ISO 27852:2024

Space systems - Estimation of orbit lifetime

This document describes a process for the long-duration orbit lifetime prediction of orbit lifetime for spacecraft, launch vehicles, upper stages and associated debris in LEO-crossing orbits after mission phase (including any mission lifetime extensions). The document also clarifies: a) modelling approaches and resources for solar and geomagnetic activity modelling; b) resources for atmosphere model selection; c) approaches for spacecraft ballistic coefficient estimation.

Systèmes spatiaux — Estimation de la durée de vie en orbite

General Information

• Status: Published
• Publication Date: 22-Feb-2024
• ICS: 49.140 - Space systems and operations
• Technical Committee: ISO/TC 20/SC 14 - Space systems and operations
• Drafting Committee: ISO/TC 20/SC 14 - Space systems and operations
• Current Stage: 6060 - International Standard published
• Start Date: 23-Feb-2024
• Due Date: 12-Jan-2024
• Completion Date: 23-Feb-2024

Relations

• Revises: ISO 27852:2016 - Space systems - Estimation of orbit lifetime
• Effective Date: 16-Jul-2022

Overview

ISO 27852:2024 - "Space systems - Estimation of orbit lifetime" (3rd edition) provides a consensus-based process for long-duration orbit lifetime prediction of spacecraft, launch vehicle stages and associated debris in LEO-crossing orbits (perigee ≤ 2 000 km). Updated in 2024, this standard replaces the 2016 edition and clarifies modelling approaches for solar and geomagnetic activity, atmosphere model selection, and spacecraft ballistic coefficient estimation. It is intended to support compliance with space debris mitigation requirements (notably ISO 24113) and to harmonize with IADC and United Nations guidance.

Key Topics

• Scope & definitions: Lays out terms such as orbit lifetime, end of mission, disposal phase and protected regions; defines long-duration predictions spanning multiple solar cycles (e.g., 25-year lifetime).
• Orbit lifetime methods:
  • Method 1: high-precision numerical integration (detailed propagation).
  • Method 2: rapid semi-analytical orbit propagation.
  • Method 3: numerical table look-up, fitted equation evaluations and statistical approaches for high-eccentricity orbits (e.g., GTO).
• Atmospheric density & solar forcing:
  • Selection and use of atmospheric drag models and thermospheric considerations (including global cooling implications).
  • Approaches for solar and geomagnetic activity modelling: Monte Carlo random-draw, predicted solar activity profiles, equivalent constant indices, and reference solar forcing scenarios (multiple methods explained).
  • Reference to solar flux metrics (e.g., F10.7) and incorporation of recommended datasets (including alignment with CMIP6 forcing where appropriate).
• Ballistic coefficient (β) estimation:
  • Methods to estimate aerodynamic and solar radiation pressure coefficients (panel models).
  • Adjustments for rarefied gas flow (Knudsen number) and treatments for tumbling vs stabilized configurations.
  • Mass and cross-sectional area estimation guidance.
• Supplementary material: informative annexes on space population distribution, example 25-year predictions, and treatment of solar radiation pressure and 3rd-body perturbations.

Applications

ISO 27852 is practical for:

• Satellite designers and mission planners performing end-of-life and disposal analysis.
• Launch providers and operators assessing post-mission orbital decay of upper stages.
• Spacecraft operators demonstrating conformity with debris mitigation requirements (e.g., ISO 24113).
• Regulatory agencies and orbital debris analysts conducting risk assessments, licensing reviews, and long-term population modeling.
• Researchers and tool developers building orbit lifetime prediction software, atmospheric model selection tools, or ballistic coefficient estimators.

Related standards

• ISO 24113 - Space debris mitigation requirements (primary conformity target).
• ISO 23312 - Spacecraft disposal guidance (derivative standard).
• ISO/TR 20590 - Launch vehicle upper stage disposal technical report.
• IADC and United Nations space debris mitigation guidelines.

Keywords: ISO 27852, orbit lifetime prediction, LEO-crossing orbits, atmospheric density modelling, ballistic coefficient, solar activity modelling, space debris mitigation, spacecraft disposal.

Standards Content (Sample)

International
Standard
ISO 27852
Third edition
Space systems — Estimation of orbit
2024-02
lifetime
Systèmes spatiaux — Estimation de la durée de vie en orbite
Reference number
© ISO 2024
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
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CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms . 1
3.1 Terms and definitions .1
3.2 Symbols .5
3.3 Abbreviated terms .5
4 Orbit lifetime estimation . 5
4.1 General requirements .5
4.2 Definition of orbit lifetime estimation process .6
5 Orbit lifetime estimation methods and applicability . 6
5.1 General .6
5.2 Method 1: high-precision numerical integration .7
5.3 Method 2: rapid semi-analytical orbit propagation.7
5.4 Method 3: numerical table look-up, analysis and fit equation evaluations .8
5.5 Orbit lifetime sensitivity to Sun-synchronous orbit conditions .8
5.6 Orbit lifetime statistical approach for high-eccentricity orbits (e.g. GTO) .8
6 Atmospheric density modelling . 14
6.1 General .14
6.2 Atmospheric drag models .14
6.3 Long-duration solar flux and geomagnetic indices prediction .17
6.4 Method 1: Monte Carlo random draw of solar flux and geomagnetic indices .18
6.5 Method 2: predicted F solar activity prediction profile .24
10.7 Bar
6.6 Method 3: equivalent constant solar flux and geomagnetic indices .24
6.7 Method 4: reference solar forcing scenario . 28
7 Atmospheric density implications of thermospheric global cooling .28
8 Estimating ballistic coefficient (β).29
8.1 General . 29
8.2 Estimating aerodynamic force and solar radiation pressure coefficients . 29
8.2.1 General . 29
8.2.2 Aerodynamic and solar radiation pressure coefficient estimation via a “panel
model” . 29
8.2.3 Hypersonic rarefied gas flow adjustments via the Knudsen number and other
considerations . 33
8.3 Estimating cross-sectional area with tumbling and stabilization modes . 33
8.4 Estimating mass . 34
Annex A (informative) Space population distribution .35
Annex B (informative) 25-year lifetime predictions using random draw approach .38
Annex C (informative) Solar radiation pressure and 3rd-body perturbations .44
Bibliography .46

iii
Foreword
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This document was prepared by Technical Committee ISO/TC 20, Aircraft and space vehicles, Subcommittee
SC 14, Space systems and operations.
This third edition cancels and replaces the second (ISO 27852:2016) edition, which has been technically
revised.
The main changes are as follows:
— clarified that this document does not apply to non-LEO protected regions (e.g. GEO);
— harmonized terms and definitions with those in ISO 24113;
[1] [2] –[3]
— updated to harmonize with IADC and United Nations guidelines;
— added a subclause on the use of the recommended solar forcing dataset for the Coupled Model
Intercomparison Project 6.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
Introduction
Constraining estimated orbit lifetime of human-made objects is increasingly important as space debris
continues to increase (as documented in Annex A) and as such is one of the central tenets of the global space
debris mitigation strategy. This document is a supporting document to ISO 24113, its derivative spacecraft
disposal standard ISO 23312 and launch vehicle upper stage disposal technical report ISO/TR 20590. The
purpose of this document is to provide a common, consensus-based approach to determining orbit lifetime,
one that is sufficiently precise and easily implemented for the purpose of demonstrating conformity with
ISO 24113. This document offers standardized guidance and analysis methods to estimate orbital lifetime
for all LEO-crossing orbit classes. This document only deals with orbit lifetime issues (orbit decay out of
orbits crossing the LEO protected region); for other important requirements related to how long a space
object will, or will not, cross or occupy a protected region, the user is directed to ISO 24113 and its derivative
ISO 23312.
v
International Standard ISO 27852:2024(en)
Space systems — Estimation of orbit lifetime
1 Scope
This document describes a process for the long-duration orbit lifetime prediction of orbit lifetime for
spacecraft, launch vehicles, upper stages and associated debris in LEO-crossing orbits after mission phase
(including any mission lifetime extensions).
The document also clarifies:
a) modelling approaches and resources for solar and geomagnetic activity modelling;
b) resources for atmosphere model selection;
c) approaches for spacecraft ballistic coefficient estimation.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 24113, Space systems — Space debris mitigation requirements
3 Terms, definitions, symbols and abbreviated terms
3.1 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1.1
disposal
actions performed by a spacecraft (3.1.22) or launch vehicle orbital stage (3.1.9) to permanently reduce
its chance of accidental break-up and to achieve its required long-term clearance of the protected regions
(3.1.17)
Note 1 to entry: Actions can include removing stored energy and performing post-mission orbital manoeuvres.
3.1.2
disposal phase
interval between the end of mission (3.1.5) of a spacecraft (3.1.22) or launch vehicle orbital stage (3.1.9) and
its end of life (3.1.4)
3.1.3
Earth orbit
bound or unbound Keplerian orbit (3.1.14) with Earth at a focal point, or Lagrange point orbit which includes
Earth as one of the two main bodies

3.1.4
end of life
instant when a spacecraft (3.1.22) or launch vehicle orbital stage (3.1.9):
a) is permanently turned off, nominally as it completes its disposal phase (3.1.2),
b) completes its manoeuvres to perform a controlled re-entry (3.1.18) into the Earth’s atmosphere, or
c) can no longer be controlled by the operator
3.1.5
end of mission
instant when a spacecraft (3.1.22) or launch vehicle orbital stage (3.1.9):
a) completes the tasks or functions for which it has been designed, other than its disposal (3.1.1),
b) becomes incapable of accomplishing its mission (3.1.12), or
c) has its mission (3.1.12) permanently halted through a voluntary decision
3.1.6
GEO
Earth orbit (3.1.3) having zero inclination, zero eccentricity, and an orbital period equal to the Earth's
sidereal rotation period
3.1.7
high area-to-mass
having a ratio of area to mass exceeding 0,1 m /kg
3.1.8
launch vehicle
DEPRECATED: launcher
system designed to transport one or more payloads into outer space
3.1.9
launch vehicle orbital stage
complete element of a launch vehicle (3.1.8) that is designed to deliver a defined thrust during a dedicated
phase of the launch vehicle’s operation and achieve orbit (3.1.14)
Note 1 to entry: Non-propulsive elements of a launch vehicle, such as jettisonable tanks, multiple payload structures
or dispensers, are considered to be part of a launch vehicle orbital stage while they are attached.
3.1.10
LEO-crossing orbit
orbit (3.1.14) having perigee within the LEO protected zone, i.e. with perigee altitude of 2 000 km or less
Note 1 to entry: As shown in Figure A.3, orbits having this definition encompass the majority of the high spatial density
spike of spacecraft (3.1.22) and space debris (3.1.20).
3.1.11
long-duration orbit lifetime prediction
orbit lifetime (3.1.15) prediction spanning two solar cycles (3.1.19) or more (e.g. 25-year orbit lifetime)
3.1.12
mission
set of tasks or functions to be accomplished by a spacecraft (3.1.22) or launch vehicle orbital stage (3.1.19),
other than its disposal (3.1.1)
3.1.13
mission phase
phase where the space system fulfils its mission (3.1.12), beginning at the end of the launch phase and ending
when the space system no longer performs its intended mission or purpose

3.1.14
orbit
regular recurring path that a space object (3.1.21) takes about its primary attracting body
3.1.15
orbit lifetime
elapsed time between the orbiting spacecraft’s (3.1.22) initial or reference position and its re-entry (3.1.18)
Note 1 to entry: Examples of "initial position" are the injection into orbit (3.1.14) of a spacecraft or launch vehicle
orbital stage (3.1.9), or the instant when space debris (3.1.20) is generated. An example of a "reference position" is the
orbit of a spacecraft or launch vehicle orbital stage at the end of mission (3.1.5).
Note 2 to entry: The orbit’s decay is typically represented by the reduction in perigee and apogee altitudes (or radii)
as shown in Figure 1.
Note 3 to entry: Ballistic flight re-entry typically begins at 25 km to 50 km altitude.
Key
t time, expressed as calendar date
H apogee height, expressed in km
a
H perigee height, expressed in km
p
Figure 1 — Sample of orbit lifetime perigee and apogee decay profile
3.1.16
post-mission orbit lifetime
duration of the orbit (3.1.14) after completion of the mission phase (3.1.13)
Note 1 to entry: The disposal phase (3.1.2) duration is a component of the post-mission duration.
3.1.17
protected region
region in outer space that is protected with regard to the generation of space debris (3.1.20) to ensure its
safe and sustainable use in the future

3.1.18
re-entry
permanent return of a space object (3.1.21) into the Earth’s atmosphere
Note 1 to entry: Several alternative definitions are available for the delineation of a boundary between the Earth’s
atmosphere and outer space.
3.1.19
solar cycle
≈11-year time period which encompasses the 13-month oscillatory variation of solar radio flux, as observed
by monthly sunspot number and highly correlated with the 13-month running mean of measurements taken
at the 10,7 cm wavelength
Note 1 to entry: Historical records back to the earliest recorded data (1945) are shown in Figure 2.
Note 2 to entry: For reference, the 25-year post-mission orbit lifetime (3.1.16) constraint specified in ISO 24113 is
overlaid onto the historical data; it can be seen that multiple solar cycles are encapsulated by this long-time duration.
Key
X year
F adjusted daily Ottawa/Penticton solar radio flux (at 10,7 cm wavelength)
10.7
Figure 2 — Solar cycle (≈11-year duration)
3.1.20
space debris
DEPRECATED: orbital debris
objects of human origin in Earth orbit (3.1.3) or re-entering the atmosphere, including fragments and
elements thereof, that no longer serve a useful purpose
Note 1 to entry: Spacecraft (3.1.22) in reserve or standby modes awaiting possible reactivation are considered to serve
a useful purpose.
3.1.21
space object
object of human origin which has reached outer space

3.1.22
spacecraft
system designed to perform a set of tasks or functions in outer space, excluding launch vehicle (3.1.8)
3.2 Symbols
a orbit semi-major axis
A spacecraft cross-sectional area with respect to the relative wind
A Earth daily geomagnetic index
p
β ballistic coefficient of spacecraft = C A / m
D *
C spacecraft drag coefficient
D
C spacecraft reflectivity coefficient
R
e orbit eccentricity
-22 -2 -1
F solar radio flux observed daily at 2 800 MHz (10,7 cm) in solar flux units (10 W m Hz )
10.7
F solar radio flux at 2 800 MHz (10,7 cm), averaged over three solar rotations
10.7 Bar
H apogee altitude = a (1 + e) − R
a e
H perigee altitude = a (1 – e) − R
p e
m mass of spacecraft
R equatorial radius of the Earth
e
3.3 Abbreviated terms
GEO geosynchronous Earth orbit
GTO geosynchronous transfer orbit
LEO low Earth orbit
RAAN orbit right ascension of the ascending node (angle between vernal equinox and orbit as-
cending node, measured counter-clockwise in equatorial plane, looking in the –Z direction
of the chosen inertial frame)
SRP solar radiation pressure
4 Orbit lifetime estimation
4.1 General requirements
The orbital lifetime of LEO-crossing mission-related objects shall be estimated using the processes specified
in this document. In addition to any user-imposed constraints, the post-mission portion of the resulting orbit
lifetime estimate shall then be constrained to a maximum of 25 years per ISO 24113 using a combination of:
a) initial orbit selection;
b) spacecraft vehicle design;
c) spacecraft launch and early orbit concepts of operation which minimize LEO-crossing objects;

d) spacecraft ballistic parameter modifications at end of life;
f) spacecraft deorbit manoeuvres.
4.2 Definition of orbit lifetime estimation process
The orbit lifetime estimation process is represented generically in Figure 3.
[6]
Figure 3 — Orbit lifetime estimation process
5 Orbit lifetime estimation methods and applicability
5.1 General
There are three basic analysis methods used to perform a long-duration orbit lifetime prediction (ISO 24113),
as depicted in Figure 1. Determination of the method used to estimate orbital lifetime for a specific space
object shall be based upon the orbit type and perturbations experienced by the spacecraft as shown in
Table 1.
Table 1 — Applicable method with mandated conservative margins of error (in per cent) and
required perturbation modelling
Special orbit: Conservative margin applied to each method:
Orbit apogee altitude (km) Sun sync? High area-to- Method 1: Method 2: Method 3: table Method 3: graph,
mass? numerical inte- semi-analytic look-up equation fit
gration
Apogee < 2 000 km No No Use β; no margin Use β; 5 % margin Use β; 10 % Use β; 25 %
required margin margin
Apogee < 2 000 km No Yes Use β and SRP; no Use β and SRP; Use β; 10 % N/A
margin required 5 % margin margin
Apogee < 2 000 km Yes No Use β; no margin Use β and SRP; N/A N/A
required 5 % margin
Apogee < 2 000 km Yes Yes Use β and SRP; no Use β and SRP; N/A N/A
margin required 5 % margin
Apogee > 2 000 km Either Either Use β and SRP and Use β and SRP N/A N/A
3Bdy; no margin and 3Bdy; 5 %
required margin
Key
N/A  not applicable
β  satellite ballistic coefficient
3Bdy  third-body perturbations
SRP  solar radiation pressure
Method 1, certainly the highest fidelity model, utilizes a numerical integrator with a detailed gravity model,
third-body effects, solar radiation pressure, and a detailed spacecraft ballistic coefficient model. Method
[7] - [8]
2 utilizes a definition of mean orbital elements, semi-analytic orbit theory and average spacecraft
ballistic coefficient to permit the very rapid integration of the equations of motion, while still retaining
reasonable accuracy. Method 3 is simply a table lookup, graphical analysis or evaluation of equations fit
to pre-computed orbit lifetime estimation data obtained via the extensive and repetitive application of
methods 1 or 2, or both.
5.2 Method 1: high-precision numerical integration
Method 1 is the direct numerical integration of all accelerations in Cartesian space, with the ability to
incorporate a detailed gravity model (e.g. using a larger spherical harmonics model to address resonance
effects), third-body effects, solar radiation pressure, vehicle attitude rules or aero-torque-driven attitude
torques, and a detailed spacecraft ballistic coefficient model based on the variation of the angle-of-
attack with respect to the relative wind. Atmospheric rotation at the Earth’s rotational rate is also easily
incorporated in this approach. The only negative aspects to such simulations are:
a) they run much slower than method 2;
b) many of the detailed data inputs required to make this method realize its full accuracy potential are
simply unavailable;
c) any gains in orbit lifetime prediction accuracy are frequently overwhelmed by inherent inaccuracies of
atmospheric modelling and associated inaccuracies of long-term solar activity predictions or estimates.
However, to analyse a few select cases where such detailed model inputs are known, this is undoubtedly
the most accurate method. At a minimum, method 1 orbit lifetime estimations shall account for J and J
2 3
perturbations and drag using an accepted atmosphere model and an averaged ballistic coefficient. In the
case of high apogee orbits (e.g. GTO) or other resonant orbits, Sun and Moon third-body perturbations and
solar radiation pressure effects shall also be modelled.
5.3 Method 2: rapid semi-analytical orbit propagation
[7] - [8]
Method 2 analysis tools utilize semi-analytic propagation of mean orbit elements influenced by
gravity zonals J and J and selected atmosphere models. The primary advantage of this approach over direct
2 3
numerical integration of the equations of motion (method 1) is that long-duration orbit lifetime cases can be
quickly analysed (e.g. 1 s versus 1 700 s CPU time for a 30-year orbit lifetime case). While incorporation

of an attitude-dependent ballistic coefficient is possible for this method, an average ballistic coefficient is
typically used. At a minimum, method 2 orbit lifetime estimations shall account for J and J perturbations
2 3
and drag using an accepted atmosphere model and an average ballistic coefficient. In the case of high apogee
orbits (e.g. GTO), Sun and Moon third-body perturbations shall also be modelled.
5.4 Method 3: numerical table look-up, analysis and fit equation evaluations
In this final method, one uses tables, graphs and equations representing data that was generated by
exhaustively using methods 1 and 2 (see 5.2 and 5.3). Graphs and equations provided in this document, along
with other table lookup, analysis, and fit equations, can help the analyst crudely estimate orbit lifetime for
their case of interest, permitting the analyst to estimate orbit lifetime for their particular case of interest via
interpolation of method 1 or method 2 gridded data; all such method 3 data in this document were generated
using method 2 approaches. At a minimum, method 3 orbit lifetime products shall be derived from method 1
or method 2 analysis products meeting the requirements. When using this method, the analyst shall impose
at least a ten-percent margin of error to account for table look-up interpolation errors. When using graphs
and equations, the analyst shall impose a 25 % margin of error.
5.5 Orbit lifetime sensitivity to Sun-synchronous orbit conditions
For Sun-synchronous orbits, orbit lifetime has some sensitivity to the initial value of RAAN due to the
density variations with the local sun angle. Results from numerous orbit lifetime estimations show that
orbits with 6:00 am local time have longer lifetime than orbits with 12:00 noon local time by about 5,5 %.
[6]
This maximum difference (500 days) translates into a 5 % error which can be corrected by knowing the
local time of the orbit. As a result, method 1 or 2 analyses of the actual Sun-synchronous orbit condition
shall be used when estimating the lifetime of Sun-synchronous orbits, with a 5 % error margin required for
the semi-analytic approach.
5.6 Orbit lifetime statistical approach for high-eccentricity orbits (e.g. GTO)
For high-eccentricity orbits (particularly GTO), it can be difficult to iterate to lifetime threshold constraints
[9],[10]
due to the coupling in eccentricity between the third-body perturbations and the drag decay. Due to
this convergence difficulty, only method 1 or 2 analyses shall be used when determining initial conditions
which achieve a specified lifetime threshold for such orbits.
[11]-[12]
Sample analyses of GTO launcher stages highlight this orbit lifetime sensitivity to initial conditions
(orbit, spacecraft characteristic and force model), leading to a wide spectrum of orbital lifetimes.
Some theoretical considerations about the dynamical properties of GTO orbits are provided in References [11]
and [13].
A test case illustrates the complex dynamical properties of GTO. Initial parameters are provided in Table 2.
Table 2 — GTO Initial Conditions for the Monte Carlo simulation
Perigee altitude 200 km
Apogee altitude GEO altitude
Inclination 2°
Area to mass ratio 5e-3 m /kg
Solar activity Constant (F =140 sfu A =15)
10.7 p
Drag coefficient Constant = 2,2
Reflectivity coefficient Constant = 2
Figure 4 shows lifetime results (years) when varying the initial date and the initial local time of perigee.
This latest parameter is defined as the angle in the equator between the Sun direction and the orbit perigee,
measured in hours. The date was chosen from day 1 to 365 in year 1998 and the local time of perigee was
chosen by varying the right ascension of ascending node from 0 to 2π. A total of 2 500 different initial
conditions were generated.
Key
D initial day of year, 1998
T initial local time of perigee passage, hours UTC
p
Figure 4 — Orbit lifetime as a function of initial day of year and local time of perigee
The shapes of the lifetime contours confirm that initial day of year and local time of perigee are initial
conditions that make sense to describe GTO evolution since strong patterns are visible. The amplitudes of
lifetimes variations are worth noting: from several months to more than 50 years. Previous results (see
References [10] and [12]) are illustrated in Figure 4: the longest lifetimes are obtained for initial Sun-pointing
(12 h local time) or anti Sun-pointing (24 h local time) perigee with an initial date around the solstices. The
dark red pixels drawn in dark blue areas, as seen for initial day 60 and local time 7 h, are an indication of
the presence of strong resonance phenomena. The year is also known to have an influence, to a lesser extent,
through the Moon’s perturbative effects.
Figure 5 shows semi-major axis evolution for several propagations of a typical low-inclined GTO. The
different curves correspond to changes of 0,1 % or 1 % in the area to mass ratio of the object (A/m), which is
far below the level of incertitude on this parameter. These dispersions lead to variations of decades in the re-
entry duration. Such a strong non-linear behaviour is explained by the aforementioned resonances. One can
see that semi-major axis evolutions are quite similar between all propagation cases until the entrance in the
coupling between J and Sun perturbations, for a semi-major axis equal to about 15 500 km. The duration of
the resonance (period when the semi-major axis remains constant) and thus the rest of the propagation are
completely different. A similar figure can be plotted by keeping the area to mass ratio constant and slightly
changing the solar activity.
Key
t time, expressed in years
a semi-major axis, expressed in km
a
Nominal A/m ratio (100 %).
Figure 5 — SMA evolution sensitivity to slight A/m variations (from 0,1 % to 2 %)
These examples show that resonance phenomena have substantial impacts on orbital elements evolution that
can neither be predicted nor managed. Cumulated uncertainties on drag force between the extrapolation
start (mission disposal manoeuvre for example) and the instant when the resonance occurs make the entry
condition in this resonance prone to strong variations. As a consequence, trying to estimate lifetime of GTOs
using only one extrapolation can lead to erroneous conclusion since tiny changes in the initial conditions,
spacecraft characteristics or force models end in very different lifetime results. Exceptions to that would
be objects on a GTO whose semi major axis has already decreased enough to avoid resonances or to be very
close to them. However, since resonance conditions change with regards to the possible resonant angles,
one can see that performing several propagation cases is advised to get robust results. As a conclusion, only
statistical results are adequate to estimate the strong variations of GTO lifetimes.
As a consequence, one should not say “this object’s lifetime is Y years” in GTO but rather “the lifetime of this
object is shorter than Y years with a probability p”, coming from a cumulative distribution function.
Key parameter uncertainties shall be taken into account in the lifetime estimation:
— initial conditions (date, orbit parameters);
— ballistic coefficient and drag coefficient;
— solar activity.
[14]
A Monte Carlo simulation test case yields results that illustrate the variability in lifetime estimates.
Initial parameters for this test case are described in Table 3. A total of 2 500 different initial conditions were
generated.
Table 3 — Hypothesis conditions for the Monte Carlo simulation
Parameter Nominal value Dispersions
Perigee altitude 180 km Small dispersions: 1 sigma standard
deviation about 1 km, correlated to
other orbit parameters
Apogee altitude GEO altitude Small dispersions: 1 sigma standard
deviation about 50 km, correlated to
other orbit parameters
Inclination 6° Small dispersions: 1 sigma standard
deviation about 0,01°, correlated to
other orbit parameters
Area to mass ratio 5.e-3 m /kg Uniform distribution ±20 % with
respect to nominal value
Drag coefficient Function of geodetic altitude None
Reflectivity coeffi- Constant =1,5 None
cient
Solar activity Randomly chosen using data from the past None
Date Uniform distribution between day 1 and day 365, for The dispersion of the year addresses
years between 2015 and 2033 Moon perturbations.
Local time of perigee Gaussian distribution with a mean value of 22 h Standard deviation of 50 min for time
of perigee passage
Figure 6 and Figure 7 provide a statistical histogram and cumulative distribution function of orbit lifetime
for this test case.
Key
L lifetime, expressed in years
N number of occurrences in this lifetime bin
Figure 6 — Histogram of orbital lifetimes

Key
L lifetime, expressed in years
C cumulative distribution function
Figure 7 — Cumulative distribution function of orbital lifetimes
The question of statistical convergence can be addressed by computing a confidence interval for the
Monte Carlo results, associated to a confidence level. The so-called “interval of Wilson with correction for
[15]
continuity” has been well-adapted for this purpose.
In this approach, the upper p and lower p limits of this interval are given by Formulae (1) and (2):
1 2
2 2
21nf +−uu−−un21−+/ 41fn()()− f +1
αα//2 22α/
p = (1)
2 nu+
()
α/2
2 2
21nf ++uu++un21−+/ 41fn()− f −1
()
αα//2 22α/
p = (2)
2 nu+
()
α/2
Where
n number of single runs (orbit propagations);
f observed probability = number of lifetimes estimated to be lower than a cer-
tain value, divided by n;
-1
u  = Φ  (1- α/2) (= 1,96 for example for a confidence interval of 95 %). Φ is the cumulative nor-
α/2
mal distribution function.
As shown in Figure 8 and Figure 9, after N Monte Carlo runs one can compare the limit (upper or lower) of
the confidence interval with the targeted probability for the lifetime to be lower than a certain value.

Key
N number of simulations
P probability
P max probability of confidence interval
max
P observed probability over N simulations
o
P min probability of confidence interval
min
Figure 8 — Example of evolution of the observed probability (lifetimes lower than 25 years) and
95 % confidence interval
Key
L lifetime, expressed in years
P probability
P max probability of confidence interval
max
P observed probability over N simulations
o
P min probability of confidence interval
min
Figure 9 — Example of cumulative distribution function of orbital lifetimes with a 95 % confidence
interval (500 runs)
6 Atmospheric density modelling
6.1 General
The three biggest factors in orbit lifetime estimation are:
a) the selection of an appropriate atmosphere model to incorporate into the orbit acceleration formulation;
b) the selection of appropriate atmosphere model inputs;
c) determination of a space object’s ballistic coefficient.
Each of these three aspects is examined.
6.2 Atmospheric drag models
There are a wide variety of atmosphere models available to the orbit analyst. The background, technical
basis, utility, and functionality of these atmosphere models are described in detail in References [16] to [25].
This document does not presume to dictate which atmosphere model the analyst shall use. However, it is
worth noting that in general, the heritage, expertise and especially the observational data that went into

creating each atmosphere model play a key role in that model’s ability to predict atmospheric density, which
is in turn a key factor in estimating orbit lifetime. Many of the early atmosphere models are of low fidelity
and were originally created based on only one, or perhaps even just a part of one, solar cycle’s worth of data.
The advantage of some of these early models is that they typically run much faster than the latest high-
fidelity models (Table 4), without a significant loss of accuracy. However, the use of atmosphere models that
were designed to fit a select altitude range (e.g. the “exponential” atmosphere model, “static” models, or
models that do not accommodate solar activity variations) should be avoided in cases where they might miss
too much of the atmospheric density variational complexity to be sufficiently accurate.
There are some early models (e.g. Jacchia 1971 of Table 4) which accommodate solar activity variations and
also run very fast; these models can work well for long-duration orbit lifetime studies where numerous
cases are to be examined. Conversely, use of the more recent atmosphere models are encouraged because
they have substantially more atmospheric drag data incorporated as the foundation of their underlying
assumptions. A crude comparison of a sampling of atmosphere models for a single test case is shown in
Figure 10 and Figure 11, illustrating the range of temperatures and densities exhibited by the various
models. ISO 14222 provides guidance on a variety of suitable atmosphere models and associated indices.
Although this document does not presume to direct which atmosphere model the analyst should use, the
lengthy prediction timespan associated with this document makes several of the atmosphere models listed
in ISO 14222 suitable for estimation of orbital lifetimes spanning 25 years or more, to include, but not limited
[20] [27] [21] [22] [23] [24]
to, the NRLMSISE-00, NRL MSIS Version 2, JB2006, JB2008, GRAM-07, DTM-2000 and
[25]
GOST models.
Table 4 — Comparison of normalized density evaluation runtimes
Atmosphere model 0 < Alt < 5 000 km 0 < Alt < 1 000 km
Exponential 1,00 1,00
Standard Atmosphere 1962 1,43 1,51
Standard Atmosphere 1976 1,54 1,54
Jacchia 1971 13,68 17,31
MSIS 2000 141,08 222,81
JB2006 683,85 584,47
Key
H altitude, expressed in km
T temperature, expressed in K
a
1962 std atmosphere model.
b
2006 Jacchia-Bowman atmosphere model.
c
1976 std atmosphere model.
d
2000 MSIS atmosphere model.
Figure 10 — Temperature comparison by atmosphere model

Key
H altitude, expressed in km
L log10(density in kg/m )
a
Exponential model.
b
1962 std atmos.
c
MSIS E 2000.
d
Jacchia 1976.
e
Jacchia 1971.
f
JB2006.
Figure 11 — Comparison of a small sampling of atmosphere models
6.3 Long-duration solar flux and geomagnetic indices prediction
Utilization of the higher-fidelity atmosphere models mentioned in 6.2 requires the orbit analyst to specify
the solar and geomagnetic indices required by such models. Compatible input indices are needed for each
model; subtle difference can exist in the interpretation of similarly named indices when used by different
atmosphere models (e.g. centrally averaged vs. backward averaged F ).
10.7 Bar
Key issues associated with any prediction of solar and geomagnetic index modelling approach are as follows.
a) F predictions should reflect the estimated mean solar cycle as accurately as possible. One such
10.7 Bar
prediction is shown in Figure 12.
b) Large daily F and A index variations about the mean value induce non-linear variations in
10.7 p
atmospheric density, and the selected prediction approach should account for this fact; i.e. one should
account for the highly non-linear aspects of solar storms versus quiet periods.
c) The frequency of occurrence across the day-to-day index values is highest near the lowest prediction
boundary (Figure 13).
d) F cycle timing/phase are always imprecise and should be accounted for; the resultant time bias that
10.7
such a prediction error would introduce can yield large F prediction errors of 100 % or more.
10.7
e) The long-time duration orbit lifetime constraint specified in ISO 24113 (i.e. 25 years) would require
that the solar/geomagnetic modelling approach provide at least that many years (i.e. 25) of predictive
capability.
f) Predicted F values should be adjusted to correct for Earth-Sun distance variations.
10.7
g) Some atmosphere models (e.g. JB2006 and JB2008), due to the newly invented indices adopted thereby,
preclude the use of historical indices for long-term orbit lifetime studies, while currently also precluding
use of any predictive forecasting model(s) for those indices until such time as those become publicly
available.
Accounting for these constraints, the user shall adopt one of the four acceptable approaches.
[28],[29]
— Space weather approach #1: Utilize Monte Carlo sampling of historical data mapped to a common
solar cycle period.
— Space weather approach #2: Utilize a predicted F solar activity prediction profile generated by a
10.7 Bar
[24]
model such as is detailed in Figure 12, coupled with a stochastic or similar generation of corresponding
F and A values (e.g. see Reference [30]).
10.7 p
— Space weather approach #3: Utilize a “mean equivalent static” set of solar and geomagnetic activity.
While such an approach produces equivalent solar and geomagnetic indices that are suitable for efficient
and equivalent orbit lifetime estimation, such static values are only valid for the cycles fit, the selected
orbit prediction span (i.e. 25 years) with an associated probability level and the adopted atmosphere
model. New sets of mean equivalent static indices would likely need to be generated for any changes in
these functional dependencies.
— Spa
...