



Systems and Protocol Aspects for Circumstellar Environments RG M. Piraux
Internet-Draft                                              Aerospacelab
Intended status: Informational                              J. A. Fraire
Expires: 3 September 2026                    Inria / Saarland University
                                                            2 March 2026


              A code to describe satellite constellations
                draft-piraux-space-constellation-code-01

Abstract

   When considering a satellite constellation forming a non-terrestrial
   network, the characteristics of this constellation heavily influences
   the network topology it forms.  To improve the analysis of such non-
   terrestrial networks across various tools developed by the network
   community, this document proposes a notation to describe common
   constellation patterns.  In addition, this document may serve as an
   introduction to satellite constellations for IETF participants.

About This Document

   This note is to be removed before publishing as an RFC.

   The latest revision of this draft can be found at
   https://mpiraux.github.io/draft-piraux-space-constellation-code/
   draft-piraux-space-constellation-code.html.  Status information for
   this document may be found at https://datatracker.ietf.org/doc/draft-
   piraux-space-constellation-code/.

   Discussion of this document takes place on the Systems and Protocol
   Aspects for Circumstellar Environments RG Research Group mailing list
   (mailto:space@irtf.org), which is archived at
   https://mailarchive.ietf.org/arch/browse/space/.  Subscribe at
   https://www.ietf.org/mailman/listinfo/space/.

   Source for this draft and an issue tracker can be found at
   https://github.com/mpiraux/draft-piraux-space-constellation-code.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.



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   Internet-Drafts are draft documents valid for a maximum of six months
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Copyright Notice

   Copyright (c) 2026 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Conventions and Definitions . . . . . . . . . . . . . . . . .   4
   3.  Satellite constellations  . . . . . . . . . . . . . . . . . .   4
     3.1.  Walker constellations . . . . . . . . . . . . . . . . . .   4
       3.1.1.  Walker Star . . . . . . . . . . . . . . . . . . . . .   5
       3.1.2.  Walker Delta  . . . . . . . . . . . . . . . . . . . .   6
   4.  Constellation code  . . . . . . . . . . . . . . . . . . . . .   7
   5.  Examples of constellation codes . . . . . . . . . . . . . . .   9
   6.  Describing links in a shell . . . . . . . . . . . . . . . . .   9
     6.1.  Detailed specification  . . . . . . . . . . . . . . . . .  10
       6.1.1.  Top-level keys  . . . . . . . . . . . . . . . . . . .  10
       6.1.2.  Shell . . . . . . . . . . . . . . . . . . . . . . . .  10
       6.1.3.  Link pattern  . . . . . . . . . . . . . . . . . . . .  11
       6.1.4.  Condition . . . . . . . . . . . . . . . . . . . . . .  11
       6.1.5.  Expression  . . . . . . . . . . . . . . . . . . . . .  11
   7.  Considerations for future versions of this document . . . . .  11
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  12
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  12
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  12
     10.2.  Informative References . . . . . . . . . . . . . . . . .  12
   Appendix A.  Changelog  . . . . . . . . . . . . . . . . . . . . .  13
     A.1.  Since draft-piraux-space-constellation-code-00  . . . . .  13
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  13






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1.  Introduction

   The network topology of a satellite constellation is heavily
   influenced by its orbital characteristics.  With recent technologies
   enabling Optical Inter-Satellite Links (OISL) between satellites, a
   network is formed by establishing links between neighbour satellites.
   The resulting topology can be dynamic as the distance between
   neighbour satellites changes throughout their orbital period.  A
   common notation for the network community could improve the
   reproducibility of evaluations, measurements and simulations of
   satellite constellation networks.

   The true position of a satellite is often represented using a Two-
   Line Element set (TLE).  A TLE contains a number of fields describing
   the orbital elements at a given time of a given satellite.  Combined
   with a simplified perturbation model, the TLE can be used to predict
   the future position and velocity of the satellite relatively
   accurately.  However, when studying satellite constellations, TLEs
   may not be appropriate.  First, they assume each satellite has a
   known absolute position, which is derived from the launch time and
   parameters which may not be known at the time of study.  Second, they
   involve complex calculations given the chosen perturbation model
   which may not scale well to large-scale experiments.  Third, TLEs are
   not sufficient to determine how the links are established within the
   constellation as they do not indicate its characteristics but only
   the position of its satellites.

   The approach of this document is based on the mission parameters of a
   satellite constellation.  Based on these parameters, the expected
   position of each satellite within the constellation can then be
   computed.  While this approach does not capture the small
   discrepancies that can occur during the launch and operation of the
   satellites, we argue that it is sufficient in our context.

   This version of the specification applies only to circular orbital
   shells.  The rationale for this restriction is that circular orbits
   are the most common in current satellite constellations and simplify
   the code syntax.  Elliptical orbits, such as those used in Molniya or
   Flower constellations, are outside the current scope but could be
   supported in a future extension of this document.

   The notation defined in this document can also specify patterns for
   links within a shell of a constellation.  Each pattern is repeated to
   establish the connectivity of a satellite with its neighbours within
   the shell.  This is inspired by the works of network researchers on
   constellation network topology design [BhSi2019].





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   The rest of this document is organised as follows.  Section 3
   introduces two variants of the Walker pattern for orbital shells.
   These are used to define many of the existing satellite
   constellations.  Section 4 defines the constellation code syntax
   using an ABNF grammar [RFC5234] and the code semantics.  Section 5
   contains examples of existing constellations defined using the
   constellation code.  Section 6 augments the constellation code with a
   pattern notation to describe links within a shell.  Finally,
   Section 7 concludes with considerations for future versions of this
   document.

2.  Conventions and Definitions

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Satellite constellations

   A constellation greatly improves the availability of a satellite
   service up to global or near-global coverage on Earth.  From the user
   perspective, a constellation offers more guarantees that a satellite
   can be reached at all times.  A constellation is composed of a set of
   orbital planes.  Typically, several satellites are present on an
   orbital plane.  They can be close together to perform formation
   flying or are equally spread within the plane.  Orbital planes are
   distributed in a complementary manner, i.e., they share some
   properties (e.g. altitude and inclination) but differ in others (e.g.
   longitude of ascending node).

   When all orbital planes of a constellation are circular orbits
   sharing the same altitude, they are said to constitute an orbital
   shell.  Constellations often consist of a single orbital shell but
   more complex deployments can have several shells.

   The rest of this section describes two common shells based on the
   Walker pattern.

3.1.  Walker constellations

   A Walker constellation consists of circular orbits sharing the same
   inclination.  Two variants of the Walker pattern exist:

   *  Walker Star, where orbits are distributed over 180 degrees around
      the equator.




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   *  Walker Delta, where orbits are distributed over 360 degrees around
      the equator.

3.1.1.  Walker Star

   Figure 1 is an illustration of a Walker Star constellation
   considering the Earth equator as horizontal in the Figure.  The orbit
   trajectories are depicted by a dashed line, while satellites and
   their travel direction are indicated by arrow heads.

   The orbits of a Walker Star constellation typically have an
   inclination close to 90 degrees with respect to the equator plane,
   though this is not a geometric constraint and other inclinations are
   possible.  Given that they are distributed over 180 degrees around
   the equator plane, one half-sphere has satellites ascending from the
   south pole to the north pole while the other has them descending from
   north pole to south pole.  This is depicted on the two sides of
   Figure 1.  Over the south and north poles, all orbits are crossing
   paths before going over the other half-sphere.

                                 /  / \  \
                               , - ~ ~ ~ - ,
                           , '/    ^   v    \' ,
                         ,   ^    /     \    v  ,
                        ,   /    ^       v    \   ,
                       ,   ^     |       |     v   ,
                       ,   |     ^       v     |   ,
                       ,   ^     |       |     v   ,
                        ,   \    ^       v    /   ,
                         ,   ^   \       /   v   ,
                           ,  \   ^     v   / , '
                             ' - , _ _ _ ,  '
                                 \  \ /  /

                   Figure 1: A Walker Star constellation

   In a Walker Star constellation, a seam can be observed at the start
   and end of the orbit distribution around the equator plane.  That is
   the first orbit (resp. last orbit) is next to the last orbit (resp.
   first orbit) going in the opposite direction of the sphere.  It can
   be observed at the center of the Figure 1.  The seam effect in Walker
   Star constellations may limit cross-plane ISL links at the seam
   boundary, though cross-plane links are still possible elsewhere; for
   instance, the Iridium constellation uses a Walker Star pattern with
   cross-plane ISLs.  However, the Delta variant is often preferred for
   OISL-capable constellations due to the absence of the seam effect.





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   Figure 2 illustrates a part of a possible network topology for Walker
   Star constellations, with four orbital planes depicted vertically,
   each containing three satellites.  In this example, links are only
   established in-plane, i.e., within the same orbit, though cross-plane
   links are also possible.  Each orbit forms a ring, where the last
   satellite is connected to the first satellite.

                       :        :        :        :
                       |        |        |        |
                     +~~~+    +~~~+    +~~~+    +~~~+
                     [0/0]    [1/0]    [2/0]    [3/0]
                     +~~~+    +~~~+    +~~~+    +~~~+
                       |        |        |        |
                       |        |        |        |
                     +~~~+    +~~~+    +~~~+    +~~~+
                     [0/1]    [1/1]    [2/1]    [3/1]
                     +~~~+    +~~~+    +~~~+    +~~~+
                       |        |        |        |
                       |        |        |        |
                     +~~~+    +~~~+    +~~~+    +~~~+
                     [0/2]    [1/2]    [2/2]    [3/2]
                     +~~~+    +~~~+    +~~~+    +~~~+
                       |        |        |        |
                       :        :        :        :

           Figure 2: A Walker Star constellation network topology

3.1.2.  Walker Delta

   Figure 3 is an illustration of a Walker Delta constellation with only
   two orbits due to graphical constraints.  The orbits of a Walker
   Delta constellation typically have an inclination ranging from 45 to
   65 degrees with respect to the equator plane, though any inclination
   is geometrically valid.  Combined with the altitude, the inclination
   directly limits the latitude coverage of a constellation, while
   Walker Star constellations have a complete latitude coverage.

   Given that the orbits are distributed around the entire equator
   plane, there is no seam effect as in the Walker Star pattern.
   Instead, each orbit progresses in the same direction and cross paths
   twice with every other orbit.  In this case, satellites can establish
   links with neighbouring orbits in addition to links within the same
   orbit.








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                           /   , - ~ ~ ~ - ,   \
                           , '               ' ,
                         ,   \                   ,
                        ,      ^           /      ,
                       ,         \        v        ,
                       ,           ^   /           ,
                       ,             \v            ,
                        ,           /  ^          ,
                         ,         v     \       ,
                           ,    /             , '
                             ' - , _ _ _ ,  '
                             \               /

                   Figure 3: A Walker Delta constellation

   Figure 4 illustrates a part of a possible network topology for Walker
   Delta constellations, with four orbital planes depicted vertically,
   each containing three satellites.  Links are established in-plane and
   cross-plane, i.e., from one orbit to the other.

                       :        :        :        :
                       |        |        |        |
                     +~~~+    +~~~+    +~~~+    +~~~+
                 ..--[0/0]----[1/0]----[2/0]----[3/0]--..
                     +~~~+    +~~~+    +~~~+    +~~~+
                       |        |        |        |
                       |        |        |        |
                     +~~~+    +~~~+    +~~~+    +~~~+
                 ..--[0/1]----[1/1]----[2/1]----[3/1]--..
                     +~~~+    +~~~+    +~~~+    +~~~+
                       |        |        |        |
                       |        |        |        |
                     +~~~+    +~~~+    +~~~+    +~~~+
                 ..--[0/2]----[1/2]----[2/2]----[3/2]--..
                     +~~~+    +~~~+    +~~~+    +~~~+
                       |        |        |        |
                       :        :        :        :

          Figure 4: A Walker Delta constellation network topology

4.  Constellation code

   Figure 5 defines the constellation code using an ABNF grammar
   [RFC5234].  The code can define a constellation with multiple shells.
   Each shell can follow a Walker Star or Walker Delta pattern.






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       constellation = shell [ "+" constellation ]
       shell = walker ":" altitude ":" inclination ":" plane-params
       shell =/ [ ":" mean-anomaly ]
       walker = "D" / "S"
       altitude = float
       inclination = float
       plane-params = no-sats "/" no-planes "/" phasing-factor
       no-sats = int
       no-planes = int
       phasing-factor = int
       mean-anomaly = float

       int = 1*DIGIT
       float = 1*DIGIT [ "." 1*DIGIT ]
       DIGIT = %x30-39

             Figure 5: ABNF Grammar for the constellation code

   In addition to the grammar presented above defining the syntax of the
   code, a number of requirements on the semantics of the code are
   listed below.

   *  The altitude is expressed in kilometres with reference to the
      Earth's surface.

   *  The inclination is expressed in degrees and MUST be within the
      range of [0, 180] degrees.  Inclinations greater than 90°
      represent retrograde orbits.

   *  The number of satellites must be evenly divisible by the number of
      planes.

   *  The phasing factor must be within the range [0, no-planes - 1].
      It represents the relative offset between satellites in adjacent
      orbital planes.  It determines how satellites in one plane are
      shifted in their orbital position compared to the satellites in
      the neighbouring plane, enabling optimal coverage patterns.

   *  The mean anomaly is expressed in degrees and MUST be within the
      range of [0, 360] degrees.  It is optional and represents the
      orbital position of the first satellite in the first plane of the
      constellation.  When absent it is considered equal to zero.  The
      reference epoch for the mean anomaly is defined by the user's
      simulation environment or application context.







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5.  Examples of constellation codes

   This section provides some examples of how the constellation code can
   be used to define existing satellite constellations sourced from
   public information.  In some cases, when the phasing factor is not
   known, it is speculative.

    +==========+==============================+=======================+
    | Name     | Description                  | Constellation code    |
    +==========+==============================+=======================+
    | Iridium  | Walker Star, 780 km          | S:780:86.4:66/6/1     |
    |          | altitude, 86.4° inclination, |                       |
    |          | 66 satellites, 6 planes      |                       |
    +----------+------------------------------+-----------------------+
    | OneWeb   | Walker Star, 1 200 km        | S:1200:87.9:672/12/11 |
    |          | altitude, 87.9° inclination, |                       |
    |          | 672 satellites, 12 planes    |                       |
    +----------+------------------------------+-----------------------+
    | Starlink | Walker Delta, 550 km         | D:550:53:1584/72/39   |
    | (shell   | altitude, 53° inclination,   | [StFrHe2022]          |
    | 1)       | 1584 satellites, 72 planes   |                       |
    +----------+------------------------------+-----------------------+
    | GPS      | Walker Delta, 20 180 km, 55° | D:20180:55:24/6/1     |
    |          | inclination, 24 satellites,  |                       |
    |          | 6 planes                     |                       |
    +----------+------------------------------+-----------------------+

                  Table 1: Examples of constellation codes

6.  Describing links in a shell

   In this section, we extend the code notation with a complementary
   YAML format to specify the patterns of links within a shell.  Each
   YAML document following the format defined in this I-D specifies a
   constellation that may be composed of several shells.  An example of
   such a document is as follows:















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version: draft-piraux-space-constellation-code-01
shells:
- code: D:1200:55:400/20/19
  link_patterns:
  - rank_offset: 1   # Establish an in-plane link towards the next sat.
  - plane_offset: 1  # Establish a cross-plane link in a staggered pattern
    conditions:      # e.g. when only three links are possible.
    - eq: [{mod: [rank, 2]}, {mod: [plane, 2]}] # rank % 2 == plane % 2

- code: S:1210:89:52/4/1
  link_patterns:
  - rank_offset: 1   # Establish an in-plane link towards the next sat.

      Figure 6: Example of YAML document specifying a two-shell
                            constellation

   Figure 6 specifies a two-shell constellation.  The first shell is a
   Walker Delta shell in which satellites have three links towards
   neighbours.  The second one is a Walker Star pattern with two in-
   plane links per satellite.

   These patterns are encoded through the link_patterns key.  It
   contains a list of patterns with optional conditions.  Each pattern
   can specify how to reach a neighbour given local plane and rank
   offsets to establish a bidirectional link.  For instance, the first
   pattern of the first shell specifies that a link is formed with the
   next satellite in the same orbit.

   For each pattern, a list of conditions can be expressed with the
   conditions key.  These are evaluated for each satellite within the
   shell to determine whether the corresponding pattern should be
   applied to form a link.  By applying each patterns to all satellites,
   the set of links within the constellation shell is established.

6.1.  Detailed specification

6.1.1.  Top-level keys

   version  Indicates the version of this I-D that the YAML document
      should be interpreted with.

   shells  A list of shells.

6.1.2.  Shell

   code  The shell code following the specification in Section 4.

   link_patterns  A list of link patterns.



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6.1.3.  Link pattern

   rank_offset  An integer specifying the offset in rank to reach the
      neighbour for this link.

   plane_offset  An integer specifying the offset in plane to reach the
      neighbour for this link.  When this offset causes the plane index
      to wrap around to the first plane, the rank index of the target
      satellite is adjusted according to the phasing factor of the
      shell.

   Both types of offset can be included for a single pattern.  When one
   is absent, it is considered to be equal to zero.  In addition, they
   naturally wrap around at the boundaries of a shell.

   conditions  A list of conditions that must be met for this link to be
      added.

6.1.4.  Condition

   Each condition is a predicate on two expressions encoded as mapping.
   The predicate is the key while the two expressions form a sequence as
   the value.  This version of the document only specifies the equality
   predicate indicated by the eq key.

6.1.5.  Expression

   It can be an integer, a context element or an operation on two
   expressions.  Context elements are strings and include rank for the
   current rank index and plane for the current plane index of the
   satellite considered when evaluating a given link pattern.

   An operation is encoded as mapping, with the key defining the type of
   operation and the value containing a sequence with the two
   expressions.  This version of the document only specifies the modulo
   operation indicated by the mod key.

7.  Considerations for future versions of this document

   The code presented in this document does not consider the
   capabilities of satellites within a constellation to establish links.
   It focuses on defining the stable network topology that is expected
   for a constellation.  Future versions of this document could consider
   means to define the capabilities of Optical Communication Terminals
   (OCTs) used to establish ISLs.  This is complementary to the
   description of the network topology, which forms more of an intent,
   while capabilities define the space of possible links.




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8.  Security Considerations

   As the code specified in this document is foreseen as a user input
   into software that performs simulations, evaluations and analysis of
   satellite constellations, implementers SHOULD consider validation and
   sanitisation measures.

9.  IANA Considerations

   This document has no IANA actions.

10.  References

10.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/rfc/rfc2119>.

   [RFC5234]  Crocker, D., Ed. and P. Overell, "Augmented BNF for Syntax
              Specifications: ABNF", STD 68, RFC 5234,
              DOI 10.17487/RFC5234, January 2008,
              <https://www.rfc-editor.org/rfc/rfc5234>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/rfc/rfc8174>.

10.2.  Informative References

   [BhSi2019] Bhattacherjee, D. and A. Singla, "Network topology design
              at 27,000 km/hour", ACM, Proceedings of the 15th
              International Conference on Emerging Networking
              Experiments And Technologies pp. 341-354,
              DOI 10.1145/3359989.3365407, December 2019,
              <https://doi.org/10.1145/3359989.3365407>.

   [StFrHe2022]
              Stock, G., Fraire, J., and H. Hermanns, "Distributed On-
              Demand Routing for LEO Mega-Constellations: A Starlink
              Case Study", IEEE, 2022 11th Advanced Satellite Multimedia
              Systems Conference and the 17th Signal Processing for
              Space Communications Workshop (ASMS/SPSC) pp. 1-8,
              DOI 10.1109/asms/spsc55670.2022.9914716, September 2022,
              <https://doi.org/10.1109/asms/spsc55670.2022.9914716>.





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   [TvdLCode] Tim van der Lee, "Constellation Code", July 2023,
              <https://github.com/Tim024/ConstellationCode>.

Appendix A.  Changelog

A.1.  Since draft-piraux-space-constellation-code-00

   *  Add YAML format to specify link patterns within shells of a
      constellation.

   *  Improvement of the text and examples.

Acknowledgments

   We thank Tim van der Lee for his work on a code [TvdLCode] that
   served as the basis for this document.

Authors' Addresses

   Maxime Piraux
   Aerospacelab
   Email: maxime.piraux@aerospacelab.com


   Juan A. Fraire
   Inria / Saarland University
   Email: juan.fraire@inria.fr
























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