ISO 26872:2010

INTERNATIONAL ISO
STANDARD 26872
First edition
2010-09-15
Space systems — Disposal of satellites
operating at geosynchronous altitude
Systèmes spatiaux — Élimination des satellites opérant à une altitude
géostionnaire
Reference number
©
ISO 2010
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ii © ISO 2010 – All rights reserved

Contents Page
Foreword .iv
Introduction.v
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Symbols and abbreviated terms .2
4.1 Symbols.2
4.2 Abbreviated terms .2
5 Geosynchronous region.3
6 Protected region .3
7 Primary requirements .5
7.1 Disposal manoeuvre planning .5
7.2 Probability of successful disposal .6
7.3 Criteria for executing disposal action.6
7.4 Contingency planning.6
8 Disposal planning requirements.6
8.1 General .6
8.2 Estimating propellant reserves.6
8.3 Computing the initial perigee increase .7
8.4 Developing basic manoeuvre requirements for a stable disposal orbit.7
8.5 Developing long-term (100-year) disposal orbit characteristics .7
8.6 Determining the manoeuvre sequence .8
8.7 Developing a vehicle securing plan .8
8.8 Developing a contingency plan .8
Annex A (informative) Tabulated values of the optimal eccentricity vector.9
Annex B (informative) Optimal manoeuvre sequences .31
Annex C (informative) Example calculations .37
Annex D (informative) Disposal strategy and analysis for sample GEO satellite .43
Annex E (informative) Discussion of conditional probability.50
Bibliography.53

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 26872 was prepared by Technical Committee ISO/TC 20, Aircraft and space vehicles, Subcommittee
SC 14, Space systems and operations.
iv © ISO 2010 – All rights reserved

Introduction
This International Standard prescribes requirements for planning and executing manoeuvres and operations
to remove an operating satellite from geosynchronous orbit at the end of its mission and place it in an orbit for
final disposal where it will not pose a future hazard to satellites operating in the geosynchronous ring.
This International Standard includes requirements related to the following:
⎯ when the disposal action needs to be initiated,
⎯ selecting the final disposal orbit,
⎯ executing the disposal action successfully, and
⎯ depleting all energy sources to prevent explosions after disposal.
End-of-mission disposal of an Earth-orbiting satellite broadly means the following:
a) removing the satellite from the region of space where other satellites are operating, so as not to interfere
or collide with these other users of space in the future, and
b) ensuring that the disposed object is left in an inert state and is incapable of generating an explosive event
1)
that could release debris which might threaten operating satellites .
For satellites operating in the geosynchronous belt, the most effective means of disposal is first to re-orbit the
satellite to a super-synchronous orbit above the region of operating spacecraft and the manoeuvre corridor
used for relocating operating satellites to new longitudinal slots, and then to discharge batteries and vent
propellants and take other actions to preclude a debris-producing event.

1) Further information will be provided in the future International Standard, ISO 16127.
INTERNATIONAL STANDARD ISO 26872:2010(E)

Space systems — Disposal of satellites operating at
geosynchronous altitude
IMPORTANT — The electronic file of this document contains colours which are considered to be
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1 Scope
This International Standard specifies requirements for the following:
⎯ planning for disposal of satellites operating at geosynchronous altitude to ensure that final disposal is
sufficiently characterized and that adequate propellant will be reserved for the manoeuvre;
⎯ selecting final disposal orbits where the satellite will not re-enter the operational region within the next
100 years;
⎯ executing the disposal manoeuvre successfully;
⎯ depleting all energy sources on board the vehicle before the end of its life to minimize the possibility of an
event that can produce debris.
This International Standard provides techniques for planning and executing the disposal of space hardware
that reflect current internationally accepted guidelines and consider current operational procedures and best
practices.
2 Normative references
The following referenced documents are indispensable for the application 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 24113:2010, Space systems — Space debris mitigation requirements
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 24113 and the following apply.
3.1
inclination excursion region
region in space occupied either by a non-operational geostationary satellite or by an operational
geosynchronous satellite without inclination station-keeping
3.2
re-orbit manoeuvre
action of moving a satellite to a new orbit
3.3
satellite
manufactured object or vehicle intended to orbit the earth, the moon or another celestial body
4 Symbols and abbreviated terms
4.1 Symbols
a semi-major axis
2)
C solar radiation pressure coefficient of the spacecraft (0 < C < 2)
R R
e eccentricity
h perigee altitude
p
i inclination
I specific impulse
sp
L solar longitude
S
M mean anomaly
p semilatus rectum or semi-parameter [p = a(1 − e )]
r radius of orbit
v true anomaly
µ Earth gravitational constant
σ standard deviation or the positive root of the variance, which measures the dispersion of the data
Ω right ascension of ascending node (RAAN)
ω argument of perigee
A/m effective area-to-mass ratio: projected area of the spacecraft perpendicular to the sun's ray divided
by the mass of the spacecraft
∆H change in altitude
∆V delta velocity or total velocity change
4.2 Abbreviated terms
EGM Earth gravitational model
EOMDP end-of-mission disposal plan
GEO geosynchronous (geostationary) Earth orbit
RAAN right ascension of ascending node

2) In some references, the C is defined as the index of surface reflection.
R
2 © ISO 2010 – All rights reserved

5 Geosynchronous region
The geosynchronous region is a circular ring around the Earth in the equatorial plane. Within this region, an
object in space moves along the ring at a mean angular rate that is equal or very close to the Earth's rotation,
meaning that the satellite appears to be positioned over a fixed location on the ground.
Without so-called north-south station-keeping, the inclination of a GEO satellite will gradually cycle between 0°
(equatorial orbit) and a maximum of approximately 14,6° and back again. In addition to maintaining the
accuracy of its inclination, a GEO satellite must execute station-keeping manoeuvres to maintain longitudinal
accuracy, so as to prevent a naturally occurring drift to the east or to the west caused by asymmetries in the
Earth's gravitational field, unless the satellite is located at one of the two “gravity wells” on the geostationary
arc.
Figure 1 shows a three-dimensional view of the geosynchronous ring with a cross-section defining the
approximate size of the ring. Figure 2 gives the dimensions of three regions of the cross-section. The
cross-section is defined by two axes: the latitudinal axis and radial axis. This plane of the cross-section is
perpendicular to the Earth's equatorial plane.
The three concentric boxes shown in Figure 2 give the approximate boundaries for three types of orbits. The
smallest box represents the region where a geostationary satellite will be confined under station-keeping, and
the next larger box approximates the region where a geosynchronous satellite may be located when its
inclination is not controlled but it remains under a mission-specified value. For example, the upper value for
some specific geosynchronous missions may range from 3° to 5° depending on the ground user's antenna
design. The largest box represents the inclination excursion region for a non-operational GEO satellite and the
±200 km protected region. For most communication satellites, the longitude station-keeping limit is ±0,1°.
6 Protected region
The GEO protected region, defined by ISO 24113 and indicated by Region B in Figure 1, includes the
rectangular toroid centred on geostationary altitude, with an extent 200 km above and below this altitude and
with inclination limits of +15° to −15°. While operations are usually conducted within about 75 km of
geostationary altitude, the GEO protected region is extended in altitude to create a manoeuvre corridor for
relocating spacecraft. Passivation of the disposed spacecraft is necessary to ensure that accidental
explosions from on-board energy sources do not create debris that could re-enter the protected region.
NOTE Reproduced by kind permission of the Centre National d'Études Spatiales.
Figure 1 — Three-dimensional view of geosynchronous ring
4 © ISO 2010 – All rights reserved

Dimensions in kilometres
Key
X radial (away from Earth)
Y latitude (north)
1 protected region
2 geostationary control box (±37,5 km × ±37,5 km)
3 geosynchronous control box (±40 km radial; ±3° to ±5° in inclination)
NOTE The dimensions in the figure are not to scale.
Figure 2 — Cross-section of the geosynchronous ring
7 Primary requirements
7.1 Disposal manoeuvre planning
An EOMDP shall be developed, maintained and updated in all phases of mission and spacecraft design and
operation. The EOMDP shall be an integral part of the space debris mitigation plan specified by ISO 24113.
The EOMDP shall include the following:
a) details of the nominal mission orbit;
b) details of the targeted disposal orbit;
c) estimates of the propellant required for the disposal action;
d) identity of systems and capabilities required for successful completion of the disposal action;
e) criteria that, when met, shall dictate initiation of the disposal action;
f) identities of energy sources required to be depleted before end of life;
g) timeline for initiating and executing the disposal action;
h) timeline for depleting the remaining energy sources;
i) those individuals or entities, or individuals and entities to be notified of the end of mission and disposal
and a timeline for notification.
7.2 Probability of successful disposal
In accordance with the requirements of ISO 24113:2010, 6.3.1, a spacecraft shall be designed such that the
joint probability of having sufficient energy (propellant) remaining to achieve the final disposal orbit and
successfully executing commands to deplete energy sources equals or exceeds 0,9 at the time disposal is
executed. ISO 24113:2010, 6.3.1, also requires that the disposal success probability shall be evaluated as
conditional probability (weighted on the mission success). Annex E provides a discussion of the conditional
probability. Details of the design that provide the basis for the probability estimate shall be included in the
EOMDP.
7.3 Criteria for executing disposal action
Specific criteria for initiating the disposal action shall be developed, included in the EOMDP and monitored
throughout the mission life.
EXAMPLE Propellant amount remaining; redundancy remaining; status of electrical power; status of systems critical
to a successful disposal action; time required to execute disposal action.
Projections of mission life based on these criteria shall be made as a regular part of mission status reviews.
7.4 Contingency planning
Independent of the success or failure of other aspects of a disposal action, a contingency plan shall be
developed to deplete all energy sources and secure the vehicle before the final demise of the spacecraft. The
objective shall be to ensure that actions necessary to secure the vehicle are taken before end of life. The
contingency plan shall include criteria that define when the securing actions are to be taken, the rationale for
each criterion, and a schedule for securing actions. The contingency plan shall be included in the EOMDP.
8 Disposal planning requirements
8.1 General
Planning activities for end-of-mission disposal shall start in the mission design phase. Planning for the actual
disposal action should begin at least six months before the date of re-orbit manoeuvres. The steps described
in 8.2 to 8.8 shall be followed in all mission phases and shall be documented in the EOMDP.
8.2 Estimating propellant reserves
The amount of fuel necessary to perform spacecraft disposal shall be estimated from the design phase, in
accordance with the needed accuracy level, and reserved for the disposal phase. The minimum ∆V capability
(3−σ) to reach the targeted disposal orbit shall be determined and specified in the EOMDP. The fuel required
3)
to provide this ∆V shall be maintained for end-of-life disposal .

3) Further information will be provided in the future International Standard, ISO 23339.
6 © ISO 2010 – All rights reserved

8.3 Computing the initial perigee increase
In accordance with the requirements of ISO 24113:2010, 6.3.2, a spacecraft operating within the GEO
protected region must, after completion of its GEO disposal manoeuvres, have an orbital state that satisfies at
least one of the two conditions outlined below.
a) The orbit has an initial eccentricity of less than 0,003, and a minimum perigee altitude, ∆H, expressed in
kilometres, above the geostationary altitude (35 786 km) calculated according to Equation (1):
∆=H 235+()1 ×000CA× /m (1)
R
The minimum value of C for computing the initial perigee increase shall be no less than 1,5 (a
R
conservative estimate for C , so as to adequately predict the solar radiation pressure effect). Justification
R
shall be provided for using a value less than 1,5. Equation (1) was derived to ensure that the long-term
perturbations will not cause the GEO debris to re-enter a protected zone of GEO plus 200 km.
b) The orbit has a perigee altitude sufficiently above the geostationary altitude that the spacecraft will not
enter the GEO protected region within 100 years, irrespective of long-term perturbation forces.
8.4 Developing basic manoeuvre requirements for a stable disposal orbit
A stable disposal orbit shall be established by one of the two options described below.
a) Use Equation (1) and the eccentricity constraint to determine initial disposal orbit conditions.
b) Perform long-term (100-year) numerical integrations of the selected disposal orbit. The predicted
minimum perigee altitude shall be greater than the 200 km protected region (see 8.5). It is recommended
that the optimal eccentricity vector be determined from Tables A.1 to A.3, as a function of the date of
orbital insertion and the value of C × A/m.
R
The altitude stability will be improved for either method if the following apply:
⎯ the initial disposal perigee points toward the sun (perigee is sun-pointing);
⎯ the disposal manoeuvres are performed in the most favourable season of the year, such that the same
amount of perigee altitude increase will give the largest clearance over 100 years.
NOTE 1 The true optimal direction will differ slightly from the actual sun-pointing direction as a result of lunar
perturbations.
NOTE 2 See Annex A for the optimal eccentricity and argument of perigee as a function of time for various values of
C × A/m. Disposal orbits defined in accordance with Equation (1) are stable if the final eccentricity is less than 0,003.
R
Tables A.1 to A.3 can be used to select the initial guess if option b) is used to determine the initial orbit parameters.
Should the intention be to operate the vehicle after placing it in a disposal orbit, the effects of such operation
on the orbit shall be estimated, and this estimate and computations verifying that the operations will not
compromise the long-term stability of the orbit (i.e. perigee shall remain above the protected region for
100 years) shall be included in the EOMDP. In all cases, the spacecraft shall be passivated (see 8.7) prior to
end of life.
8.5 Developing long-term (100-year) disposal orbit characteristics
Long-term (100-year) orbit histories are needed only when the second option [see 8.4 b)] is chosen to
establish a stable disposal orbit. If 8.4 b) is chosen, orbit propagation results developed by a reliable orbit
propagator, either semi-analytic or numerical, shall be used to predict histories of perigee heights above GEO
for a period of 100 years after initial insertion into the disposal orbit. The orbit propagator shall be of high
precision and include as a minimum the perturbing forces of Earth's gravitational harmonics (up to a
degree/order of 6 by 6), lunisolar attractions and solar radiation pressure. The precision of long-term
propagation of the propagator shall be verified against another well-established orbit propagator. Details on
the orbit propagator used, assumptions made and analysis results shall be included in the EOMDP.
8.6 Determining the manoeuvre sequence
The manoeuvre sequence shall be determined that will place the GEO satellite in the required disposal orbit,
have the optimal near-sun-pointing perigee and exhaust all the propellant on board. The disposal orbit is
obtained after passivation and complete tank depletion, which can have unpredictable effects on orbital
parameters and altitude. See Annex B for examples. The initial conditions of the disposal orbit shall be
determined using the steps outlined in 8.4 and 8.5.
8.7 Developing a vehicle securing plan
Depletion of propellant creates forces that can affect a vehicle's orbit. The vehicle securing plan shall specify
the following:
a) steps to deplete on-board energy sources after the satellite has been placed into the disposal orbit;
b) the effects the depletion action will have on the final orbit of the vehicle (the goal should be either to
increase altitude or at least to limit a possible decrease in altitude);
c) criteria for when the plan will be executed; and
d) a schedule to be followed.
8.8 Developing a contingency plan
If a malfunction or other circumstance makes it necessary to proceed to the disposal phase earlier than
planned, a contingency plan shall be developed that includes provisions for the following:
a) selecting an alternative orbit that is the least likely to interfere with the protected area (see Annex C): the
contingency plan shall include criteria and techniques for selecting this orbit;
b) manoeuvring the satellite to the alternative orbit;
c) securing the satellite after the move; and
d) securing the vehicle if specified criteria are met at any time in the mission.
Annex D provides an example in which the quantity of propellant remaining is uncertain.
8 © ISO 2010 – All rights reserved

Annex A
(informative)
Tabulated values of the optimal eccentricity vector
Tables A.1 to A.3 contain the optimal eccentricity vector [eccentricity and argument of perigee plus RAAN (or
longitude of periapsis)] as a function of time and a function of (C × A/m), expressed in square metres per
R
kilogram, that will yield the highest perigee over the next 100 years. The optimal values were calculated in a
−5
brute-force fashion using increments of 2,3 × 10 in eccentricity and 5° in longitude of periapsis. The benefit
gained from using the optimal vector over the sun-pointing strategy varied from 0 km to 20 km (the average
was approximately 9 km). However, if the sun-pointing strategy is chosen for the disposed vehicle, then the
longitude of periapsis should be set equal to the value of the solar longitude (depicted as L in Tables A.1
S
to A.3) with an eccentricity equal to 0,01 × C × A/m. These charts can be interpolated to find the optimal
R
vector for any particular satellite at a given time. However, the following should be noted when using these
tables.
The initial conditions used to generate the data assumed a constant semi-major axis of 300 km above GEO
(i.e. a constant ∆V was used in the disposal), mean anomaly of 180° (i.e. the last burn occurs at apogee,
raising the perigee so that the eccentricity is equal to the tabulated value), an inclination of 7,74° (maximum at
end of life if inclination drift is allowed) and an epoch of 0:00 Universal Time on the first day of each month.
Additional analysis has shown that the optimal vector depends little upon these elements (the minimum
perigee altitude may vary by approximately 2 km for each component), but if a high level of accuracy is
required for a given disposal, the interpolated values found from the tables should be used as an initial guess
so as to find the optimum for a particular disposal situation. The exception is the RAAN: in the search process,
the initial RAAN was set to 62,3° and the argument of perigee was changed in 5° increments until the optimal
value was found. Different RAANs were then checked and it was found that the relevant angular parameter
was the argument of perigee plus RAAN; if this value is held constant, then the results will again be consistent
with 1 km to 2 km, irrespective of the particular RAAN.
In addition, care should be taken if interpolating the values. In searching for optimal values in the angular
argument, it was found that, at times, there was not one pure maximum, but multiple local maximums. As
either the time or C × A/m advanced, the true maximum jumped from one peak to another. For example,
R
consider the 2008-05-01 disposal. A C × A/m of 0,015 m /kg has an optimal eccentricity of 0,000 04 and a
R
longitude of periapsis and 262,3°, whereas the C × A/m of 0,03 m /kg has optimal values of 0,000 09 and
R
37,3°. Linearly interpolating would imply optimal values of 0,000 057 and 307,3° for a C × A/m of 0,02 m /kg.
R
Instead, the C × A/m = 0,02 optimal value was actually 0,000 015 and 47,3°. In this case, the optimal point
R
switched from one maximum to another, and therefore the intermediate maximum would actually be close to
one point or the other.
Therefore, when confronted with angular changes greater than 90°, it is recommended that interpolation not
be performed. Instead, the closer value should be used either directly or as a starting point for a more refined
search.
A few final comments on the general behaviour of the system are warranted. When the A/m was small
(C × A/m < 0,01), the optimal angle was pointed at the lunar apogee; when the A/m was large
R
(C × A/m > 0,03), the solar radiation pressure force became dominant and the optimal angle was directed
R
toward the sun.
Table A.1 — Optimal eccentricity vector for C × A/m = 0,00 m /kg,
R
2 2
C × A/m = 0,005 m /kg and C × A/m = 0,01 m /kg
R R
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2006 1 281 0,000 115 132,3 0,000 065 142,3 0,000 090 177,3
2 314 0,000 140 112,3 0,000 115 102,3 0,000 065 102,3
3 341 0,000 140 117,3 0,000 115 117,3 0,000 115 92,3
4 10 0,000 140 142,3 0,000 115 132,3 0,000 090 117,3
5 38 0,000 140 162,3 0,000 115 147,3 0,000 090 127,3
6 68 0,000 115 177,3 0,000 115 167,3 0,000 090 122,3
7 99 0,000 065 167,3 0,000 090 122,3 0,000 140 117,3
8 131 0,000 090 142,3 0,000 140 137,3 0,000 190 137,3
9 160 0,000 115 157,3 0,000 165 157,3 0,000 215 157,3
10 187 0,000 090 167,3 0,000 140 172,3 0,000 215 177,3
11 216 0,000 090 187,3 0,000 140 202,3 0,000 215 207,3
12 246 0,000 165 177,3 0,000 115 207,3 0,000 165 222,3
2007 1 281 0,000 140 187,3 0,000 140 207,3 0,000 140 222,3
2 314 0,000 165 207,3 0,000 165 217,3 0,000 165 232,3
3 341 0,000 165 212,3 0,000 115 227,3 0,000 115 242,3
4 10 0,000 090 217,3 0,000 065 237,3 0,000 040 257,3
5 37 0,000 040 192,3 0,000 015 167,3 0,000 015 147,3
6 68 0,000 115 192,3 0,000 090 172,3 0,000 115 162,3
7 99 0,000 140 202,3 0,000 165 192,3 0,000 140 177,3
8 130 0,000 190 222,3 0,000 165 212,3 0,000 140 197,3
9 159 0,000 165 237,3 0,000 165 222,3 0,000 190 207,3
10 186 0,000 115 207,3 0,000 165 212,3 0,000 240 212,3
11 215 0,000 190 227,3 0,000 240 227,3 0,000 290 227,3
12 246 0,000 165 232,3 0,000 215 237,3 0,000 290 242,3
2008 1 280 0,000 115 237,3 0,000 165 252,3 0,000 215 252,3
2 313 0,000 090 222,3 0,000 115 247,3 0,000 140 262,3
3 342 0,000 115 227,3 0,000 090 252,3 0,000 115 272,3
4 10 0,000 140 227,3 0,000 115 242,3 0,000 065 267,3
5 38 0,000 190 237,3 0,000 115 242,3 0,000 090 252,3
6 69 0,000 165 247,3 0,000 115 247,3 0,000 040 242,3
7 100 0,000 140 237,3 0,000 115 227,3 0,000 140 212,3
8 131 0,000 215 237,3 0,000 240 232,3 0,000 215 222,3
9 160 0,000 215 252,3 0,000 165 242,3 0,000 165 232,3
10 187 0,000 140 262,3 0,000 165 247,3 0,000 190 237,3
11 216 0,000 215 247,3 0,000 115 252,3 0,000 165 242,3
12 247 0,000 090 237,3 0,000 140 242,3 0,000 190 247,3

10 © ISO 2010 – All rights reserved

Table A.1 (continued)
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2009 1 280 0,000 140 242,3 0,000 165 252,3 0,000 265 257,3
2 313 0,000 165 257,3 0,000 190 267,3 0,000 265 272,3
3 342 0,000 165 262,3 0,000 190 272,3 0,000 215 287,3
4 10 0,000 115 262,3 0,000 115 287,3 0,000 140 312,3
5 38 0,000 115 252,3 0,000 065 267,3 0,000 040 347,3
6 69 0,000 115 272,3 0,000 065 282,3 0,000 040 287,3
7 100 0,000 090 287,3 0,000 040 277,3 0,000 015 272,3
8 131 0,000 015 292,3 0,000 015 342,3 0,000 015 192,3
9 160 0,000 040 267,3 0,000 040 227,3 0,000 090 222,3
10 187 0,000 140 297,3 0,000 115 247,3 0,000 115 237,3
11 216 0,000 115 282,3 0,000 140 272,3 0,000 165 262,3
12 247 0,000 090 302,3 0,000 115 287,3 0,000 165 277,3
2010 1 280 0,000 040 33 2,3 0,000 040 277,3 0,000 115 282,3
2 313 0,000 065 282,3 0,000 090 297,3 0,000 165 297,3
3 341 0,000 040 302,3 0,000 090 312,3 0,000 140 307,3
4 10 0,000 065 332,3 0,000 090 342,3 0,000 140 347,3
5 38 0,000 090 352,3 0,000 115 7,3 0,000 165 7,3
6 68 0,000 090 22,3 0,000 115 27,3 0,000 140 37,3
7 99 0,000 065 27,3 0,000 090 47,3 0,000 115 57,3
8 131 0,000 015 337,3 0,000 040 67,3 0,000 065 77,3
9 160 0,000 065 342,3 0,000 015 352,3 0,000 015 322,3
10 187 0,000 090 7,3 0,000 040 7,3 0,000 015 7,3
11 216 0,000 140 37,3 0,000 090 32,3 0,000 040 32,3
12 246 0,000 140 47,3 0,000 065 32,3 0,000 040 17,3
2011 1 279 0,000 140 27,3 0,000 140 12,3 0,000 140 357,3
2 313 0,000 215 42,3 0,000 190 27,3 0,000 215 17,3
3 341 0,000 215 47,3 0,000 215 32,3 0,000 265 27,3
4 10 0,000 165 57,3 0,000 215 52,3 0,000 240 42,3
5 37 0,000 115 57,3 0,000 165 57,3 0,000 215 52,3
6 68 0,000 115 42,3 0,000 165 52,3 0,000 215 57,3
7 99 0,000 190 37,3 0,000 190 47,3 0,000 215 57,3
8 130 0,000 265 47,3 0,000 265 57,3 0,000 265 62,3
9 159 0,000 265 62,3 0,000 265 72,3 0,000 290 77,3
10 186 0,000 215 62,3 0,000 165 72,3 0,000 140 92,3
11 215 0,000 265 57,3 0,000 190 57,3 0,000 165 62,3
12 246 0,000 265 62,3 0,000 190 62,3 0,000 140 62,3

Table A.1 (continued)
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2012 1 279 0,000 240 72,3 0,000 190 67,3 0,000 140 57,3
2 312 0,000 190 67,3 0,000 190 57,3 0,000 165 42,3
3 342 0,000 190 67,3 0,000 215 52,3 0,000 215 42,3
4 10 0,000 240 62,3 0,000 265 57,3 0,000 340 52,3
5 38 0,000 315 67,3 0,000 340 62,3 0,000 415 62,3
6 69 0,000 315 77,3 0,000 365 77,3 0,000 415 72,3
7 100 0,000 240 72,3 0,000 290 77,3 0,000 390 82,3
8 131 0,000 315 72,3 0,000 340 77,3 0,000 365 82,3
9 160 0,000 340 82,3 0,000 340 87,3 0,000 340 92,3
10 187 0,000 290 87,3 0,000 290 97,3 0,000 265 107,3
11 216 0,000 215 87,3 0,000 215 102,3 0,000 190 112,3
12 247 0,000 215 82,3 0,000 140 82,3 0,000 090 87,3
2013 1 279 0,000 290 77,3 0,000 240 72,3 0,000 190 62,3
2 312 0,000 340 82,3 0,000 315 77,3 0,000 290 72,3
3 342 0,000 340 87,3 0,000 340 82,3 0,000 315 77,3
4 10 0,000 315 97,3 0,000 290 87,3 0,000 315 77,3
5 38 0,000 290 92,3 0,000 315 87,3 0,000 365 82,3
6 69 0,000 315 97,3 0,000 390 97,3 0,000 415 92,3
7 100 0,000 290 107,3 0,000 340 102,3 0,000 390 102,3
8 131 0,000 240 112,3 0,000 290 112,3 0,000 340 117,3
9 160 0,000 215 107,3 0,000 240 117,3 0,000 290 122,3
10 187 0,000 265 97,3 0,000 265 112,3 0,000 290 122,3
11 216 0,000 340 102,3 0,000 315 112,3 0,000 265 122,3
12 247 0,000 340 112,3 0,000 290 117,3 0,000 265 127,3
2014 1 280 0,000 265 117,3 0,000 215 127,3 0,000 165 132,3
2 313 0,000 265 112,3 0,000 215 112,3 0,000 190 102,3
3 341 0,000 290 117,3 0,000 265 107,3 0,000 240 102,3
4 10 0,000 315 127,3 0,000 290 122,3 0,000 290 117,3
5 38 0,000 315 137,3 0,000 290 132,3 0,000 265 122,3
6 68 0,000 240 142,3 0,000 240 137,3 0,000 290 122,3
7 99 0,000 190 137,3 0,000 265 127,3 0,000 265 127,3
8 131 0,000 240 127,3 0,000 315 127,3 0,000 365 127,3
9 160 0,000 265 137,3 0,000 315 137,3 0,000 365 142,3
10 187 0,000 290 142,3 0,000 340 152,3 0,000 365 152,3
11 216 0,000 265 152,3 0,000 290 157,3 0,000 315 167,3
12 246 0,000 340 162,3 0,000 265 162,3 0,000 265 177,3

12 © ISO 2010 – All rights reserved

Table A.1 (continued)
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2015 1 279 0,000 315 162,3 0,000 290 172,3 0,000 265 182,3
2 313 0,000 265 177,3 0,000 240 182,3 0,000 215 192,3
3 341 0,000 240 177,3 0,000 215 177,3 0,000 165 182,3
4 10 0,000 190 172,3 0,000 165 162,3 0,000 090 162,3
5 37 0,000 215 162,3 0,000 190 152,3 0,000 190 142,3
6 68 0,000 290 162,3 0,000 315 152,3 0,000 340 142,3
7 99 0,000 315 172,3 0,000 315 162,3 0,000 340 157,3
8 130 0,000 315 182,3 0,000 340 177,3 0,000 365 172,3
9 159 0,000 265 182,3 0,000 290 182,3 0,000 365 177,3
10 186 0,000 290 187,3 0,000 340 187,3 0,000 415 187,3
11 215 0,000 315 197,3 0,000 365 202,3 0,000 415 202,3
12 246 0,000 290 202,3 0,000 340 212,3 0,000 365 212,3
2016 1 279 0,000 215 207,3 0,000 240 217,3 0,000 290 222,3
2 312 0,000 240 192,3 0,000 215 207,3 0,000 215 217,3
3 342 0,000 240 192,3 0,000 215 202,3 0,000 165 212,3
4 10 0,000 290 202,3 0,000 240 202,3 0,000 190 202,3
5 38 0,000 315 207,3 0,000 265 207,3 0,000 190 202,3
6 69 0,000 290 217,3 0,000 240 207,3 0,000 190 207,3
7 100 0,000 290 217,3 0,000 290 202,3 0,000 315 192,3
8 131 0,000 340 222,3 0,000 365 212,3 0,000 365 207,3
9 160 0,000 315 232,3 0,000 340 222,3 0,000 365 217,3
10 187 0,000 265 237,3 0,000 290 232,3 0,000 315 227,3
11 216 0,000 215 222,3 0,000 265 222,3 0,000 315 222,3
12 247 0,000 240 222,3 0,000 290 222,3 0,000 340 232,3
2017 1 279 0,000 315 227,3 0,000 340 232,3 0,000 390 237,3
2 312 0,000 340 237,3 0,000 365 242,3 0,000 390 252,3
3 342 0,000 340 242,3 0,000 340 247,3 0,000 340 257,3
4 10 0,000 290 242,3 0,000 265 252,3 0,000 240 257,3
5 38 0,000 315 242,3 0,000 240 247,3 0,000 190 247,3
6 69 0,000 315 252,3 0,000 265 252,3 0,000 215 252,3
7 100 0,000 290 257,3 0,000 240 257,3 0,000 190 257,3
8 131 0,000 215 257,3 0,000 190 247,3 0,000 190 232,3
9 160 0,000 240 247,3 0,000 240 237,3 0,000 265 227,3
10 187 0,000 265 247,3 0,000 315 242,3 0,000 340 237,3
11 216 0,000 315 257,3 0,000 365 257,3 0,000 415 252,3
12 247 0,000 290 267,3 0,000 365 262,3 0,000 390 262,3

Table A.1 (continued)
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2018 1 280 0,000 240 262,3 0,000 290 267,3 0,000 365 272,3
2 313 0,000 315 262,3 0,000 340 272,3 0,000 365 277,3
3 341 0,000 315 272,3 0,000 340 272,3 0,000 340 287,3
4 10 0,000 290 282,3 0,000 290 292,3 0,000 315 297,3
5 38 0,000 215 287,3 0,000 240 302,3 0,000 240 312,3
6 68 0,000 165 287,3 0,000 115 302,3 0,000 090 312,3
7 99 0,000 190 267,3 0,000 115 277,3 0,000 065 257,3
8 131 0,000 240 277,3 0,000 215 267,3 0,000 165 267,3
9 160 0,000 265 287,3 0,000 215 282,3 0,000 215 272,3
10 187 0,000 240 297,3 0,000 215 277,3 0,000 215 272,3
11 216 0,000 215 292,3 0,000 265 277,3 0,000 265 272,3
12 246 0,000 240 302,3 0,000 290 292,3 0,000 315 282,3
2019 1 279 0,000 190 312,3 0,000 240 307,3 0,000 290 302,3
2 313 0,000 140 327,3 0,000 190 322,3 0,000 240 322,3
3 341 0,000 140 327,3 0,000 190 332,3 0,000 265 337,3
4 10 0,000 115 312,3 0,000 140 332,3 0,000 190 337,3
5 37 0,000 140 307,3 0,000 140 322,3 0,000 140 342,3
6 68 0,000 190 312,3 0,000 165 327,3 0,000 190 342,3
7 99 0,000 215 332,3 0,000 190 342,3 0,000 165 352,3
8 130 0,000 165 347,3 0,000 115 352,3 0,000 140 12,3
9 159 0,000 140 327,3 0,000 090 327,3 0,000 065 307,3
10 186 0,000 165 342,3 0,000 115 332,3 0,000 090 322,3
11 215 0,000 165 2,3 0,000 140 352,3 0,000 115 342,3
12 246 0,000 165 12,3 0,000 140 357,3 0,000 115 342,3
2020 1 279 0,000 115 17,3 0,000 090 347,3 0,000 115 332,3
2 312 0,000 090 352,3 0,000 140 342,3 0,000 190 337,3
3 342 0,000 115 352,3 0,000 165 352,3 0,000 215 347,3
4 10 0,000 165 7,3 0,000 215 7,3 0,000 265 7,3
5 38 0,000 165 22,3 0,000 215 22,3 0,000 290 27,3
6 69 0,000 165 32,3 0,000 190 42,3 0,000 265 47,3
7 100 0,000 165 32,3 0,000 190 47,3 0,000 215 57,3
8 131 0,000 240 37,3 0,000 240 52,3 0,000 240 57,3
9 160 0,000 215 52,3 0,000 215 62,3 0,000 215 72,3
10 187 0,000 165 62,3 0,000 140 72,3 0,000 140 87,3
11 216 0,000 115 52,3 0,000 040 47,3 0,000 015 52,3
12 247 0,000 115 37,3 0,000 090 27,3 0,000 090 12,3

14 © ISO 2010 – All rights reserved

Table A.1 (continued)
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2021 1 279 0,000 215 47,3 0,000 215 37,3 0,000 190 22,3
2 312 0,000 265 62,3 0,000 240 52,3 0,000 190 42,3
3 342 0,000 265 67,3 0,000 265 57,3 0,000 265 52,3
4 10 0,000 215 72,3 0,000 240 62,3 0,000 265 47,3
5 38 0,000 215 67,3 0,000 290 62,3 0,000 365 57,3
6 69 0,000 265 72,3 0,000 340 72,3 0,000 390 72,3
7 100 0,000 265 77,3 0,000 290 82,3 0,000 365 82,3
8 131 0,000 215 77,3 0,000 240 87,3 0,000 265 92,3
9 160 0,000 190 72,3 0,000 190 87,3 0,000 215 97,3
10 187 0,000 240 72,3 0,000 190 82,3 0,000 190 92,3
11 216 0,000 290 77,3 0,000 240 82,3 0,000 215 87,3
12 247 0,000 290 87,3 0,000 240 92,3 0,000 165 92,3
2022 1 280 0,000 240 87,3 0,000 190 82,3 0,000 140 72,3
2 313 0,000 290 82,3 0,000 290 72,3 0,000 265 67,3
3 341 0,000 290 87,3 0,000 290 77,3 0,000 315 67,3
4 10 0,000 290 97,3 0,000 290 92,3 0,000 290 82,3
5 38 0,000 240 102,3 0,000 265 92,3 0,000 290 87,3
6 68 0,000 165 97,3 0,000 215 92,3 0,000 265 92,3
7 99 0,000 190 87,3 0,000 215 92,3 0,000 290 92,3
8 131 0,000 240 92,3 0,000 290 97,3 0,000 365 97,3
9 160 0,000 315 97,3 0,000 340 102,3 0,000 340 112,3
10 187 0,000 315 102,3 0,000 290 117,3 0,000 315 122,3
11 216 0,000 240 102,3 0,000 215 107,3 0,000 190 122,3
12 246 0,000 265 102,3 0,000 240 107,3 0,000 190 112,3
2023 1 279 0,000 215 117,3 0,000 165 117,3 0,000 115 127,3
2 313 0,000 140 122,3 0,000 090 117,3 0,000 040 107,3
3 341 0,000 140 122,3 0,000 090 117,3 0,000 090 82,3
4 10 0,000 165 107,3 0,000 165 97,3 0,000 165 82,3
5 37 0,000 190 112,3 0,000 240 102,3 0,000 265 87,3
6 68 0,000 240 117,3 0,000 290 107,3 0,000 315 102,3
7 99 0,000 190 127,3 0,000 240 122,3 0,000 290 117,3
8 130 0,000 140 112,3 0,000 190 117,3 0,000 240 117,3
9 159 0,000 190 117,3 0,000 190 127,3 0,000 265 127,3
10 186 0,000 190 132,3 0,000 215 142,3 0,000 240 147,3
11 215 0,000 165 152,3 0,000 190 167,3 0,000 215 172,3
12 246 0,000 140 177,3 0,000 140 177,3 0,000 165 192,3

Table A.1 (continued)
2 2 2
L C × A/m = 0,00 m /kg C × A/m = 0,005 m /kg C × A/m = 0,01 m /kg

S R R R
Year Month
(°) e ω + Ω e ω + Ω e ω + Ω
2024 1 279 0,000 090 132,3 0,000 065 177,3 0,000 090 207,3
2 312 0,000 140 127,3 0,000 090 127,3 0,000 040 127,3
3 342 0,000 140 137,3 0,000 090 132,3 0,000 065 117,3
4 10 0,000 140 157,3 0,000 090 147,3 0,000 065 142,3
5 38 0,000 115 172,3 0,000 090 152,3 0,000 090 117,3
6 69 0,000 090 177,3 0,000 115 142,3 0,000 165 127,3
7 100 0,000 115 177,3 0,000 140 162,3 0,000 165 152,3
8 131 0,000 165 217,3 0,000 190 182,3 0,000 215 172,3
9 160 0,000 140 207,3 0,000 165 197,3 0,000 215 192,3
10 187 0,000 090 212,3 0,000 140 202,3 0,000 190 197,3
11 216 0,000 090 172,3 0,000 115 197,3 0,000 165 202,3
12 247 0,000 140 182,3 0,000 140 197,3 0,000 140 202,3
2025 1 279 0,000 165 197,3 0,000 165 217,3 0,000 190 222,3
2 312 0,000 165 217,3 0,000 190 232,3 0,000 190 242,3
3 342 0,000 190 227,3 0,000 190 242,3 0,000 165 252,3
4 10 0,000 115 222,3 0,000 040 172,3 0,000 015 152,3
5 38 0,000 165 217,3 0,000 090 212,3 0,000 040 187,3
6 69 0,000 190 227,3 0,000 140 217,3 0,000 090 207,3
7 1
...