“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

CNES/DCT/SB/MS

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

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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

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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

* 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 / ”J2 secular effect” resonance (orbit inclination about 40, 80, 110 and 125°, see back-up chart)

Perturbation LEO orbits GEO orbits

Earth’s gravity field J2 to J4 zonal model* Full 4x4 model

Solar and Lunar gravity yes** yes

Atmospheric drag yes no

Solar Radiation Pressure (SRP)

yes*** yes

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Good Practices: summary

Definition of computation parameters for the Solar Pressure and Drag Forces

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

udd

APCFp R

2

00

rrd VVCAFa 2

1

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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”

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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

Equivalent constant solar activity

Possible Future solar activities

25 years lifetime25 years lifetime in Z % of the cases

t

2 4 6 6 3

t

t

t

Z%

25 years0%

100%

F10.7

lifetime

1 Space Object 1 End of life orbit

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Focus on Solar activity : algorithm

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

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

Algorithm to tune the constant equivalent solar activity (1/4)

These solar activities are considered as representative samples of the possible future solar activity.

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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

Focus on Solar activity : algorithm

Algorithm to tune the constant equivalent solar activity (2/4)

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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

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)

N.B. : tuning of F10.7

Ap = 15 (arbitrary choice)

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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

The algorithm works for any probability level of reentry within 25 years: 50% has been chosen in the frame of the French Space law

Focus on Solar activity : algorithm

Algorithm to tune the constant equivalent solar activity (4/4)

Constant Flux

130,00

132,00

134,00

136,00

138,00

140,00

142,00

144,00

146,00

148,00

0 0,01 0,02 0,03 0,04 0,05 0,06 0,07

Cx*S/mF

(sfu

)

1100 km

800 km

1100 km

800 km

1000 km

700 km

Constant Flux

126,00

128,00

130,00

132,00

134,00

136,00

138,00

140,00

142,00

144,00

146,00

148,00

500 700 900 1100 1300 1500 1700 1900 2100

ha (km)

F(s

fu)

S/m 0.0104

S/m 0.03

S/m 0.02

S/m 0.05

S/m 0.015

dga_1100

dga_797

S/m 0.001

S/m 0.0104

Cd = 2.2

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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%)

)ln(7).

ln(25.3201

15

7.10 ad Z

m

CAF

AP

A.Cd/m : ballistic coefficient (m2/kg)

Za : apogee altitude (km)

Focus on Solar activity : result

Z%=50% law

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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

Focus on Solar activity : Synthesis

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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

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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

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LEO propagation

GEO propagation

Mean area computation

Cd = f(alt)

Solar activity = f(t)

GTO propagation

Simulation configuration .xml

Log File .txt

Simulation Synthesis .txt

Ephemeris (CCSDS) .txt

Computation configuration .xml

Plots

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Back-up

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ha, hp, i, S/m

( Generate Solar Activity files)

Compute the 1250 OLT values with this hp value (monte carlo)

Guess an new hp value that

would lead to a OLTz%

close to 25 years

Compute the distribution function and the OLT z %

no

Guess an equivalent constant solar activity that lead to an OLT z % of 25 years

Z% Constant equivalent solar activity

OLT(F10.7) = 25 years

OLT z %

= 25 years

yes

yes

no

Algorithm for an equivalent solar activity

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J2/SRP resonant orbits

• (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

00 satsunsatsatsunsat or • Resonance condition: