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Orbit Propagator Kepler (unperturbed)

Propagate orbit of one or more spacecraft using Kepler universal variable formulation

Since R2020b

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  • Orbit Propagator Kepler (unperturbed) block

Libraries:
Aerospace Blockset / Spacecraft / Spacecraft Dynamics

Alternative Configurations of Orbit Propagator Kepler (unperturbed) Block:
Orbit Propagator Numerical (high precision)

Description

The Orbit Propagator Kepler (unperturbed) block propagates the orbit of one or more spacecraft using the Kepler universal variable formulation. The Orbit Propagator Kepler (unperturbed) and Orbit Propagator Numerical (high precision) blocks are alternative configurations of the same block.

  • Orbit Propagator Kepler (unperturbed) — Kepler universal variable formulation (quicker)

  • Orbit Propagator Kepler Numerical (high precision) — More accurate

The Orbit Propagator Kepler (unperturbed) block does not take into account atmospheric drag, third body gravity, or solar radiation pressure. For orbit propagations that take these effects into account, see the Orbit Propagator Numerical (high precision) block.

The size of the provided initial conditions determines the number of spacecraft being modeled. If you supply more than one value for a parameter in the Orbit tab, the block outputs a constellation of satellites. Any parameter with a single provided value is expanded and applied to all the satellites in the constellation. For example, if you provide a single value for all the parameters on the block except True anomaly, which contains six values, the block creates a constellation of six satellites, varying true anomaly only.

The block applies the same expansion behavior to input port A_icrf (applied acceleration). This port accepts either a single value expanded to all spacecraft being modeled, or individual values to apply to each spacecraft.

For more information on the propagation methods the Orbit Propagator blocks use, see Orbit Propagation Methods.

You can define initial orbital states in the Orbit tab as:

  • A set of orbital elements

  • Position and velocity state vectors in International Celestial Reference Frame (ICRF) or fixed-frame coordinate systems.

The block uses quaternions, which are defined using the scalar-first convention.

For more information on the coordinate systems the Orbit Propagator blocks use, see Coordinate Systems.

Examples

Constellation Modeling with the Orbit Propagator Block

Constellation Modeling with the Orbit Propagator Block

Propagate the orbits of a constellation of satellites and compute and visualize access intervals between the individual satellites and several ground stations.

Mission Analysis with the Orbit Propagator Block

Mission Analysis with the Orbit Propagator Block

Compute and visualize line-of-sight access intervals between satellites and a ground station.

Lunar Mission Analysis with the Orbit Propagator Block

Lunar Mission Analysis with the Orbit Propagator Block

Compute and visualize access intervals between the Apollo Command and Service module and a rover on the lunar surface. The module's orbit is modeled using Reference Trajectory #2 from the NASA report Variations of the Lunar Orbital Parameters of the Apollo CSM-Module [2]. This is a lunar orbit studied by NASA for the Apollo program. The example uses:

High Precision Orbit Propagation of the International Space Station

High Precision Orbit Propagation of the International Space Station

Propagate the order of the International Space Station (ISS) using high precision numerical orbit propagation.

Ports

Output

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Position of the spacecraft with respect to (ICRF or fixed-frame), returned as a 3-element vector or numSat-by-3 array, where m is number of spacecraft, at the current time step. The size of the initial conditions provided in the Orbit tab control the port dimension. numSat is the number of spacecraft.

Data Types: double

Velocity of the spacecraft with respect to ICRF or fixed-frame, returned as a 3-element vector or numSat-by-3 array, at the current time step. numSat-by-3 array. The size of the initial conditions provided in the Orbit tab control the port dimension.

Data Types: double

Time at current time step, returned as a:

  • scalar — If you specify the Start data/time parameter as a Julian date.

  • 6-element vector — If you specify the Start data/time parameter as a Gregorian date with six elements (year, month, day, hours, minutes, seconds).

This value is equal to the Start date/time parameter value + the elapsed simulation time.

Dependencies

To enable this parameter, select the Output current date/time (UTC Julian date) check box.

Data Types: double

Parameters

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Main

Orbit propagation method, specified as:

  • Kepler (unperturbed) — Uses a universal variable formulation of the Kepler problem to determine the spacecraft position and velocity at each time step. This method is faster than Numerical (high precision).

  • Numerical (high precision) — Determine the spacecraft position and velocity at each time step using numerical integration. This option models central body gravity based on the settings in the Central body tab. This method is more accurate than Kepler (unperturbed), but slower.

Programmatic Use

Block Parameter: propagator
Type: character vector
Values: 'Kepler (unperturbed)' | 'Numerical (high precision)'
Default: 'Kepler (unperturbed)'

To enable additional external accelerations to be included in the integration of the spacecraft equations of motion, select this check box. Otherwise, clear this check box.

Dependencies

To enable this check box, set Propagation method to Numerical (high precision).

Programmatic Use

Block Parameter: accelIn
Type: character vector
Values: 'off' | 'on'
Default: 'off'

Input additional accelerations, specified as ICRF or Fixed-frame. These accelerations are included in integration of the spacecraft equations of motion.

Dependencies

To enable this parameter:

  • Set Propagation method to Numerical (high precision)

  • Select the Input external accelerations check box

Programmatic Use

Block Parameter: accelFrame
Type: character vector
Values: 'ICRF' | 'Fixed-frame'
Default: 'ICRF'

Coordinate frame for output ports, specified as ICRF or Fixed-frame. These port labels are affected:

  • Output port X

  • Output port V

Dependencies

To enable this parameter, set Propagation method to Numerical (high precision).

Programmatic Use

Block Parameter: outportFrame
Type: character vector
Values: 'ICRF' | 'Fixed-frame'
Default: 'ICRF'

Initial start date and time of simulation, specified as a Julian or Gregorian date. The block defines initial conditions using this value.

Tip

To calculate the Julian date, use the juliandate function.

Programmatic Use

Block Parameter: startDate
Type: character vector
Values: 'juliandate(2020, 1, 1, 12, 0, 0)' | valid scalar Julian date | valid Gregorian date including year, month, day, hours, minutes, seconds as 6-element vector
Default: 'juliandate(2020, 1, 1, 12, 0, 0)'

To output the current date or time, select this check box. Otherwise, clear this check box.

Programmatic Use

Block Parameter: dateOut
Type: character vector
Values: 'off' | 'on'
Default: 'off'

Out-of-range block behavior, specified as follows:

ActionDescription
None No action.
Warning

Warning in the Diagnostic Viewer, model simulation continues.

Error (default)

Error in the Diagnostic Viewer, model simulation stops.

Programmatic Use

Block Parameter: action
Type: character vector
Values: 'None' | 'Warning' | 'Error'
Default: 'Warning'

Orbit

Define the initial states of the space craft.

Input method for initial states of orbit, specified as Orbital elements or ICRF state vector.

Programmatic Use

Block Parameter stateFormatKep
Type: character vector
Values: 'Orbital elements' | 'ICRF state vector'
Default: 'Orbital elements'

Orbit classification, specified as:

  • Keplerian — Model elliptical orbits using six standard Keplerian orbital elements.

  • Elliptical equatorial — Define an equatorial orbit, where inclination is 0 or 180 degrees and the right ascension of the ascending node is undefined.

  • Circular — Define a circular orbit, where eccentricity is 0 and the argument of periapsis is undefined.

  • Circular equatorial — Define a circular orbit, where eccentricity is 0 or 10 degrees. Argument of periapsis and the right ascension of the ascending node are undefined.

Dependencies

To enable this parameter, set Initial state format to Orbital elements.

Programmatic Use

Block Parameter: orbitType
Type: character vector
Values: 'Keplerian' | 'Elliptical equatorial' | 'Circular inclined' | 'Circular equatorial'
Default: 'Keplerian'

Half of ellipsis major axis, specified as a 1D array whose size is the number of spacecraft.

  • For parabolic orbits, this block interprets this parameter as the periapsis radius (distance from periapsis to the focus point of orbit).

  • For hyperbolic orbits, this block interprets this parameter as the distance from periapsis to the hyperbola center.

Dependencies

To enable this parameter, set Initial state format to Orbital elements.

Programmatic Use

Block Parameter: semiMajorAxis
Type: character vector
Values: scalar | 1D array of size m, number of spacecraft
Default: '6786000'

Deviation of the orbit from a perfect circle, specified as a scalar or 1D array of size that is number of spacecraft.

If Orbit type is set to Keplerian, value can be:

  • 0 for circular orbit

  • Between 0 and 1 for elliptical orbit

  • 1 for parabolic orbit

  • Greater than 1 for hyperbolic orbit

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements.

  • Orbit type to Keplerian or Elliptical equatorial.

Programmatic Use

Block Parameter: eccentricity
Type: character vector
Values: 0.01 | scalar | value between 0 and 1, or greater than 1 for Keplerian orbit type | 1D array of size numSat
Default: '0.01'

Vertical tilt of the ellipse with respect to the reference plane measured at the ascending node, specified as a scalar or 1D array of size numSat, in specified units. numSat is the number of spacecraft.

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements

  • Orbit type to Keplerian or Circular inclined

Programmatic Use

Block Parameter: inclination
Type: character vector
Values: 50 | scalar | 1D array of size numSat | degrees between 0 and 180 | radians between 0 and pi
Default: '50'

Right ascension of ascending node (RAAN), specified as a scalar value between 0 and 360 or 1D array of size numSat, in specified units. numSat is the number of spacecraft. RAAN is the angular distance along the reference plane from the ICRF x-axis to the location of the ascending node (the point at which the spacecraft crosses the reference plane from south to north).

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements.

  • Orbit type to Keplerian or Circular inclined.

Programmatic Use

Block Parameter: raan
Type: character vector
Values: 95 | scalar value between 0 and 360 | 1D array of size m number of spacecraft
Default: '95'

Angle from the spacecraft ascending node to periapsis (closest point of orbit to the central body), specified as a 1D array of size m that is number of spacecraft, in specified units.

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements

  • Orbit type to Keplerian

Programmatic Use

Block Parameter: argPeriapsis
Type: character vector
Values: '95' | scalar value between 0 and 360 | 1D array of size numSat
Default: '93'

Angle between periapsis (closest point of orbit to the central body) and the initial position of spacecraft along its orbit at Start date/time, specified as a scalar or 1D array of size numSat, in specified units. numSat is the number of spacecraft.

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements.

  • Orbit type to Keplerian or Elliptical inclined.

Programmatic Use

Block Parameter: trueAnomaly
Type: character vector
Values: '203' | scalar | degrees between 0 and 360 | radians between 0 and 2*pi | 1D array of size numSat
Default: '203'

Angle between the ascending node and the initial position of spacecraft along its orbit at Start date/time, specified as a scalar or 3-element vector or 1D array of size number of spacecraft, in specified units.

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements.

  • Orbit Type to Circular inclined.

Programmatic Use

Block Parameter: argLat
Type: character vector
Values: '200' | scalar | degrees between 0 and 360 | radians between 0 and 2*pi | 1D array of size numSat
Default: '200'

Angle between the ICRF x-axis and the eccentricity vector, specified as a scalar or 3-element vector or 1D array of size number of spacecraft, in specified units.

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements.

  • Orbit type to Elliptical equatorial.

Programmatic Use

Block Parameter: lonPeriapsis
Type: character vector
Values: 100 | scalar | degrees between 0 and 360 | radians between 0 and 2*pi | 1D array of size m, number of spacecraft
Default: '100'

Angle between the ICRF x-axis and the initial position of spacecraft along its orbit at Start date/time, specified as a scalar or 1D array of size numSat, in specified units. numSat is the number of spacecraft.

Dependencies

To enable this parameter, set:

  • Initial state format to Orbital elements.

  • Orbit type to Circular equatorial.

Programmatic Use

Block Parameter: trueLon
Type: character vector
Values: '150' | scalar | degrees between 0 and 360 | radians between 0 and 2*pi | 1D array of size numSat
Default: '150'

Cartesian position vector of spacecraft in ICRF coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or numSat-by-3 array for multiple spacecraft. numSat is the number of spacecraft.

Dependencies

To enable this parameter, set Initial state format to ICRF state vector.

Programmatic Use

Block Parameter: inertialPosition
Type: character vector
Values: [3649700.0 3308200.0 -4676600.0] | 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft
Default: '[3649700.0 3308200.0 -4676600.0]'

Cartesian velocity vector of spacecraft in ICRF coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft.

Dependencies

To enable this parameter, set Initial state format to ICRF state vector.

Programmatic Use

Block Parameter: inertialVelocity
Type: character vector
Values: [-2750.8 6666.4 2573.4] | 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft
Default: '[-2750.8 6666.4 2573.4]'

Cartesian position vector of spacecraft in fixed-frame coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft.

Dependencies

To enable this parameter, set:

  • Propagation method to Numerical (high precision).

  • set Initial state format to Fixed-frame state vector.

Programmatic Use

Block Parameter: fixedPosition
Type: character vector
Values: '[-4142689.0 -2676864.7 -4669861.6]' | 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft
Default: '[-2750.8 6666.4 2573.4]'

Cartesian velocity vector of spacecraft in fixed-frame coordinate system at Start date/time, specified as a 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft.

Dependencies

To enable this parameter, set:

  • Propagation method to Numerical (high precision).

  • Initial state format to Fixed-frame state vector.

Programmatic Use

Block Parameter: fixedVelocity
Type: character vector
Values: '[1452.7 -6720.7 2568.1]' | 3-element vector for single spacecraft or 2-D array of size m-by-3 array of multiple spacecraft
Default: '[1452.7 -6720.7 2568.1]'

Central Body

Configure the central body environment around which the spacecraft orbits.

Celestial body, specified as Earth, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune, Sun, or Custom, around which the spacecraft defined in the Orbit tab orbits.

Programmatic Use

Block Parameter: centralBody
Type: character vector
Values: 'Earth' | 'Moon' |'Mercury' | 'Venus' | 'Mars' | 'Jupiter' | 'Saturn' | 'Uranus' | 'Neptune' | 'Sun' | 'Custom' |
Default: 'Earth'

Units

Parameter and port units, specified as:

UnitsDistance Velocity AccelerationMassAreaDensity
Metric (m/s)metersmeters/secmeters/sec2Kilogramsm2kg/m3, some density outputs 1/m3
Metric (km/s)kilometerskilometers/seckilometers/sec2Kilogramsm2kg/m3, some density outputs 1/m3
Metric (km/h)kilometerskilometers/hourkilometers/hour2Kilogramsm2kg/m3, some density outputs 1/m3
English (ft/s)feetfeet/secfeet/sec2Slugsfeet2lbm/ft3, some density outputs 1/ft3
English (kts)nautical mileknotsknots/secSlugsfeet2lbm/ft3, some density outputs 1/ft3

Programmatic Use

Block Parameter: units
Type: character vector
Values: 'Metric (m/s)' | 'Metric (km/s)' | 'Metric (km/h)' | 'English (ft/s)' | 'English (kts)'
Default: 'Metric (m/s)'

Parameter and port units for angles, specified as Degrees or Radians.

Programmatic Use

Block Parameter: angleUnits
Type: character vector
Values: 'Degrees' | 'Radians'
Default: 'Degrees'

Time format for Start date/time (UTC Julian date) and output port tutc, specified as Julian date or Gregorian.

Programmatic Use

Block Parameter: timeFormat
Type: character vector
Values: 'Julian date' | 'Gregorian'
Default: 'Julian date'

Alternative Configurations

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The Orbit Propagator Numerical (high precision) block propagates the orbit of one or more spacecraft by a numerical (high precision) propagation method. To enable this block, set Propagation method to Numerical (high precision).

Libraries:
Aerospace Blockset / Spacecraft / Spacecraft Dynamics

Algorithms

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References

[1] Vallado, David. Fundamentals of Astrodynamics and Applications, 4th ed. Hawthorne, CA: Microcosm Press, 2013.

[2] Gottlieb, R. G., "Fast Gravity, Gravity Partials, Normalized Gravity, Gravity Gradient Torque and Magnetic Field: Derivation, Code and Data," Technical Report NASA Contractor Report 188243, NASA Lyndon B. Johnson Space Center, Houston, Texas, February 1993.

[3] Konopliv, A. S., S. W. Asmar, E. Carranza, W. L. Sjogen, D. N. Yuan., "Recent Gravity Models as a Result of the Lunar Prospector Mission, Icarus", Vol. 150, no. 1, pp 1–18, 2001.

[4] Lemoine, F. G., D. E. Smith, D.D. Rowlands, M.T. Zuber, G. A. Neumann, and D. S. Chinn, "An improved solution of the gravity field of Mars (GMM-2B) from Mars Global Surveyor", Journal Of Geophysical Research, Vol. 106, No. E10, pp 23359-23376, October 25, 2001.

[5] Seidelmann, P.K., Archinal, B.A., A’hearn, M.F. et al. "Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements: 2006." Celestial Mech Dyn Astr 98, 155–180 (2007).

[6] Montenbruck, Oliver, and Gill Eberhard. Satellite Orbits: Models, Methods, and Applications. Springer, 2000.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020b

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See Also

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