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gravitycentrifugal

Implement centrifugal effect of planetary gravity

Syntax

[gx gy gz] = gravitycentrifugal(planet_coordinates)
[gx gy gz] = gravitycentrifugal(planet_coordinates, model )
[gx gy gz] = gravitycentrifugal(planet_coordinates, 'Custom', rotational_rate)

Description

[gx gy gz] = gravitycentrifugal(planet_coordinates) implements the mathematical representation of centrifugal effect for planetary gravity based on planetary rotation rate. This function calculates arrays of N gravity values in the x-axis, y-axis, and z-axis of the Planet-Centered Planet-Fixed coordinates for the planet. It performs these calculations using planet_coordinates, an M-by-3 array of Planet-Centered Planet-Fixed coordinates. You use centrifugal force in rotating or noninertial coordinate systems. Gravity centrifugal effect values are greatest at the equator of a planet.

[gx gy gz] = gravitycentrifugal(planet_coordinates, model ) implements the mathematical representation of centrifugal effect based on planetary gravitational potential for the planetary model, model.

[gx gy gz] = gravitycentrifugal(planet_coordinates, 'Custom', rotational_rate) implements the mathematical representation of centrifugal effect based on planetary gravitational potential using the custom rotational rate, rotational_rate.

Input Arguments

planet_coordinates

M-by-3 array of Planet-Centered Planet-Fixed coordinates in meters. The z-axis is positive toward the North Pole. If model is 'Earth', the planet coordinates are ECEF coordinates.

model

Planetary model. Default is 'Earth'. Specify one:

  • 'Mercury'

  • 'Venus'

  • 'Earth'

  • 'Moon'

  • 'Mars'

  • 'Jupiter'

  • 'Saturn'

  • 'Uranus'

  • 'Neptune'

  • 'Custom'

'Custom' requires that you specify your own planetary model using the rotational_rate parameter.

rotational_rate

Scalar value that specifies the planetary rotational rate in radians per second. Specify this parameter only if model has the value 'Custom'.

Output Arguments

gx

Array of M gravity values in the x-axis of the Planet-Centered Planet-Fixed coordinates in meters per second squared (m/s2).

gy

Array of M gravity values in the y-axis of the Planet-Centered Planet-Fixed coordinates in meters per second squared (m/s2).

gz

Array of M gravity values in the z-axis of the Planet-Centered Planet-Fixed coordinates in meters per second squared (m/s2).

Examples

Calculate the centrifugal effect of Earth gravity in the x-axis at the equator on the surface of Earth:

gx = gravitycentrifugal( [-6378.1363e3 0 0] )

Calculate the centrifugal effect of Mars gravity at 15000 m over the equator and 11000 m over the North Pole:

p  = [2412.648e3 -2412.648e3 0; 0 0 3376.2e3]
[gx, gy, gz] = gravitycentrifugal( p, 'Mars' )

Calculate the precessing centrifugal effect of gravity for Earth at 15000 m over the equator and 11000 m over the North Pole. This example uses a custom planetary model at Julian date 2451545:

p       = [2412.648e3 -2412.648e3 0; 0 0 3376e3]
% Set julian date to January 1, 2000 at noon GMT
JD      = 2451545
% Calculate precession rate in right ascension in meters
pres_RA = 7.086e-12 + 4.3e-15*(JD - 2451545)/36525
% Calculate the rotational rate in a precessing reference
% frame
Omega   = 7.2921151467e-5 + pres_RA
[gx, gy, gz] = gravitycentrifugal( p, 'custom', Omega )

Introduced in R2010a

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