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How Geometry Is Used in Designing Satellites

Written By Monday, 20 December 2021 Add Comment Edit

Group of artificial satellites working together as a system

The GPS constellation calls for 24 satellites to be distributed equally among six orbital planes. Notice how the number of satellites in view from a given point on the Earth's surface, in this example at 40°N, changes with time.

A satellite constellation is a group of artificial satellites working together as a system. Unlike a single satellite, a constellation can provide permanent global or near-global coverage, such that at any time everywhere on Earth at least one satellite is visible. Satellites are typically placed in sets of complementary orbital planes and connect to globally distributed ground stations. They may also use inter-satellite communication.

Other satellite groups [edit]

Satellite constellations should not be confused with:

  • satellite clusters, which are groups of satellites moving very close together in almost identical orbits (see satellite formation flying);
  • satellite series or satellite programs (such as Landsat), which are generations of satellites launched in succession;
  • satellite fleets, which are groups of satellites from the same manufacturer or operator that function independently from each other (not as a system).

Overview [edit]

A bright artificial satellite flare is visible above the Very Large Telescope. Satellite constellations could have an impact on ground-based astronomy.[1]

Satellites in Medium Earth orbit (MEO) and Low Earth orbit (LEO) are often deployed in satellite constellations, because the coverage area provided by a single satellite only covers a small area that moves as the satellite travels at the high angular velocity needed to maintain its orbit. Many MEO or LEO satellites are needed to maintain continuous coverage over an area. This contrasts with geostationary satellites, where a single satellite, at a much higher altitude and moving at the same angular velocity as the rotation of the Earth's surface, provides permanent coverage over a large area.

For some applications, in particular digital connectivity, the lower altitude of MEO and LEO satellite constellations provide advantages over a geostationary satellite, with lower path losses (reducing power requirements and costs) and latency.[2] The propagation delay for a round-trip internet protocol transmission via a geostationary satellite can be over 600ms, but as low as 125ms for a MEO satellite or 30ms for a LEO system.[3]

Examples of satellite constellations include the Global Positioning System (GPS), Galileo and GLONASS constellations for navigation and geodesy in MEO, the Iridium and Globalstar satellite telephony services and Orbcomm messaging service in LEO, the Disaster Monitoring Constellation and RapidEye for remote sensing in sun-synchronous LEO, Russian Molniya and Tundra communications constellations in highly elliptic orbit, and satellite broadband constellations, under construction from Starlink and OneWeb in LEO, and operational from O3b in MEO.

Design [edit]

Walker Constellation [edit]

There are a large number of constellations that may satisfy a particular mission. Usually constellations are designed so that the satellites have similar orbits, eccentricity and inclination so that any perturbations affect each satellite in approximately the same way. In this way, the geometry can be preserved without excessive station-keeping thereby reducing the fuel usage and hence increasing the life of the satellites. Another consideration is that the phasing of each satellite in an orbital plane maintains sufficient separation to avoid collisions or interference at orbit plane intersections. Circular orbits are popular, because then the satellite is at a constant altitude requiring a constant strength signal to communicate.

A class of circular orbit geometries that has become popular is the Walker Delta Pattern constellation. This has an associated notation to describe it which was proposed by John Walker.[4] His notation is:

i: t/p/f

where:

  • i is the inclination;
  • t is the total number of satellites;
  • p is the number of equally spaced planes; and
  • f is the relative spacing between satellites in adjacent planes. The change in true anomaly (in degrees) for equivalent satellites in neighbouring planes is equal to f × 360 / t.

For example, the Galileo Navigation system is a Walker Delta 56°:24/3/1 constellation. This means there are 24 satellites in 3 planes inclined at 56 degrees, spanning the 360 degrees around the equator. The "1" defines the phasing between the planes, and how they are spaced. The Walker Delta is also known as the Ballard rosette, after A. H. Ballard's similar earlier work.[5] [6] Ballard's notation is (t,p,m) where m is a multiple of the fractional offset between planes.

Another popular constellation type is the near-polar Walker Star, which is used by Iridium. Here, the satellites are in near-polar circular orbits across approximately 180 degrees, travelling north on one side of the Earth, and south on the other. The active satellites in the full Iridium constellation form a Walker Star of 86.4°:66/6/2, i.e. the phasing repeats every two planes. Walker uses similar notation for stars and deltas, which can be confusing.

These sets of circular orbits at constant altitude are sometimes referred to as orbital shells.

List of satellite constellations [edit]

Navigational satellite constellations [edit]

Satellite constellations used for navigation
Name Operator Satellites and orbits
(latest design, excluding spares) 		Coverage Services Status Years in service
Global Positioning System (GPS) USSF 24 in 6 planes at 20,180 km (55° MEO) Global Navigation Operational 1993–present
GLONASS Roscosmos 24 in 3 planes at 19,130 km (64°8' MEO) Global Navigation Operational 1995–present
Galileo GSA, ESA 24 in 3 planes at 23,222 km (56° MEO) Global Navigation Operational 2019–present
BeiDou CNSA
  • 3 geostationary at 35,786 km (GEO)
  • 3 in 3 planes at 35,786 km (55° GSO)
  • 24 in 3 planes at 21,150 km (55° MEO)
 Global Navigation Operational
  • 2012–present, Asia
  • 2018–present, globally
NAVIC ISRO
  • 3 geostationary at 35,786 km (GEO)
  • 4 in 2 planes at 250–24,000 km (29° GSO)
 Regional Navigation Operational 2018–present
QZSS JAXA
  • 1 geostationary at 35,786 km (GEO)
  • 3 in 3 planes at 32,600–39,000 (43° GSO)
 Regional Navigation Operational 2018–present

Communications satellite constellations [edit]

Broadcasting [edit]

  • Sirius Satellite Radio
  • XM Satellite Radio
  • Othernet
  • Molniya (discontinued)

Monitoring [edit]

  • Spire (AIS, ADS-B)
  • Iridium (AIS, ADS-B)
  • Hiber Global (IoT)
  • TDRSS

Two-way communication [edit]

Operational communications satellite constellations
Name Operator Constellation design Coverage Freq. Services
Broadband Global Area Network (BGAN) Inmarsat 3 geostationary satellites 82°S to 82°N Internet access
Global Xpress (GX) Inmarsat 5 Geostationary satellites[7] Ka-band Internet access
European Aviation Network (EAN) Inmarsat 1 geostationary satellite Regional S-band Aeronautical Internet access
Globalstar Globalstar 48 at 1400 km, 52° (8 planes)[8] 70°S to 70°N[8] Internet access, satellite telephony
Iridium NEXT Iridium 66 at 780 km, 86.4° (6 planes) Global Internet access, satellite telephony
O3b SES S.A. 20 at 8,062 km, 0° (circular equatorial orbit) 45°S to 45°N Ka-band Internet access
Orbcomm ORBCOMM 17 at 750 km, 52° (OG2) 65°S to 65°N "IoT and M2M communication", AIS
Defense Satellite Communications System (DSCS) 4th Space Operations Squadron Military communications
Wideband Global SATCOM (WGS) 4th Space Operations Squadron 10 geostationary satellites Military communications
ViaSat Viasat, Inc. 4 geostationary satellites Varying Internet access
Eutelsat Eutelsat 20 geostationary satellites Commercial
Thuraya Thuraya 2 geostationary satellites EMEA and Asia Internet access, satellite telephony
Starlink SpaceX LEO in several orbital shells
  • ~1000 satellites at 550 km (Feb 2021)
  • 12000 satellites at ~350–550 km (planned)
  • 44°S to 52°N (Feb 2021)
  • Global (planned)
  • Ku (12–18 GHz)
  • Ka (26.5–40 GHz)
 Internet access[9] [10] [11]

Some systems were proposed but never realised:

Abandoned communication satellite constellation designs
Name Operator Constellation design Freq. Services Status
Celestri Motorola 63 satellites at 1400 km, 48° (7 planes) Ka-band (20/30 GHz) Global, low-latency broadband Internet services Abandoned in May 1998
Teledesic Teledesic
  • 840 satellites at 700 km, 98.2° (21 planes) [1994 design]
  • 288 satellites at 1400 km, 98.2° (12 planes) [1997 design]
 Ka-band (20/30 GHz) 100 Mbit/s up, 720 Mbit/s down global internet access Abandoned in October 2002

Other systems are proposed or currently being developed:

Proposed internet satellite constellations[12]
Constellation Manufacturer Number Weight Unveil. Avail. Altitude Offer Band Inter-sat.
links
Boeing Boeing Satellite 1,396–2,956 N/A 2016 N/A
  • 1,200 km
  • 745 mi
 Broadband V (40–75 GHz) None [13] [14]
LeoSat Thales Alenia 78–108
  • 1,250 kg
  • 2,755 lb
 2015 2022
  • 1,400 km
  • 895 mi
 100 Mbit/s increments Ka (26.5–40 GHz) Optical[15]
OneWeb constellation OneWeb and Airbus JV 882–1980[16]
  • 145 kg
  • 320 lb
 2015 2020[17]
  • 1,200 km
  • 745 mi
 Up to 595Mbit/s[17] with 32ms latency[18]
  • Ku (12–18 GHz)
  • Ka (26.5–40 GHz)
 None [19] [20]
O3b mPOWER, (SES S.A.) Boeing 11 1700 kg 2017 2021
  • 8,000 km
  • 4,970 mi
  • 50Mbit/s – 10Gbit/s, each user[21] [22]
  • 45°S to 45°N
 Ka (26.5–40 GHz) None
Telesat LEO
  • Airbus SSTL
  • SS/Loral[a]
117–512[23] N/A 2016 2021 1,000–1,248 km
621–775 mi 		Fiber-optic cable-like Ka (26.5–40 GHz) Optical[24] [25]
Hongyun[26] CASIC 156 2017 2022 160–2,000 km
99–1,243 mi
Hongyan[27] CASC 320-864[28] 2017 2023 1,100–1,175 km
684–730 mi
Project Kuiper Amazon 3236 2019 590–630 km
370–390 mi 		56°S to 56°N[29]
  1. ^ first two prototypes
Progress
  • Boeing Satellite is transferring the application to OneWeb[30]
  • LeoSat shut down completely in 2019[31]
  • The OneWeb constellation had 6 pilot satellites in February 2019, 74 satellites launched as of 21 March 2020[32] but filed for bankruptcy on 27 March 2020[33] [34]
  • Starlink: first mission (Starlink 0) launched on 24 May 2019; 955 satellites launched, 51 deorbited, 904 in orbit as of 25 November 2020[update]; public beta test in limited latitude range started in November 2020[35]
  • O3b mPOWER: first 3 satellites to launch Q3 2021; 8 more in 2022-2024[36]
  • Telesat LEO: two prototypes: 2018 launch
  • CASIC Hongyun: prototype launched in December 2018[37]
  • CASC Hongyan prototype launched in December 2018,[38] might be merged with Hongyun[39]
  • Project Kuiper: FCC filing in July 2019

Earth observation satellite constellations [edit]

  • RADARSAT Constellation
  • Planet Labs
  • Pléiades 1A and 1B
  • RapidEye
  • Disaster Monitoring Constellation
  • A-train
  • SPOT 6 and SPOT 7
  • Spire

See also [edit]

  • Satellite internet constellation
  • Light pollution
  • Types of geocentric orbit

Notes [edit]

References [edit]

  1. ^ "On the increasing number of satellite constellations". www.eso.org . Retrieved 10 June 2019.
  2. ^ LEO constellations and tracking challenges Satellite Evolution Group, September 2017, Accessed 26 March 2021
  3. ^ Real-Time Latency: Rethinking Remote Networks Telesat, February 2020, Accessed 26 March 2021
  4. ^ J. G. Walker, Satellite constellations, Journal of the British Interplanetary Society, vol. 37, pp. 559-571, 1984
  5. ^ A. H. Ballard, Rosette Constellations of Earth Satellites, IEEE Transactions on Aerospace and Electronic Systems, Vol 16 No. 5, Sep. 1980.
  6. ^ J. G. Walker, Comments on "Rosette constellations of earth satellites", IEEE Transactions on Aerospace and Electronic Systems, vol. 18 no. 4, pp. 723-724, November 1982.
  7. ^ https://www.inmarsat.com/en/solutions-services/enterprise/services/land-xpress.html. Retrieved 1 November 2021.
  8. ^ a b "Globalstar satellites". www.n2yo.com . Retrieved 2019-11-22 .
  9. ^ "This is how Elon Musk plans to use SpaceX to give internet to everyone". CNET. 21 February 2018.
  10. ^ "SpaceX Set to Launch 2 Starlink Satellites to Test Gigabit Broadband". ISPreview. 14 February 2018. Retrieved 10 January 2019.
  11. ^ Sep 2020, Michael Kan 9; P.m, 8:04 (2020-09-09). "SpaceX's Satellite Internet Service Latency Comes in Under 20 Milliseconds". PCMag UK . Retrieved 2020-10-23 . CS1 maint: numeric names: authors list (link)
  12. ^ Thierry Dubois (Dec 19, 2017). "Eight Satellite Constellations Promising Internet Service From Space". Aviation Week & Space Technology.
  13. ^ The Boeing Company (June 22, 2016). "SAT-LOA-20160622-00058". FCC Space Station Applications . Retrieved February 23, 2018.
  14. ^ The Boeing Company (June 22, 2016). "SAT-LOA-20161115-00109". FCC Space Station Applications . Retrieved February 23, 2018.
  15. ^ LeoSat Enterprises. "A NEW TYPE OF SATELLITE CONSTELLATION". Retrieved February 23, 2018.
  16. ^ "OneWeb asks FCC to authorize 1,200 more satellites". SpaceNews. 2018-03-20. Retrieved 2018-03-23 .
  17. ^ a b "OneWeb hardware finally coming together". SpaceNews. 3 October 2017. Retrieved 21 October 2018.
  18. ^ Brodkin, Jon (2019-07-17). "OneWeb's low-Earth satellites hit 400Mbps and 32ms latency in new test". Ars Technica . Retrieved 2020-10-23 .
  19. ^ WorldVu Satellites Limited (April 28, 2016). "ONEWEB NON-GEOSTATIONARY SATELLITE SYSTEM - ATTACHMENT A". FCC Space Station Applications . Retrieved February 23, 2018.
  20. ^ WorldVu Satellites Limited (April 28, 2016). "SAT-LOI-20160428-00041". FCC Space Station Applications . Retrieved February 23, 2018.
  21. ^ "Boeing to Build Four Additional 702X Satellites for SES's O3b mPOWER Fleet" (Press release). Boeing. 7 August 2020. Retrieved 29 March 2021.
  22. ^ SES building a 10-terabit O3b mPower constellation, SpaceNews, 11 September 2017, Accessed 29 March 2021
  23. ^ "Telesat says ideal LEO constellation is 292 satellites, but could be 512". SpaceNews. 11 September 2018. Retrieved 10 January 2019.
  24. ^ Telesat Canada (August 24, 2017). "Telesat Technical Narrative". FCC Space Station Applications . Retrieved February 23, 2018.
  25. ^ Telesat Canada (August 24, 2017). "SAT-PDR-20170301-00023". FCC Space Station Applications . Retrieved February 23, 2018.
  26. ^ Zhao, Lei (5 March 2018). "Satellite will test plan for communications network". China Daily . Retrieved 20 December 2018.
  27. ^ Jones, Andrew (13 November 2018). "China to launch first Hongyan LEO communications constellation satellite soon". GBTimes . Retrieved 20 December 2018.
  28. ^ @EL2squirrel (12 December 2019). "Chinese version of OneWeb: The Hongyan system consists of 864 satellites, with 8Tbps of bandwidth, Orbital altitude 1175km" (Tweet). Retrieved 16 December 2019 – via Twitter.
  29. ^ Porter, Jon (2019-04-04). "Amazon will launch thousands of satellites to provide internet around the world". The Verge . Retrieved 2019-11-17 .
  30. ^ "Boeing wants to help OneWeb satellite plans". Advanced Television. 2017-12-17. Retrieved 2018-10-21 .
  31. ^ "LeoSat, absent investors, shuts down".
  32. ^ "OneWeb increases mega-constellation to 74 satellites". 2020-03-21. Retrieved 2020-04-07 .
  33. ^ "Coronavirus: OneWeb blames pandemic for collapse". 2020-03-30. Retrieved 2020-04-07 .
  34. ^ "Voluntary Petition for Non-Individuals Filing for Bankruptcy" (PDF). Omni Agent Solutions. 2020-03-27. Retrieved 2020-04-07 .
  35. ^ Samantha Mathewson (6 November 2020). "SpaceX opens Starlink satellite internet to public beta testers: report".
  36. ^ SES S.A. "Annual Report 2020" (PDF) . Retrieved 29 March 2021.
  37. ^ Barbosa, Rui C. (21 December 2018). "Chinese Long March 11 launches with the first Hongyun satellite". NASASpaceFlight.com . Retrieved 24 December 2018.
  38. ^ Barbosa, Rui (29 December 2018). "Long March 2D concludes 2018 campaign with Hongyan-1 launch". NASASpaceFlight.com . Retrieved 29 December 2018.
  39. ^ @Cosmic_Penguin (14 December 2019). "Notice that these satellites from CASC are mentioned as part of a "national satellite Internet system". There are rumors that several of the planned Chinese private LEO comsat constellations have been recently absorbed into one big nationalized one" (Tweet). Retrieved 16 December 2019 – via Twitter.

External links [edit]

Satellite constellation simulation tools:

  • AVM Dynamics Satellite Constellation Modeler
  • SaVi Satellite Constellation Visualization
  • Transfinite Visualyse Professional

More information:

  • Internetworking with satellite constellations - a PhD thesis (2001)
  • Lloyd's satellite constellations - last updated 20 July 2011
  • Examination and analysis of polar low Earth orbit constellation-IEEE

How Geometry Is Used in Designing Satellites

Source: https://en.wikipedia.org/wiki/Satellite_constellation

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