“Good Practices” for long term orbit propagation and
associated criteria verification in the frame of the
French Space Act
Hubert.Fraysse@cnes.fr
Presentation to ISO – Berlin - May 24th 2011
Summary
1. French Space Act : disposal orbits relatively to region A and B
2. Good Practices : overview
3. Focus on Solar Activity
4. STELA software
Reference paper: Fraysse et al, « Long term orbit propagation techniques developed in
the frame of the French Space Act », 22nd ISSFD, 2011
2
CNES/DCT/SB/MS
French Space Act : disposal orbits


Technical methods are defined by CNES in the frame of the French Space
Act whose objective is to ensure that the technical risks associated with
space activities are properly mitigated
In line with IADC recommendations relative to regions A (LEO) & B (GEO)

Disposal orbits in the vicinity of these regions must not cross them within
100 years
 Disposal orbits that cross the LEO region must re-enter the atmosphere in
less than 25 years
CNES/DCT/SB/MS
Good Practices: summary

“Good Practices” definition (with ISO documents 27852 and 26872
as Guidelines) for LEO and GEO orbit types (on-going activity for
GTO type):
 To propagate disposal orbits up to 100 years
 To check the applicable criteria (25 years and 100 years rules)

“Minimum” Dynamical Models for each type of orbits
Perturbation
Earth’s gravity field
Solar and Lunar
gravity
Atmospheric drag
Solar Radiation
Pressure (SRP)
LEO orbits
GEO orbits
J2 to J4 zonal model*
Full 4x4 model
yes**
yes
yes
no
yes***
yes
* the effect on orbit eccentricity and ascending node of zonal terms up to J15 has to be considered when the inclination is
close to the critical inclination (63.4 deg). J22 considered in the semi-analytical theory.
** the luni-solar perturbation is significant for sun synchronous orbits or orbits with apogee altitude in the upper range of the
LEO region
*** the effect of SRP has to be considered for orbits that go through a SRP / ”J 2 secular effect” resonance (orbit inclination
about 40, 80, 110 and 125°, see back-up chart)
CNES/DCT/SB/MS
Good Practices: summary

Definition of computation parameters for the Solar Pressure and
2


Drag Forces

1
 d0  
Fa    A Cd Vr Vr
Fp  CR P0 A   u
d 




2
Area “A”: if attitude is unpredictable -> mean area (random tumbling mode)
Reflectivity coefficient  1.5 (ISO recommendation)
Atmospheric model: NRMLMSISE-00
Drag coefficient: reference law Cd = f(altitude)
 Key difficulty: solar activity
CNES/DCT/SB/MS
Focus on Solar activity : introduction

The result of a reentry duration computation strongly depends on
the solar activity hypothesis :
 Level (high, medium, low) of the next 3 or 4 solar cycles ~ 10 years
 End of mission date / solar cycle ~ 5 years

Problems:
 The level and the length of the next solar cycles are very uncertain
 The end of mission date may shift

Difficulty in a Space Act process :
An end of life orbit and strategy compliant at time “t” may not be compliant anymore
if the solar activity prediction changes, or the end of mission date shifts.

New approach : “constant equivalent solar activity”
6
CNES/DCT/SB/MS
Focus on Solar activity : principles

Following this approach the solar activity is designed such that :
 It is constant vs time :
The reentry duration computation no longer depends on the end of mission date and predictions
 Equivalent to future possible solar activities :
The equivalence is from a 25 years reentry point of view, with a Z% probability level
1 Space Object
1 End of life orbit
Equivalent constant
solar activity
Possible Future solar activities
t
F10.7
2
4
6
t
6
3
t
25 years lifetime
t
25 years lifetime in Z % of the cases
100%
Z%
0%
CNES/DCT/SB/MS
25 years
lifetime
Focus on Solar activity : algorithm
Algorithm to tune the constant equivalent solar activity (1/4)
The tuning of the constant equivalent solar activity has been made using solar activity data (F10.7
and Ap) from the last decades and through a statistical approach
Random Solar activity :
 Data : 5 measured solar cycles (historical F10.7 and
Ap data as in ISO approach #1)

54 = 625 possibilities of four-cycles sequences (2 1
1 5 or 3 5 1 4 or 2 4 5 3 or 4 4 4 4 …)

Random realization of the initial date within the first
cycle, twice for each sequence.
 n = 1250 random predictions of solar activity
These solar activities are considered as representative samples of the possible future
solar activity.
CNES/DCT/SB/MS
Focus on Solar activity : algorithm
Algorithm to tune the constant equivalent solar activity (2/4)


For an initial orbit and a ballistic coefficient value
Run of the n reentry duration computations using the n random solar activity samples
 Lifetime cumulative distribution function

Iteration on the initial orbit until the orbit lifetime is 25 years with a targeted Z% probability
level
CNES/DCT/SB/MS
Focus on Solar activity : algorithm
Algorithm to tune the constant equivalent solar activity (3/4)

Iterations : change of the perigee of the orbit, fixed apogee
Convergence when: 25 years  Z%
(Z% = 50% in this case)

Computation of the reentry duration of the last orbit by using a constant solar activity and
iteration on its value so that the reentry duration is 25 years
N.B. : tuning of F10.7
Ap = 15 (arbitrary
choice)
CNES/DCT/SB/MS
Focus on Solar activity : algorithm
Algorithm to tune the constant equivalent solar activity (4/4)

The F10.7 constant (vs time) value may depend on initial conditions (orbit and
ballistic coef)
1. Scan initial orbits (within LEO region) and ballistic coefficients and run the whole
algorithm for each initial state (orbit and ballistic coefficient)
2. Analyze the sensitivity to these parameters
3. Fit a reference law on these simulation results
Constant Flux
Constant Flux
148,00
148,00
Cd = 2.2
146,00
146,00
S/m 0.0104
144,00
142,00
S/m 0.03
142,00
140,00
S/m 0.02
138,00
S/m 0.05
136,00
S/m 0.015
134,00
dga_1100
132,00
dga_797
130,00
128,00
1100 km
800 km
140,00
1100 km
138,00
800 km
1000 km
136,00
S/m 0.001
134,00
S/m 0.0104
132,00
700 km
130,00
126,00
500
700
900
1100
1300
ha (km)

F(sfu)
F(sfu)
144,00
1500
1700
1900
2100
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
Cx*S/m
The algorithm works for any probability level of reentry within 25
years: 50% has been chosen in the frame of the French Space law
CNES/DCT/SB/MS
Focus on Solar activity : result
Finally the “constant equivalent solar activity” defined for LEO type orbits :

does not depend on inclination or local time of the RAAN of the initial orbit

depends on the apogee altitude of the initial orbit (log-function, R² > 99%)

depends on the ballistic coefficient of the space object (log-function, R² > 99%)
AP  15
Z%=50% law
CNES/DCT/SB/MS
F10.7  201 3.25 ln(
A.Cd
)  7 ln(Z a )
m
A.Cd/m : ballistic coefficient (m2/kg)
Za : apogee altitude (km)
Focus on Solar activity : Synthesis
The use of the “constant equivalent solar activity” approach :

removes the sensitivity of the disposal maneuver cost to solar activity prediction uncertainties
and to an end of mission date shift (during the spacecraft development process or later)

gives the information of a “mean 25 years reentry duration” (Z%=50%) considering all space
objects using this approach
Example (Parasol microsat):
- DAS Solar activity file
- Past and translated Solar Activity
- Constant Equivalent Solar Activity
CNES/DCT/SB/MS

Good Practices implemented in STELA software : Semi-Analytic Tool for
End of Life Analysis
 Used in the frame of the French Space Act to check the compliance with the
rules but usable more generally
 Rapid Semi analytical propagation (ISO “method 2” type)
 Propagation of mean orbital parameters
 Short periods added to compute osculating parameters when necessary
 Includes:
 rapid semi-analytic propagators (for LEO and GEO type orbits in the current
version)
 iterative modes helpful to choose disposal orbits parameters
 a tool that computes the mean area of a spacecraft
 JAVA based, usable as a software (GUI or batch mode) or a library
STELA is freeware  http://logiciels.cnes.fr/STELA
 Curent version is 1.2.1. New 1.3 version expected beginning of June ( SRP
for LEO, batch mode, other input frames, GUI improvements…). Version 2
including GTO propagation expected end of 2011

CNES/DCT/SB/MS

Validation by comparison with CNES reference numerical
propagators (high precision numerical integration, full dynamical
model) on the following domain:
 LEO type orbits: inside or at the vicinity of the LEO region (alt < 2200 km)
 GEO type orbits: inside or at the vicinity of the GEO region (GEO alt  1000 km),
initial inclination < 30 deg
LEO typical results
GEO typical results
CNES/DCT/SB/MS
GEO
propagation
Cd = f(alt)
Solar
activity =
f(t)
Plots
Mean area
computation
Computation
configuration
.xml
GTO
propagation
LEO
propagation
Simulation
configuration
.xml
Log File
.txt
Simulation
Synthesis
.txt
Ephemeris
(CCSDS)
.txt
16
CNES/DCT/SB/MS
CNES/DCT/SB/MS
Back-up
18
CNES/DCT/SB/MS
Algorithm for an equivalent solar activity
( Generate Solar Activity files)
ha, hp,
i, S/m
OLT z %
= 25
years
no
yes
Guess an new hp value that
would lead to a OLTz%
close to 25 years
Guess an equivalent
constant solar activity
that lead to an OLT z %
of 25 years
Compute the 1250 OLT values
with this hp value (monte
carlo)
Compute the
distribution function
and the OLT z %
OLT(F10.
7) = 25
years
no
yes
Z% Constant
equivalent
solar activity
CNES/DCT/SB/MS
19
J2/SRP resonant orbits
• Resonance condition:
 
    0 or 
 
    0

sat
sun
sat
sat
sun
sat
• (a,i) leading to a J2/SRP resonance (“0” curves on figures) for LEO quasi-circular
orbits
N.B. : slight sensitivity to eccentricity value
• J2/SRP resonance (if any) impact mainly the orbit eccentricity evolution
20
CNES/DCT/SB/MS