Note: This page has been translated by MathWorks. Click here to see

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

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

Environment/Gravity

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's gravity at
a specific location. Gravity precision is controlled via the **Type of gravity model** parameter.

The WGS84 Gravity Model block icon displays the input and output
units selected from the **Units** list.

**Type of gravity model**Specifies the method to calculate gravity:

`WGS84 Taylor Series`

`WGS84 Close Approximation`

`WGS84 Exact`

**Units**Specifies the input and output units:

Units Height Gravity `Metric (MKS)`

Meters Meters per second squared `English`

Feet Feet per second squared **Exclude Earth's atmosphere**Select for the value for the Earth's gravitational field to exclude the mass of the atmosphere.

Clear for the value for the Earth's gravitational field to include the mass of the atmosphere.

This option is available only with

**Type of gravity model WGS84 Close Approximation**or**WGS84 Exact**.**Precessing reference frame**When selected, the angular velocity of the Earth is calculated using the International Astronomical Union (IAU) value of the Earth's angular velocity and the precession rate in right ascension. To obtain the precession rate in right ascension, Julian centuries from Epoch J2000.0 is calculated using the dialog parameters of

**Month**,**Day**, and**Year**.If cleared, the angular velocity of the Earth used is the value of the standard Earth rotating at a constant angular velocity.

This option is available only with

**Type of gravity model WGS84 Close Approximation**or**WGS84 Exact**.**Input Julian date**When selected, another input port, JD, appears on the block mask. Select this check box if you want to manually specify the Julian date for the block. Otherwise, the block calculates the Julian date given the values of

**Month**,**Day**, and**Year**. The year must be after January 1, 2000 (2451545). Selecting this block disables the**Month**,**Day**, and**Year**parameters.**Month**Specifies the month used to calculate Julian centuries from Epoch J2000.0.

This option is available only with

**Type of gravity model WGS84 Close Approximation**or**WGS84 Exact**and only when**Precessing reference frame**is selected. It is disabled if you select**Input Julian Date**.**Day**Specifies the day used to calculate Julian centuries from Epoch J2000.0.

This option is available only with

**Type of gravity model WGS84 Close Approximation**or**WGS84 Exact**and only when**Precessing reference frame**is selected. It is disabled if you select**Input Julian Date**.**Year**Specifies the year used to calculate Julian centuries from Epoch J2000.0. The year must be 2000 or greater.

This option is available only with

**Type of gravity model WGS84 Close Approximation**or**WGS84 Exact**and only when**Precessing reference frame**is selected. It is disabled if you select**Input Julian Date**.**No centrifugal effects**When selected, calculated gravity is based on pure attraction resulting from the normal gravitational potential.

If cleared, calculated gravity includes the centrifugal force resulting from the Earth's angular velocity.

This option is available only with

**Type of gravity model WGS84 Close Approximation**or**WGS84 Exact**.**Action for out-of-range input**Specify if out-of-range input invokes a warning, error, or no action.

Input | Dimension Type | Description |
---|---|---|

First |
Three-element vector or |
Contains the position in geodetic latitude, longitude and altitude, with units in degrees, degrees, and selected units of length respectively. Altitude must be less than 20,000.0 m (approximately 65,620.0 feet). |

Second (Optional) |
Scalar |
Contains the Julian centuries that you specified. |

Output | Dimension Type | Description |
---|---|---|

Output |
Three-element vector or | Gravity in the north-east-down (NED) coordinate system. The Taylor Series and Close Approximation methods output only normal gravity (down in the NED Coordinate system). The Exact method outputs both normal and tangent gravity (down and north in the NED coordinate system). |

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.

See the Environment Models subsystem in the Airframe subsystem
of the `aeroblk_HL20`

model
for an example of this block.

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