Satellite Prediction Library

SatelliteKit is a library, written in Swift, implementing the SGP4/SDP4 earth-orbiting satellite propagation algorithms first published in the SpaceTrack Report #3 and later refined by Vallado et al in Revisiting Spacetrack Report #3.

The code of this library is derived from Orekit which implements the above published algorithms as a small part of it's extensive capabilities. Test output from SatelliteKit agrees, to meaninglessly high precision, with Orekit test output and the test output in the above published paper [1].

[1] "Vallado, David A.; Paul Crawford; Richard Hujsak; T. S. Kelso, (August 2006), Revisiting Spacetrack Report #3".

Some people will be surprised by some of my source code comment format; it is a style I inherited from a systems programming language I used long ago and it is really not appropriate for publicly released code in the modern age (especially since Swift has markup built in).

Also note that there is extensive use of Unicode characters in property names and other places. This attempts to match, as much as is reasonable, the mathematical notation and Greek characters usage in the original 1980 Spacetrack Report.

At the end of the README. Lastest change: Version/Tag 2.1.0 -- (2025 Aug 03)

Significant contributed changes. Source compatibility maintained.

The temporary changes to accommodate throwing in the position and velocity functions has been reversed which is a source-incompatible change. Any use of position_throwz() can be replaced with position() though the throwz versions remain available.

The core of SatelliteKit operates to generate a 6-D vector of the orbiting object's position (x, y, z) and velocity (ẋ, ẏ, ż) at the given time. That 6-D vector is the struct PVCoordinates and it is derived in the (public) getPVCoordinates function which calls the (private) computePVCoordinates function. When a propagation anomaly is detected within computePVCoordinates an error is thrown and getPVCoordinates throws it into the public API.

The programmer can catch errors from getPVCoordinates and take appropriate action, however, the two functions Satellite.position and Satellite.velocity (which make direct calls to getPVCoordinates) are more commonly used to obtain an object's position and velocity and they do not process the errors gracefully -- instead they cause an immediate failure and exit from the running program.

Some of the possible errors are not outlandish (for examples, a satellite in a low orbit may decay, elements may be loaded that contain errors, or elements way past their sell-by date may be unpropagatable).

Obviously, this is a bad experience for the user and needs to be corrected. Since merely making Satellite.position and Satellite.velocity throw errors would break existing code, new versions (same basic purpose, but with different names) have been added to catch and re-throw the propagation errors, giving the programmer the ability to dodge a failure and/or display an error alert to the user. The non-throwing versions have also been marked as deprecated so the compiler can issue an advisory message.

In the Sample Usage below, the line

    let posInKms = sat.position(minsAfterEpoch: 10.0)

should be recoded as

    do {
        let posInKms = try sat.position_throwz(minsAfterEpoch: 10.0)
    } catch {
    	// code to process the error ..
    }

(This workaround will be temporary -- the next MAJOR release of SatelliteKit will remove the non-throwing functions.)

The Elements structure is initialized from the three lines of elements in a traditional TLE set. Some sources of TLEs provide no first line (which would contain the object's informal name) and, in that case, it is OK to pass a null String into the initializer.

public init(_ line0: String, _ line1: String, _ line2: String) throws

The public properties that are exposed from in the Elements structure are:

public let commonName: String                   // line zero name (if any) [eg: ISS (ZARYA)]
public let noradIndex: UInt                     // The satellite number [eg: 25544]
public let launchName: String                   // International designation [eg: 1998-067A]

public let t₀: Double                           // the TLE t=0 epoch time (days since 1950)
public let e₀: Double                           // TLE .. eccentricity
public let i₀: Double                           // TLE .. inclination (radians).
public let ω₀: Double                           // Argument of perigee (radians).
public let Ω₀: Double                           // Right Ascension of Ascending node (radians).
public let M₀: Double                           // Mean anomaly (radians).
public var n₀: Double = 0.0                     // Mean motion (radians/min)  << [un'Kozai'd]
public var a₀: Double = 0.0                     // semi-major axis (Eᵣ)       << [un'Kozai'd]

public let ephemType: Int                       // Type of ephemeris.
public let tleClass: String                     // Classification (U for unclassified).
public let tleNumber: Int                       // Element number.
public let revNumber: Int                       // Revolution number at epoch.

Note that the operation to "un Kozai" the element data is performed inside the initialization because both SGP4 and SDP4 need that adjustment.

The initializer will throw an exception if the numeric parsing of the element data fails, however, it will not do so if the record checksum fails. More complete correctness of the element record can be verified by:

public func formatOK(_ line1: String, _ line2: String) -> Bool

which will return true if the lines are 69 characters long, format is valid, and checksums are good. Note that line0 doesn't take part in the check so is omitted for this function, and that formatOK will emit explicit errors into the log.

There has been concern for some time that the three line element sets will become limited, not least of all because they only allow 5 digits for a object's unique NORAD numeric identifier. It has been proposed to provide other, less constricted, data formats. More information on this move will be found at A New Way to Obtain GP Data (aka TLEs)

SatelliteKit has been changed to allow the ingestion of GP data in a JSON form .. for example, given JSON data, this would decode an array of Elements structures (I'm not catching errors in the example, but you should):

let jsonDecoder = JSONDecoder()
jsonDecoder.dateDecodingStrategy = .formatted(DateFormatter.iso8601Micros)

let tleArray = try jsonDecoder.decode([Elements].self, from: jsonData)
print(Satellite(withTLE: tleArray[0]).debugDescription())
print(Satellite(withTLE: tleArray[1]).debugDescription())
print(Satellite(withTLE: tleArray[2]).debugDescription())

The Elements structure also implements debugDescription which will generate this formatted String

┌─[elements :  0.66 days old]]──────────────────────────────────────────
│  ISS (ZARYA)                 25544 = 1998-067A   rev#:09857 tle#:0999
│     t₀:  2018-02-08 22:51:49 +0000    +24876.95265046 days after 1950
│
│    inc:  51.6426°     aop:  86.7895°    mot:  15.53899203 (rev/day)
│   raan: 297.9871°    anom: 100.1959°    ecc:   0.0003401
│                                        drag:  +3.2659e-05
└───────────────────────────────────────────────────────────────────────

Having obtained the Elements for a satellite (a struct which holds only a description of the orbital elements), it is used to initialize a Satellite struct to manage the propagation of the object's position and velocity as time is varied from the epochal t₀=0 of the element set.
Whether the object requires the "deep space" propagator, or not, is determined within the Satellite initialization.

The Satellite initializers are:

public init(_: String, _: String, _: String)  	// three TLE lines ..
public init(elements: Elements)             	// an Elements struct ..

The Satellite struct offers some public properties and some public functions.

The properties provide some naming information and a "grab bag" directory for whatever you want.

public let tle: Elements                    	// make TLE accessible
public let commonName: String                   // "COSMOS .."
public let noradIdent: String                   // "21332"
public let t₀Days1950: Double                   // days since 1950

public var e: Double { return propagator.e }    //### these vary slowly over time ..
public var i: Double { return propagator.i }    //###
public var ω: Double { return propagator.ω }    //###
public var Ω: Double { return propagator.Ω }    //###

public var extraInfo = [String: AnyObject]()    // the "grab bag" dictionary ..

The functions accept a time argument, either minutes after the satellite's TLE epoch, or Julian Days, and provide celestial postion (Kilometers) and velocity (Kms/sec) state vectors as output.

public func position(minsAfterEpoch: Double) -> Vector
public func velocity(minsAfterEpoch: Double) -> Vector

public func position(julianDays: Double) -> Vector
public func velocity(julianDays: Double) -> Vector

This is a simple invocation of the above:

do {
    let elements = try Elements("ISS (ZARYA)",
                                "1 25544U 98067A   18039.95265046  .00001678  00000-0  32659-4 0  9999",
                                "2 25544  51.6426 297.9871 0003401  86.7895 100.1959 15.54072469 98577")

    let sat = Satellite(elements)
    print(sat.debugDescription())
    let posInKms = sat.position(minsAfterEpoch: 10.0)

} catch {
    print(error)
}

The most commonly publically available form of TLE data is a file containing multiple concatenated TLEs.
The String content of such a file may be processed (records that are empty or start with "#" are dropped then leading and trailing whitespace is stripped and non-breaking spaces are converted to regular spaces) and checked for quality (line length is 69 characters and the checksum is good) within SatelliteKit with the function:

public func preProcessTLEs(_: String) -> [(String, String, String)]

preProcessTLEs consumes a String of TLE records and returns an array of (String, String, String) tuples, one per satellite. The tuple items are the, mildly verified, zeroth, first and second of one satellite's TLE lines. If the TLEs are the two-line variety, the first member of the tuple is an empty String.

Thus, the contents of a TLE file would be mapped to an array of Satellite by:

let satArray = preProcessTLEs(fileContents).map( { return Satellite($0.0, $0.1, $0.2) } )

A more rigorous quality check can be preformed using:

public func formatOK(_: String, _: String) -> Bool

which checks the format of TLE lines "1" and "2" .. using a regex test, a time consuming action that is not performed in preProcessTLEs.

SatelliteKit can be added to your project using the Swift Package Manager (SPM) by adding the dependency:

.package(url: "https://github.com/gavineadie/SatelliteKit.git", from: "1.0.0")

and using import SatelliteKit in code that needs it.

SatelliteKit has been used for applications on iOS devices (iPhone, iPad and TV), and Macintosh computers (SwiftUI, AppKit and command line). It has been exposed to the Windows and Unix Swift enviroment briefly, but not tested rigorously.

Translation from C++ and Java, testing and distribution by Gavin Eadie

version/tag 1.0.0 .. (2019 Jun 14)

• First Swift Package Manager (SwiftPM) version.

version/tag 1.0.8 .. (2019 Oct 03)

• Corrects an error in the computation of azimuth-elevation-distance.

version/tag 1.0.9 .. (2019 Oct 03)

• move debugDescription() from the Elements structure to the Satellite structure

• remove public access to dragCoeff (it's never used)

version/tag 1.0.16 .. (2020 Jan 27)

• update copyright year to 2020

version/tag 1.0.20 .. (2020 Feb 26)

• correct and clarify the conversion of satellite position as seen by an observer after a bug in eci2top(..) was corrected.

version/tag 1.0.21 .. (2020 Mar 09)

• include the age (time since t₀ epoch) of the Elements set in its debugDescription(..).

version/tag 1.0.22 .. (2020 Apr 25)

• Package description specifies: .macOS(.v10_12), .iOS(.v9)

version/tag 1.0.23 .. (2020 Jun 04)

• Partial preparation for new NORAD General Perturbations (GP) Element Set formats which accommodate NORAD catalog IDs that are more than 5 digits ..

version/tag 1.0.24 .. (2020 Jun 04)

• provide an (EXPERIMENTAL) Elements initializer that consumes a JSON version of the new NORAD GP Element Set.
• the TLE property launchName has been expanded from, for example: 98067A to 1998-067A .. since this property is mostly decorative, with no semantic value, this is not treated as an API change

version/tag 1.0.25 .. (2020 Jun 07)

• clean up the JSON version of the Elements initializer.
• start work on an (EXPERIMENTAL) XML version of the Elements initializer.

version/tag 1.0.26 .. (2020 Jun 30)

• move "Satellite.swift" from "Astro" group to "SGP" group.

version/tag 1.0.27 .. (2021 Jan 30)

• make the Elements struct accessible from the Satellite struct.

version/tag 1.0.27 .. (2021 Mar 05)

• SpaceTrack Alpha-5
• TLEs with the new Space-Track Alpha-5 object numbers (noradIndex) are processed correctly.
• The tag has not changed because this feature has been present for some time.

version/tag 1.0.28 .. (2021 May 14)

• Alpha-5 NORAD numbers are decoded correctly (no functional change).

version/tag 1.0.30 .. (2022 Feb 17)

• SwiftPM: remove linkerSettings .. adjust copyright year "..-22"

version/tag 1.0.31 .. (2022 Feb 19)

• Elements initialization: factored out unKozai()

• moved XML parsing to own file

• revised the XML unit test

• NOTE: API CHANGES (minor version number changed .. backward compatible, for now)**

version/tag 1.1.0 .. (2022 Feb 28)

• TLE struct replaced with Elements
• TLE typealias'd to Elements (for backward compatibility)
• (for example) debugDescription() is now a method on Elements
• TLEPropagator class replaced with Propagator .. (private anyway)
• noradIndex can't be negative so made UInt
• some time functions moved to TimeUtility.swift
• Elements.n₀ʹ removed from public

version/tag 1.1.1 .. (2022 Mar 02)

• JSON import much improved
• JSON export implemented
• TLE struct deprecated

version/tag 1.1.2 .. (2022 Mar 05)

• XML import much improved
• Objection to tleClass == "U" removed [Starlinks are "C"]

version/tag 1.1.3 .. (2022 Oct 10)

• XML import made more tolerant (eg: OBJECT_ID can be null)
• JSON import made to deal with numeric values (like INCLINATION) being numbers (Celestrak) or strings (Space-Track)
• add unit tests for above

version/tag 1.1.4 .. (2023 Jan 07)

• Copyright extended to 2023
• accommodate Xcode 14

version/tag 1.1.5 .. (2023 Aug 26)

• tag 1.0.17 changed to WGS-84 constants which caused a divergence between the Vallado results and the results of this library. That change is reversed, as it should be, because Vallado's algorithms are built expecting WGS-72 constants. Now the results from this library and Vallado's agree, again, to a ridiculous extent !
• minor edits to README (no functional changes)
• accommodate Xcode 15

version/tag 1.1.6 .. (2023 Sep 27)

• add more, and more recent, platforms to the manifest

version/tag 1.1.7 .. (2023 Nov 06)

• MathUtility .. improve vector dot and cross products (and unit tests) ..
• ThreeLineElementTests .. adjust unit tests results for reversion to WGS-72 ..

version/tag 1.1.8 .. (2023 Nov 27)

• add explicit minimum support for macOS(.v13), .iOS(.v16), .tvOS(.v16), .watchOS(.v9) ..

version/tag 1.2.0 .. (2024 Jan 08)

• copyright to 2024 ..

version/tag 1.2.1 .. (2024 Feb 27)

• correct day display in elements.prettyprint ..

version/tag 1.2.2 .. (2024 Aug 24)

• account for a blank character in the BTERM exponent ..

version/tag 1.2.3 .. (2024 Sep 11)

• throwing versions of Satellite position/velocity functions added -- for example position_throwz(minsAfterEpoch..)
• Package support for .macOS(.v11), .iOS(.v12), .tvOS(.v12), .watchOS(.v4), .visionOS(.v1)
• macOS 13 and iOS 15/16 required for non-default uses ..

version/tag 1.2.4 .. (2024 Sep 12)

• converting the non-throwing versions of Satellite position/velocity functions to throwing functions would break source compatibility if the same function names were maintained, hence the use of _throwz versions. The next MAJOR release of SatelliteKit will make those breaking changes.

  @available(*, deprecated ..) tags have been added to the non-throwing versions. They are not actually deprecated but this allows the compiler to issue a message informing of the throwing versions.

  Since the non-throwing versions are used internally by SatelliteKit, there have been private duplicates of those added for internal libaray use only.

version/Tag 2.0.0 -- (2025 Feb 16)

• SatelliteKit version 2 is, nominally, a major upgrade though, in fact, not much has changed, and nothing computationally. It is compatible with Swift 6 and required couple of minor source code changes in its clients.

  • The use of the ..._throwz() functions can be replaced with non-throwz versions.

  • The function:

    topPosition(minsAfterEpoch: Double, obsLatLonAlt: LatLonAlt)

    is now:

    topPosition(minsAfterEpoch: Double, observer: LatLonAlt)

version/Tag 2.1.0 -- (2025 Aug 03) -- contributed by Mathis Gaignet

Swift 6 Sendable compatibility and Swift Testing migration

• Migrated from class-based inheritance to protocol-based architecture
• Added Sendable conformance to all public types
• Replaced PropagatorProtocol with Propagable protocol
• Implemented SGP4Propagator, SDP4Propagator, DeepSDP4Propagator structs
• Updated Satellite to use any Propagable instead of Propagator class
• Migrated test suite from XCTest to Swift Testing framework
• Preserved 100% calculation accuracy through delegation pattern
• Added backward compatibility functions for legacy API