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WGS84 Gravity Model

Implement 1984 World Geodetic System (WGS84) representation of Earth's gravity

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  • WGS84 Gravity Model block

Libraries:
Aerospace Blockset / Environment / Gravity

Description

The WGS84 Gravity Model block implements the mathematical representation of the geocentric equipotential ellipsoid of the World Geodetic System (WGS84). The block output is the Earth gravity at a specific location. To control gravity precision, use the Type of gravity model parameter.

The block icon displays the input and output units selected from the Units list.

Limitations

  • The WGS84 gravity calculations are based on the assumption of a geocentric equipotential ellipsoid of revolution. Since the gravity potential is assumed to be the same everywhere on the ellipsoid, there must be a specific theoretical gravity potential that can be uniquely determined from the four independent constants defining the ellipsoid.

  • Use of the WGS84 Taylor Series model should be limited to low geodetic heights. It is sufficient near the surface when submicrogal precision is not necessary. At medium and high geodetic heights, it is less accurate.

  • The WGS84 Close Approximation model gives results with submicrogal precision.

  • To predict and determine a satellite orbit with high accuracy, use the EGM96 through degree and order 70.

Ports

Input

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Position in geodetic latitude, longitude, and altitude, specified as a three-element vector or M-by-3 array, in selected units. Altitude must be less than 20,000 m (approximately 65,620 feet).

For inputs outside the limits (0 to 20000 m), if the action input is specified as 'None' or 'warning', the implementation is extended. However, the usage of the block for inputs outside these limits is not recommended.

Data Types: double

Julian date, specified as a scalar. The year must be after January 1, 2000 (2451545).

Dependencies

To enable this port, select Input Julian date.

Data Types: double

Output

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Gravity in the north-east-down (NED) coordinate system.

Gravity Model MethodOutput
Taylor Series and Close ApproximationOutput only normal gravity (down in the NED coordinate system).
ExactBoth normal and tangent gravity (down and north in the NED coordinate system).

Data Types: double

Parameters

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Method to calculate gravity, specified as:

Gravity Model MethodOutput
WGS84 Taylor Series and WGS84 Close ApproximationOutput only normal gravity (down in the NED coordinate system).
WGS84 ExactBoth normal and tangent gravity (down and north in the NED coordinate system).

Programmatic Use

Block Parameter: model
Type: character vector
Values: 'WGS84 Taylor Series' | 'WGS84 Close Approximation' | 'WGS84 Exact'
Default: 'WGS84 Taylor Series'

Input and output units, specified as:

UnitsHeightGravity
Metric (MKS) MetersMeters per second squared
English FeetFeet per second squared

Programmatic Use

Block Parameter: units
Type: character vector
Values: 'Metric (MKS)' | 'English'
Default: 'Metric (MKS)'

  • To exclude the mass of the atmosphere for the Earth gravitational field, select this check box.

  • To include the mass of the atmosphere for the Earth gravitation field, clear this check box.

Dependencies

To enable this check box, set Type of gravity model to Type of gravity model WGS84 Close Approximation or WGS84 Exact.

Programmatic Use

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

  • To calculate the velocity of the Earth using the International Astronomical Union (IAU) value of the Earth's angular velocity and the precession rate in right ascension, select this check box.

  • To calculate the velocity of the Earth using the angular velocity of the standard Earth rotating at a constant angular velocity, clear this check box.

To obtain the precession rate in right ascension, the block calculates Julian centuries from Epoch J2000.0 using Month, Day, and Year.

Dependencies

  • To enable this check box, set Type of gravity model to Type of gravity model WGS84 Close Approximation or WGS84 Exact.

  • Clearing this check box disables the Input Julian date parameter and the JD input port.

Programmatic Use

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

  • To specify the Julian date for the block with an input port, select this check box.

  • To calculate the Julian date using the values of Month, Day, and Year, clear this check box. The year must be after January 1, 2000 (2451545).

Dependencies

  • To enable the JD port, select this check box.

Programmatic Use

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

Month to calculate Julian centuries from Epoch J2000.0.

Dependencies

To enable this parameter:

  • Set Type of gravity model to WGS84 Close Approximation or WGS84 Exact.

  • Select Precessing reference frame.

To disable this parameter, select Input Julian date.

Programmatic Use

Block Parameter: month
Type: character vector
Values: 'January' | 'February' | 'March' | 'April' | 'May' | 'June' | 'July' | 'August' | 'September' | 'October' | 'November' | 'December'
Default: 'January'

Day to calculate Julian centuries from Epoch J2000.0.

Dependencies

To enable this parameter:

  • Set Type of gravity model to WGS84 Close Approximation or WGS84 Exact.

  • Select Precessing reference frame.

To disable this parameter, select Input Julian date.

Programmatic Use

Block Parameter: day
Type: character vector
Values: '1' to '31'
Default: '10'

Year to calculate Julian centuries from Epoch J2000.0. The year must be 2000 or greater.

Dependencies

To enable this parameter:

  • Set Type of gravity model to WGS84 Close Approximation or WGS84 Exact.

  • Select Precessing reference frame.

  • To disable this parameter, select Input Julian date.

Programmatic Use

Block Parameter: year
Type: character vector
Values: any year
Default: '2004'

  • To base calculated gravity on pure attraction resulting from the normal gravitational potential, select this check box.

  • To enable the calculated gravity to include the centrifugal force resulting from the Earth's angular velocity, clear this check box.

This option is available only with Type of gravity model WGS84 Close Approximation or WGS84 Exact.

Programmatic Use

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

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

ValueDescription

None

No action. The block imposes upper and lower limits on an input signal. For inputs outside the limits, the implementation is extended.

Warning

Warning in the Diagnostic Viewer, model simulation continues. For Accelerator and Rapid Accelerator modes, setting the action to Warning has no effect and the model behaves as though the action is set to None.

Error

MATLAB® returns an exception, model simulation stops. For Accelerator and Rapid Accelerator modes, setting the action to Error has no effect and the model behaves as though the action is set to None.

The WGS84 Gravity Model is not recommended for inputs outside the limits.

Programmatic Use

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

References

[1] "Department of Defense World Geodetic System 1984, Its Definition and Relationship with Local Geodetic Systems." NIMA TR8350.2.

Extended Capabilities

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

Version History

Introduced before R2006a

See Also

Topics