recharge the batteries
during one orbit for an one hour burn of the arcjet (.85 kWh) at perigee.
The following example assumes a start date of
April 21, 1997 and a GTO RAAN = 200°. In figure
A.1.1A the usual four Kepler elements
(inclination, eccentricity, argument of perigee, RAAN) are shown,
figure A.1.1B includes diagrams of the sun angle,
the orbital period and the current mass.
In this example the initial
conditions are such, that the orbital period can be increased up to the
target of 16 hours only in two intervals, due to the unfavourable
sun angle between day 70 and 180 after start.
The first firing of the arcjet is planned for orbit #51, assuming
all initial testing, spinning up and adjusting the attitude has been
done successfully. Before reaching the 16 hour orbital period, the last
one or two burns of the arcjet have to be very carefully timed, in order
to achieve the exact orbital period. Otherwise a correction can be done
later also.
The deltaV requirement is around 191 m/s, with the crude
assumption of a .9 efficiency for the geometric misalignment at perigee
for one hour burns.
Major Inclination Change
The major inclination change will take place near ArgP=360°.
The example shows one initial small inclination change for
calibration purposes, four inclination changes with equal deltaV, and
one final adjustment to reach an inclination of 70°.
All these motor burns are assumed to take place at apogee, with the
attitude such that the total velocity is not changed and the
geometry of the orbit (semimajor axis and eccentricity) remains the same.
The assumption is here, that orbit determination, attitude determination
and attitude adjustment can be done within two orbital periods (two
perigee passes). This is a very tight schedule and has to be verified.
Orbit 
ArgP 
sma 
ecc 
inc 
HeightPer 
HeightApo 
VPer 
VApo 
deltaV 
# 
deg 
km 

deg 
km 
km 
m/s 
m/s 
m/s 
550 
359.09 
32252 
0.7826 
07.64 
632 
51116 
10068 
1228 
000 
551 
359.60 
32252 
0.7827 
10.65 
632 
51116 
10068 
1228 
064 
553 
000.15 
32252 
0.7826 
23.66 
633 
51115 
10067 
1228 
278 
555 
000.44 
32252 
0.7825 
36.67 
637 
51111 
10064 
1228 
278 
557 
000.59 
32252 
0.7823 
49.67 
643 
51105 
10059 
1229 
278 
559 
000.62 
32252 
0.7821 
62.65 
650 
51098 
10054 
1229 
278 
561 
000.58 
32252 
0.7820 
70.02 
654 
51094 
10050 
1230 
159 
Total deltaV = 1335 m/s
For comparison changing inclination by 63° would
need a single impulse of 1284 m/s, without changing height of perigee
but with the risk of a fatal accident when the burn is interrupted.
Second Drift Phase
After reaching i=70°, ArgP will drift between 0.04 and 0.05°/day,
depending on the actual value of RAAN. For the majority of cases the
eccentricity will decrease continuously  with halfyear periodic
variations  until the target of ArgP=315° is reached. But for a certain
range of RAAN the eccentricity will increase first before decreasing
again. In the worst case encountered in simulations so far,
the height of Perigee will drop from initially 500 km to
less than 100 km before increasing again. This is certainly unacceptable.
In case a similar situation will be caused by the start date and time,
a higher perigee has to be achieved at the end of the inclination change.
Inclination will change during this second drift phase between +4.5° and
1.0°, depending on the initial RAAN.
In our example the satellite will drift until an ArgP of 320°
is reached at orbit #1915. The inclination has increased to nearly 74°.
Final Inclination Change
This inclination change (assumed to be done with the arcjet)
is even more dependent on the RAAN than the
previous phases. The actual necessary change in inclination might be
between 6° and 17°. Due to the ArgP around 315°, the
required deltaV is
higher than for similar inclination changes at ArgP=0° or 180°.
Simulation of other cases show, that we have to consider
the major and the final
inclination change, including the second drift phase, as a whole.
When the final inclination change would be too high, the major
inclination change has to be reduced. The second drift phase would then
last longer. Another possibility is still, to increase the orbital period
beyond 16 hours for the inclination changes. Also the ArgP at the beginning
of the final inclination change
can be properly chosen for an optimal final drift phase.
The major problem with this second inclination change is the mechanical
configuration.
After the major inclination change the satellite will be despun
and the solar panels will be unfolded.
The center of gravity will no longer be
on the central axis aligned with the two motors. Some strategy, a
combination of short arcjet burns together with
proper actions of the momentum wheels at the descending node
and unloading the momentum wheels by magnetic torquing around perigee,
has to be developed, considering also the power budget.
The considerations which led to the proposed ``final'' orbit are documented in
``Drifting P3D Orbits: Perigee at 225° or 315°?'',
which is the English version of an article which appeared in
AMSATDL Journal, Vol.21, No.4, pp. 3340, Dec. 1994.
A slight modification of the proposal
might reduce the deltaV requirements. The final
inclination change could be done already around 325° or 320°
and the inclination
adjusted such that the ArgP drifts within a range from 330° and
300°. Examples for four different values of RAAN are shown in figures
A.5.1 (RAAN = 0°),
A.5.2 (RAAN = 90°),
A.5.3 (RAAN = 180°), and
A.5.4 (RAAN = 270°), with an assumed
begin date of August 2000.
From these examples it is evident, that the "optimal" inclination for
the final drift phase should be reached with an accuracy of .1 °
or .2°.
In our specific example we start at an ArgP of 320° (orbit #1915)
and assume half hour burns of the arcjet at the descending node
every orbit until orbit #2955, when we reach an inclination of 61°,
a value chosen from different simulations for the begin of
the final drift phase. The deltaV required for this final inclination change
is 477 m/s.
We can show now diagrams for the whole period of propulsive action.
In figure A.1.2A the four Kepler elements
(inclination, eccentricity, argument of perigee, RAAN) are shown,
figure A.1.2B includes diagrams of the sun angle,
the orbital period, the current mass, and an expanded view of the
ArgP at the major inclination change.
Figure A.1.2C shows the height of perigee.
Final Drift Phase
The final drift phase is shown in figures
A.1.3A and A.1.3B.
We can expect an ArgP between 320° and 300° for nearly twenty
years, and afterwards the ArgP will move to 270°, at least for stations in
the northern hemisphere quite acceptable. And, since the height of perigee
is increasing from 3000 km to over 14000 km, stations in the the southern
hemisphere are also served.
Summary  Scenario A
 Start date April 21, 1997
 GTO RAAN = 200°
 Increasing orbital period to 16 hours (arcjet, deltaV = 191 m/s)
 Major inclination change to 70° around ArgP = 360°
(400N motor, deltaV = 1335 m/s)
 Final inclination change to 61° around ArgP = 320°
(arcjet, deltaV = 477 m/s)
 Total deltaV = 2003 m/s
Scenario B
This scenario represents an attempt to reach the final drift phase much
faster than with the approach of scenario A. The intent is to have a similar
initial drift phase but only until an ArgP of around 315°.
During this drift phase the orbital period will be increased stepwise
to 16 hours. Then follows immediately the major inclination change at
the descending node to the proper inclination for the final drift phase.
This inclination change is, in terms of deltaV, much more expensive than
at apogee. This will be the price for an earlier threeaxisstabilised
operation.
Initial Drift Phase
A start date of April 21, 1997 is assumed, as in scenario A. Since the
major inclination change will take place already at ArgP=315° and
not at 360°, the increase of the orbital period has to be started
earlier (orbit #25), leaving only about ten days for initial testing and
spinning up the satellite. The deltaV requirement for the initial drift
phase is identical to that of scenario A, 191 m/s.
Figures
B.1.1A and B.1.1B
show the four Kepler elements
(inclination, eccentricity, argument of perigee, RAAN)
and sun angle, orbital period, and satellite mass for the initial drift phase.
Major Inclination Change
With orbit #429, on day 232, an ArgP of 315° is reached and the
inclination change can begin. With three inclination changes of 3°,
28°, and 22°, which will need deltaV's of
118, 1127,and 938 m/s respectively, an inclination of 60° can be
reached.
Final Drift Phase
The final drift phase is shown in figures
B.1.3A and B.1.3B.
Although the initial inclination for the final drift phase is most probably
not yet "optimal", the overall trend can be seen. ArgP will increase for
about three years and then decrease continuously, passing through 270°
 after 14 years 
and finally through 180°. The apogee will remain over the
northern hemisphere for thirty years. The height of perigee will vary
between 2000 and 12000 km.
Summary  Scenario B
 Start date April 21, 1997
 GTO RAAN = 200°
 Increasing orbital period to 16 hours (arcjet, deltaV = 191 m/s)
 Major inclination change to 60° around ArgP = 315°
(400N motor, deltaV = 2183 m/s)
 Total deltaV = 2374 m/s
Although the total deltaV of this example is beyond the assumed capabilities
and also the balance of the two motors/propellants is not achieved, this
example will be a base for further refinements.
Scenario C
This scenario is intended to investigate possibilities to reduce
the deltaV requirements of scenario B by moving the inclination change
towards the apogee, to ArgP = 330°.
This causes some deviation from the initially assumed target range for the ArgP
of 315° +/15°.
Initial Drift Phase
The initial drift phase is similar to that one of scenario B. Only
the start of the orbit period changes can be delayed to orbit #45 (day 21).
Major Inclination Change
The major inclination change is done here in five steps like scenario A,
compared to the three steps in scenario B. The direction of the impulses
is assumed to have an alongtrack and an outofplane component only.
Since the inclination change does not occur at 0° or180°, we
get changes in eccentricity also.
Orbit 
ArgP 
sma 
ecc 
inc 
HeightPer 
HeightApo 
VPer 
VApo 
deltaV 
# 
deg 
km 

deg 
km 
km 
m/s 
m/s 
m/s 
459 
330.13 
32252 
0.7847 
7.108 
565 
51182 
10122 
1221 
0 
460 
330.35 
32252 
0.7844 
10.11 
577 
51170 
10113 
1222 
95 
462 
330.22 
32252 
0.7846 
24.83 
891 
50856 
9864 
1253 
465 
464 
330.03 
32252 
0.7846 
39.56 
1214 
50534 
9625 
1284 
471 
466 
329.7 
32252 
0.7543 
54.3 
1545 
50202 
9394 
1316 
477 
468 
329.74 
32252 
0.7531 
59.08 
1584 
50164 
9368 
1319 
155 
Total deltaV = 1663 m/s
Final Drift Phase
The final drift phase is shown in figures
C.1.3A and C.1.3B.
Due to the slightly different initial inclination compared to scenario B
we get a drift of ArgP first to about 345° and then back to 270°
after about 25 years.
Summary  Scenario C
 Start date April 21, 1997
 GTO RAAN = 200°
 Increasing orbital period to 16 hours (arcjet, deltaV = 191 m/s)
 Major inclination change to 59° around ArgP = 330°
(400N motor, deltaV = 1663 m/s)
 Grand Total deltaV = 1854 m/s
Scenario D
In scenarios B and C the inclination changes have been done by assuming
alongtrack and perpendiculartoorbit velocity changes only. This causes
not only changes in inclination, but also minor changes in the other
orbital elements, notably in eccentricity. To preserve the precise
orbital configuration and change inclination only, also a small radial
velocity change is necessary. Scenarion D implements such a more
sophisticated manoeuver. The constant height of perigee (500 km) will improve
the magnetic torquing manoeuvers for the neccessary attitude changes.
The major inclination change takes place at ArgP = 320°. This
requires an earlier start of the orbit period changes and also an
increased deltaV, compared to scenario C. The advantage is an earlier
threeaxis stabilised operation.
Initial Drift Phase
Orbit period changes start with orbit #15 (day 8).
Major Inclination Change
Orbit 
ArgP 
sma 
ecc 
inc 
HeightPer 
HeightApo 
VPer 
VApo 
deltaV 
# 
deg 
km 

deg 
km 
km 
m/s 
m/s 
m/s 
428 
320.12 
32248 
0.7855 
6.991 
539 
51201 
10144 
1219 
0 
429 
320.49 
32248 
0.7855 
10.00 
540 
51199 
10142 
1219 
117 
431 
321.15 
32248 
0.7853 
25.02 
545 
51195 
10139 
1219 
576 
433 
321.64 
32248 
0.7851 
40.03 
550 
51189 
10134 
1220 
570 
435 
321.93 
32248 
0.7850 
55.03 
555 
51185 
10130 
1220 
566 
437 
322.02 
32248 
0.7849 
59.03 
558 
51181 
10128 
1220 
151 
Total deltaV = 1980 m/s
Final Drift Phase
The final drift phase is shown in figures
D.1.3A and D.1.3B.
The apogee remains over the Northern hemisphere for more than thirty years.
Summary  Scenario D
 Start date April 21, 1997
 GTO RAAN = 200°
 Increasing orbital period to 16 hours (arcjet, deltaV = 191 m/s)
 Major inclination change to 59° around ArgP = 320°
(400N motor, deltaV = 1980 m/s)
 Grand Total deltaV = 2171 m/s
Scenario E
Scenario E shows the reduction of total deltaV by an increased orbital
period for the inclination change. The drawback is a longer time span for
readjusting the orbital period to 16 hours.
Initial Drift Phase
Orbit period changes start with orbit #15 (day 8). 1.5 hour burns of
the arcjet at each perigee has been assumed. With such an strategy
the orbital period can be increased to 22 hours before reaching an
ArgP of 325°. Figures
E.1.1A and E.1.1B
show this drift phase. A correction for the efficiency for the longer
arcjet burns (1.5 vs. 1.0 hours) has not yet been applied.
Major Inclination Change
The major inclination change has been moved slightly to 325° in order to
allow the arcjet to achieve the orbital period of 22 hours.
Orbit 
ArgP 
sma 
ecc 
inc 
HeightPer 
HeightApo 
VPer 
VApo 
deltaV 
# 
deg 
km 

deg 
km 
km 
m/s 
m/s 
m/s 
435 
325.20 
39888 
0.8257 
7.358 
576 
66444 
10229 
977 
0 
436 
325.51 
39888 
0.8255 
10.36 
582 
66438 
10225 
977 
94 
438 
326.10 
39888 
0.8254 
25.38 
587 
66433 
10221 
978 
461 
440 
326.56 
39888 
0.8254 
40.39 
587 
66433 
10221 
978 
455 
442 
326.86 
39888 
0.8254 
55.43 
587 
66433 
10221 
978 
452 
444 
326.97 
39888 
0.8252 
59.00 
594 
66425 
10215 
978 
106 
Total deltaV = 1568 m/s
Adjustment of orbital period
Figures
E.1.2A and E.1.2B
show the whole powered flight period.
Final Drift Phase
The final drift phase is shown in figures
E.1.3A and E.1.3B.
The apogee remains over the Northern hemisphere also in this scenario
for more than thirty years.
Summary  Scenario E
 Start date April 21, 1997
 GTO RAAN = 200°
 Increasing orbital period to 22 hours (arcjet, deltaV = 307 m/s)
 Major inclination change to 59° around ArgP = 325°
(400N motor, deltaV = 1568 m/s)
 Decreasing orbital period to 16 hours (arcjet, deltaV = 118 m/s)
 Grand Total deltaV = 1993 m/s
Dr. Viktor Kudielka, OE1VKW
viktor.kudielka@ieee.org